Eric Jacobsen (@Slartibartfast)
Understanding and Implementing the Sliding DFT
IntroductionIn many applications the detection or processing of signals in the frequency domain offers an advantage over performing the same task in the time-domain. Sometimes the advantage is just a simpler or more conceptually straightforward algorithm, and often the largest barrier to working in the frequency domain is the complexity or latency involved in the Fast Fourier Transform computation. If the frequency-domain data must be updated frequently in a...
Frequency-Domain Periodicity and the Discrete Fourier Transform
Introduction
Some of the better understood aspects of time-sampled systems are the limitations and requirements imposed by the Nyquist sampling theorem [1]. Somewhat less understood is the periodic nature of the spectra of sampled signals. This article provides some insights into sampling that not only explain the periodic nature of the sampled spectrum, but aliasing, bandlimited sampling, and the so-called "super-Nyquist" or IF sampling. The approaches taken here include both mathematical...
Time-Domain Periodicity and the Discrete Fourier Transform
Introduction
The Discrete Fourier Transform (DFT) and it's fast-algorithm implementation, the Fast Fourier Transform (FFT), are fundamental tools for processing and analysis of digital signals. While the continuous Fourier Transform and its inverse integrate over all time from minus infinity to plus infinity, and all frequencies from minus infinity to plus infinity, practical application of its discrete cousins can only be made over finite time and frequency intervals. The discrete nature...
Understanding and Relating Eb/No, SNR, and other Power Efficiency Metrics
Introduction
Evaluating the performance of communication systems, and wireless systems in particular, usually involves quantifying some performance metric as a function of Signal-to-Noise-Ratio (SNR) or some similar measurement. Many systems require performance evaluation in multipath channels, some in Doppler conditions and other impairments related to mobility. Some have interference metrics to measure against, but nearly all include noise power as an impairment. Not all systems are...
Some Observations on Comparing Efficiency in Communication Systems
IntroductionEngineering is usually about managing efficiencies of one sort or another. One of my favorite working definitions of an engineer says, "An engineer is somebody who can do for a nickel what any damn fool can do for a dollar." In that case, the implication is that the cost is one of the characteristics being optimized. But cost isn't always the main efficiency metric, or at least the only one. Consider how a common transportation appliance, the automobile, is optimized...
Frequency Dependence in Free Space Propagation
Introduction
It seems to be fairly common knowledge, even among practicing professionals, that the efficiency of propagation of wireless signals is frequency dependent. Generally it is believed that lower frequencies are desirable since pathloss effects will be less than they would be at higher frequencies. As evidence of this, the Friis Transmission Equation[i] is often cited, the general form of which is usually written as:
Pr = Pt Gt Gr ( λ / 4πd )2 (1)
where the...
Pulse Shaping in Single-Carrier Communication Systems
Some common conceptual hurdles for beginning communications engineers have to do with "Pulse Shaping" or the closely-related, even synonymous, topics of "matched filtering", "Nyquist filtering", "Nyquist pulse", "pulse filtering", "spectral shaping", etc. Some of the confusion comes from the use of terms like "matched filter" which has a broader meaning in the more general field of signal processing or detection theory. Likewise "Raised Cosine" has a different meaning or application in this...
Handling Spectral Inversion in Baseband Processing
The problem of "spectral inversion" comes up fairly frequently in the context of signal processing for communication systems. In short, "spectral inversion" is the reversal of the orientation of the signal bandwidth with respect to the carrier frequency. Rick Lyons' article on "Spectral Flipping" at http://www.dsprelated.com/showarticle/37.php discusses methods of handling the inversion (as shown in Figure 1a and 1b) at the signal center frequency. Since most communication systems process...
I'm confused about what you're trying to do since things like frequency response and cutoff frequency shouldn't be applicable to an all-pass filter, which by definition...
Reciprocity applies, so the basestation beam formed to transmit to the handset will also work for receiving the signal from the handset.Other systems, like WiFi,...
FWIW, most channel effects of interest to comm systems that are processed in a demodulator are linear, e.g., multipath reflections, doppler, pathloss, etc., so...
What is your motivation for only wanting real-valued output? Previously you mentioned using only one DAC, but that's already pretty easy if the complex-valued...
It looks to me like you're just describing using complex values. Sin and Cos are orthogonal to each other, which is how orthogonality is maintained modulating...
I thought I should follow up a little bit better than my last response. There's a link here on comp.dsp that at least shows some of the basic concepts of using...
I'm very familiar with OFDM as well as single-carrier modulation. I've been developing modems for nearly forty years, so it's all pretty familiar.Unless s1(t)...
At baseband, the real part has even symmetry about the y-axis. Likewise the quadrature (imaginary) part has odd symmetry about the y-axis. So each has really...
If you're already upsampled to 40 MHz, you can accomplish the same thing by mixing the usual IFFT from baseband to fs/4 with a simple +/-1 multiplication mixer. ...
Usually all or most of that is determined by the requirements of the target application(s). In other words, what do you need it to do?
That architecture limits you somewhat, and will have its own error and distortion sources, but there's still likely room for improvement. Mixing the center frequency...
Ouch, yes, you may have other effects happening with near-field antenna coupling that could be causing trouble.It sounds like you may be using a linear-FM waveform...
If you aren't resource limited, FMCW can be mixed and processed as a complex-valued signal, if that's an option to help get around the problem. I think others...
If your inputs are real-valued sinusoids this is a common problem, since the frequency response can be thought of as folding, or reflecting, across DC, which some...
That's one of the ones I was looking for! It's still not the easiest read, but it does show using an NCO for selecting coefficients from a memory. I put...
If you have a very high processing clock relative to the sample clock, as you described, then a relatively easy way to get arbitrary resampling is to up-sample the...
Well, crap. I thought there were some useful references, and I've seen several good examples over the years, but you're right that it seems that not much pops...
The diagram isn't very good to show the issues, and imho to do the topic justice requires more than can be conveyed in an internet forum like this. This is why...
This doesn't need to be a Farrow filter explicitly, but is essentially a polyphase filter resampling problem. There are a lot of papers on this topic, and fred...
Filtering is necessary to maximize SNR and BER performance, e.g., matching the pulse shapes and/or spectrum in the modulator and demodulator. Doing this with...
You're correct that the phase response of IRR filters usually prevent them from use in modulators or demodulators. There is usually BER performance degradation...
What do you mean by "discard the bin"? Do you mean shorten the IFFT to smaller N? Or do you mean zeroing the bins you are "discarding"?The behavior of zeroing...
The issue is that putting a zero at the FFT bin center only zeros the frequency at that point. The frequencies between that bin center and the next bin center...
If the packets are contiguous samples, i.e., there's no time gap between the last sample of a packet and the first sample of the next, then you can combine them...
The frequency of the sine wave (aka, local oscillator, in a tuning application) determines which frequency gets mixed (translated) to baseband (DC, zero frequency). ...
+1 that that's a mixer followed by an amplitude detector. What you're describing is a tuner and a demodulator for AM radio.Usually that does include a filter,...
You'll need to determine whether amplitude or variance metrics are suitable for detecting the "quiet region" in your application, and how long the detection window...
I'm not quite sure what you're trying to do, but you can recover the phase of an FM carrier at baseband by detecting the angle of the complex vector at baseband...
For BPSK the symbol rate is equal to the 3dB bandwidth, which won't change for most pulse filter shapes. The payload bit rate then depends on consideration for...
If you were intending to take an FFT, the phase information in any particular FFT output bin, for example one with a lot of energy for an input sinusoid, will be...
Think of phase resolution and amplitude resolution as being related. Neither has anything to do with the sample rate. Both have to do with the number of...
I'll +1 that it's not entirely clear what you're doing so questions will be asked. On the other hand, your description of your processing steps sounds reasonable.Are...
Who says nobody talks about it? It's why we have spatial and frequency nulls due to multipath, and whole bunch of other effects.
If you're not in a huge hurry I can take a look. I've been involved in standards development for multiple OFDM systems.You can send me a note via the contact...
It sounds like you have the basics right. If you want to simulate a channel for longer than the coherence time, don't create a step discontinuity between channel...
Because the final output filter response has to be different for each it is possible that the designer of those two stages wanted a narrower output (or more stopband...
A DDS or NCO has some noise sources that have been treated in literature fairly thoroughly, with a lot of tricks on how to mitigate noise effects in them. Whether...
This is the example I was going to give as well. The symbol clock rate may change due to oscillator drift in the modulator or Doppler, or there've even been implementations...
You have to account for everything that is going on. There is processing gain in the FFT as well as an increase in dynamic range by suppressing the quantization...
There is no "false gain". I think there is just a gap in your understanding of what people mean by "processing gain".
Parseval's theorem says the total power in and out will be the same in a linear transform. So if you scale them so that the total power is the same, fine, that's...
I think you've missed the point of what "process gain" means. It is independent of scaling.Filters generally give SNR gain by removing the noise in the stopbands,...
Eventually Planck and Boltzmann weigh in and the noise overcomes the signal. You can keep making the integration time longer or increasing the transmit power,...
The signal characteristics matter a lot. This sort of thing is done in practice a lot but the signal must have sufficient entropy and auto-correlation properties...
The carrier phase detector used to lock the phase recovery loop uses the constellation points as the expected phase reference. It can only do reliably that if...
Parseval's theorem says that power is maintained across domains, so if you increase or decrease power in one domain, the same thing happens in the other, if that's...
I think you're typing DSP when you mean psd, but that's okay. ;)Regardless, you can set the amplitude of each subcarrier however you want, to make them all the...
There are a number of books on OFDM and signal synchronization that cover all of those topics well. A short search turns up a few candidates. What you're asking...
It looks like nobody looked at your references. In a generic sense I think there are a couple of different concept getting conflated, and to be honest I'm not...
I'm not familiar with that particular book, but I'll second that the bit reversal is done on the sample addresses, not their values. There are alternate algorithms...
It definitely sounds interesting. If all of your claims are correct it could be very interesting in some applications.It sounds a little like a sparse (pruned)...
Sounds like you want to apply FEC to the MSBs and don't care so much about the LSBs. This isn't too hard to do, and you could apply a Hamming code to the MSBs...
Is the first plot you posted the detected magnitude of the output or the real or imaginary part or...?And, yes, your second zd is the conjugate of the first, so...
Something is not being done correctly. The magnitude of the output of the correlation function should have a strong peak if the functions are correlated. If...
Don't rely on a single performance point to figure out what's going on. Vary the Eb/No and plot BER against Eb/No. If you get a normal waterfall curve then...
I think it was kinda like Fuzzy Logic. Lots of initial hype, but it eventually settled into the niches where it is actually useful.
Using the numbers from the example above with N = 512, if the slide distance, M = N and a new FFT is needed every 512 samples, then the FFT requires fewer computations...
As others have alluded, any adaptive equalizer design has limited degrees of freedom in which to work, and a certain amount of complexity required to provide that...
Especially with a wide bandwidth of interest it will likely not have a perfectly flat frequency reponse. The gain and phase balance will likely not be perfect,...
Yes, this is a very common way to build a receiver. The specifications on the hybrid will be important to determine gain and phase balance between the I and...
There's a decent article about it on dsprelated:https://www.dsprelated.com/showarticle/168.phpIf you know the SNR, the noise BW, and the bit rate, it is pretty...
Look into the Sliding DFT algorithm. It is a recursive sliding-window computation that greatly reduces the computational load for sparse outputs (like what you...
To answer your questions:1. A typical convolutional filter has constant coefficients, while a polyphase filter adjusts coefficients depending on the relative phases...
The LPF FIR filters have delays proportional to the length to the peak of the impulse response. e.g., if it is a symmetric impulse response, the delay is N/2. ...
Remember that the time-domain "impulse response" determined from the frequency-domain pilot tones will be periodic, so what you'll see is one period of an estimate...
It's a difficult problem. I've built signal classifiers like this, and what we found was that you nearly always need to start with the BW estimate. That's...
For satellite communications Doppler and multipath are generally not big problems, at least not compared to many terrestrial applications. Usually the frequency...
Well, requirements matter, and you haven't really stated any, so it's hard to say what would work for you or not work.In many systems frequency offset is removed...
Yes, a PLL is a feedback control loop. Usually the loop architecture and development use something like a 2nd order loop filter, which is the same 2nd order...
You can certainly estimate occupied signal bandwidth using an FFT. That will be a close approximation to the deviation depending on details.
Usually synchronization of both timing and phase are done with feedback control loops. Usually timing is synchronized first so that phase can be synchronized using...
How to define SNR in fading channels is always confusing and a reasonable way to start arguments among comm engineers.Are you measuring the signal level before or...
As Tim said, check where all the intermods land wrt harmonics, etc., but the architecture described might not be too bad. Since the Tx is direct conversion, as...
That's not a very thorough test, as many processes will produce constrained random output for random input. So you could have something other than an FFT and get...
You should know the filter gain vs frequency, so the input/output relationship for tones at various frequencies should be straightforward to calculate, or determine...
In a basic sense it's a design decision that you have control over. You control the gain of the filter, and you control the sizes of the registers used and therefore...
Looks like a nice upgrade to the Beaglebone Black SoC, so that's kinda cool. The rest of it seems to be the library support for AI, which is always dubious these...
How much is the difference? If it is a factor of two or a factor of sqrt(2) or their inverses, there is an arbitrary scaling factor that can be applied. If...
Remember that frequency is the derivative of phase, so if s(t) is a slowly advancing ramp, it just means an increase in frequency. Likewise if s(t) is a quadratic...
Is there are reason to not just use a mixer (i.e., complex mix to baseband)? Hilbert transformers tend to add distortion, which can affect performance in a link. ...
It could mean at least a couple of different things, so I'd hope the documentation for the modulator clarifies which is meant.If IF sampling is used, it may be correcting...
If the amplitudes and/or phases of the components are random, then they'll reinforce/cancel randomly. You can bound the extremes by assuming at one point all...
You give no detail about what you might be doing, so it is impossible to offer any detailed criticism or make any assumptions about what you might or might not be...
This is a typical remote-sensing (e.g., radar, sonar), or channel sounding (e.g., training an equalizer for a communication channel) problem. Since you are using...
I'm not sure what you mean by the three steps you describe in your post, especially what "shape into a NRZ signal" means or why you'd do it to something you just...
Very cool. I'm glad you're getting it sorted out.The same problems exist for single-carrier signals, where the resulting DC offset in a constellation must be...
The only mix that will put the LO energy at the DC subcarrier is a direct-conversion complex mix to baseband, since the LO is exactly at the center carrier frequency. ...
In the cases where the DC subcarrier is left vacant it was usually so that an analog direct-conversion mixer could be used. It usually wasn't possible to completely...
dB scales are relative to something, so the positive numbers just mean that whatever the reference is, those values are above it. The filter response plot you...
There's a big difference in the answer depending on what kind of downconversion you used to mix it from 30MHz to the 300kHz remaining offset. If you used a complex-valued...
Some easy generalizations suggest that any noise events longer than the filter may not be able to be cancelled by the filter.The adaptation rate can certainly be...
Ahg, you made me go back and remember a bunch of things.I wasn't assuming audio PDM as there are other PDM applications. We used PDM as a single-wire interface...
Pulse Density Modulation. Basically the amplitude is encoded in the density or duty cycle of a binary signal.
There are a couple guiding design principles that may be able to help you out.The first is that the maximum output value of a FIR filter is the sum of the absolute...
In practice, no, the roll-off doesn't matter because with raised-cosine matched filters the 3dB point is always at the symbol rate. This is where the inflection...
The noise enters the system mostly in the receiver RF, which is between the two matched filters. Remember that the 3dB point of the matched filter is at the symbol...
IF Flatness usually refers to the flatness of the IF filter, which would indicate whether it is likely to introduce distortion or not.RF levelling often means setting...
The answer to your question is completely dependent on the sensitivity of your system to latency or jitter or dropouts in the control signal. If it is insensitive...
I think you are misunderstanding the figure in Proakis. I have the 4th Ed which doesn't have that figure, so can't comment directly on what might be being shown...
Usually there's only one matched filter in the receiver, that is matched to the filter shape in the transmitter. Signal levels coming out of that matched filter...
For the most part, that's what I'd do, yes, but for stuff like that I'm usually simulating something that will ultimately be implemented. If the implementation...
To answer your first question, yes, you can simulate CIC filters in Matlab or Octave or whatever tool you wish. One caveat with Matlab/Octave is that you have...
No, that's not why precoding is done, or, probably more correctly, predistortion. Precoding often refers to coding related to space-time diversity or spatial...
It sounds like what you're doing has a lot of unstated details, e.g., PPS, OFDM, etc., etc. As such I can't really help you other than to say that carrier recovery...
What PPS? I've no idea what signalling you're trying to use other than one of the pics you posted appears to have a QAM constellation. Usually a receiver...
If the channel has a phase component and is rotating the signal, you need to make sure that the predistortion (precoder, whatever), rotates it back in the other...
Are you phase-locking the receive signal and using differential decoding or are you using differential demodulation as a non-coherent signal?If you are using coherent...
I'm with kaz, the answer was in your question. As the number of carriers increases the PAPR increases, which decreases the average power available for the signal,...
Do you mean that you're using a fading channel model in one case and not the other? That'd definitely explain the difference. They should be the same, and...
The filters need to be compatible from a sampling perspective. One way to think of it is that the filter is designed assuming a certain number of samples per...
You have the idea correct, as far as I can tell. Think of it in the frequency domain, where a frequency-selective filter is just multiplying the input frequencies...
Remember that A and B are mirror images of each other, so just mixing them down separately and adding them would be a bit of a mess.Even if you reverse one before...
I don't know what you mean by "baseband different copies at different Nyquist zones using a complex phasor", or "multiple copies of that signal".Until you explain...
Because the industry is constantly changing, your experience will be different than what people have experienced in the past. My career included a lot of working...
Remember that in the vast majority of implementations the quantities will already be cartesian, specifically I and Q components of a signal. So doing the operation...
Maybe I'm missing something, but what is not trivial about this? In his thesis he shows the simple relationship of the discriminator in Eq. 4.7, which I can't...
The data sheet indicates that the 3dB rolloff is at 8GHz, and rolls off from there to 10GHz. So I think the blue channel that is highlighted would be the least...
The short answer is no, matched filtering is not done in OFDM like it is in single carrier communications. Consider that the single-carrier matched filters only...
If this is the preamble detection in a burst signal it's going to be difficult. There's always a tradeoff between low SNR operation and susceptibility to interference,...
It sounds like the symbol rate is 18kHz, and the raw (undecoded) bit rate is 36kHz. The raised cosine filter needs to be matched to the symbol rate. The idea...
You're on the right track, and being able to see the constellation points by following the signal trace is possible but tedious. The phase of the constellation...
There are a lot of things that could be wrong, but it's hard to tell without knowing the configuration of your sim. You need a very high sample rate to mix up...
A properly implemented DUC or DDC should not affect BER at all. Something in your processing chain is distorting the signal.
Hi, Rick,Twenty years ago such tutorials were pretty easy to come across, because it was all new and exciting. Now it's pretty widely recognized that there are...
Are you trying to optimize for a fixed resample rate or are you trying to find a good architecture for a flexible multi-rate resampling filter?The multi-rate problem...
As Kaz mentioned, Timing Error Detectors, like early-late, just need to know the symbol period, Ts, and then provide a suitable error curve vs phase error for up...
The symbol clocks at each end of the link, the Tx and Rx, are independent and so will have random phase relationships to each other. They also won't be exactly...
When mixing a complex signal up to an IF for transmission, it effectively becomes a real-valued signal, or, more specifically, one transmits the real part of the...
Well, dangit, I had made another, long clarifying post, but it appears to have disappeared into the ether.FWIW, Class-C amp appears to mean something to many people...
The paper may be referring to a complex tone, which has a PAPR of 0dB as I mentioned. From that reference, 2dB is a higher PAPR.When a PA transmits a fully saturated...
That is correct, any M-PSK or M-QAM or M-ASK signal requires only one (complex) sample per symbol to recover the information. Again, this assumes that a matched...
If a matched filter is applied and the sample timing is synchronized to the symbols, you only need one sample per symbol to fully recover M-PSK.
This may sound weird, but the PAPR of a complex-valued tone is 0dB. That's usually the reference point for optimizing PAPR. Class C amps can be useful in applications...
Increasing the number of effective bits essentially boils down to increasing the dynamic range by approximately 6dB for every 4:1 reduction in BW, or decimation. ...
Kind of, but some of those terms, like "block code" aren't universally defined. e.g., a "block code" can be a code with a finite-length or fixed-length codeword,...
A possibility of a next thing to do, since you know the frequency range of interest, is to filter out everything but that range. i.e., isolate the 120-240Hz spectrum...
Do you have a pulse matching filter in the demodulator? It should use all of the received samples and potentially downsample to one sample per symbol, based...
The subcarriers near the edges of the band are not used in order to provide "guard band" to facilitate the rolloff of channel selection filters and to prevent interference...
A good topic to search on that will help understand this is "window functions" for DFT or FFT. There are many good papers and tutorials. There is always a window,...
RF mixing or "modulating" doesn't change the signal, it just translates it in frequency. It is still OFDM.20MHz bandwidth means the signal occupies 20MHz of...
1) Inter Carrier Interference (ICI) is minimized by proper synchronization in both time and frequency. Multipath and Doppler can still spread ICI energy around,...
I think what you really want for timing synchronization is estimation and correction of phase offset, not frequency. As mentioned, usually with a burst protocol...
The old tried-and-true way to deal with the hardware clock metastability is just to put two flip-flops (registers) in series on the 96MHz clock. Some people...
Since you said the signal was 1000x oversampled, e.g., 10kHz sps for a 10Hz signal, there are 1000 samples/cycle of the 10 Hz signal, or 1000 samples per 2*pi radians...
With a BW of 10Hz and a sample rate of 10kHz, you have a very high oversample rate. So without any interpolation, just picking the nearest sample, the max jitter...
Since you're highly oversampled wrt your desired signal the jitter due to just sample skipping or repeating might be relatively low. Whether such a scheme will...
Most comm satellites don't do demod-remod, they just mix an uplink band by a fixed amount and retransmit it in the downlink band. Any shift on the uplink will...
In my experience the terms are used interchangeably, and if whoever is using the terms intends for there to be a distinction between them they need to be clear about...
Hi, MrColly,The spectral response of a sampled sine wave from which a finite-time sequence is taken (i.e., any practical sampled signal) is a dirichlet kernel. ...
That is one valid way to look at it, but not the only way. The DFT is just a matrix multiply of an input vector by a transformation matrix. There do not...
Do you reduce the sample rate when you average? In other words, when you average eight samples, is it a sliding average (i.e., a FIR filter) where you output...
There are a number of frequency estimation techniques that use the FFT output. A web search on "frequency estimation" and author's names like Candan, Aboutanios...
How is theta different for each subcarrier? All of the subcarriers come through each propagation path, so all experience the same thetas and the same dopplers,...
What is the mechanism by which one subcarrier will have a significantly different frequency offset than another? All of the subcarriers go through the same multipath...
The Forward Error Correction is not just for ICI, but for all impairments which includes noise, synchronization errors, unmitigated multipath effects, interference,...
Some good suggestions have already been made, and another simple thing that can be done is to just occasionally repeat or drop an output sample. Whether that's...
You haven't specified the need to do anything with the phase or with the imaginary portion, so you haven't indicated anything that would make me think that downsampling...
Like Gardner, I've always found it easier to run the loop filter at the symbol rate. There's not really any reason to run it faster, since it's not getting information...
I think it may be a semantic issue with some poor nomenclature in this case."Decimation" in the context of FFTs isn't downsampling. i.e., "decimation" in time...
Dr Mike mentioned a way that may work in the time domain, especially if you have enough "quiet" time before and after the signal to get sufficient noise statistics.Depending...
If you have a particular type of code you're interested in there may be better selections than others. e.g., if you're mostly interested in algebraic codes (e.g.,...
Rick's book should have some good treatments on upsampling, also called interpolating or interpolation. There are many techniques, but for a modulator it will...
Yes, the spectrum in that pic is what I would expect to see. That looks a lot better.If you have the processing bandwidth to upsample the baseband signal by a...
I've been away all day and just coming back to this. Kaz is on the right track in that I think you're not implementing the mixer correctly and you're winding...
The multiplication by +1, 0, -1... is the mixer, so, yes, you are mixing from baseband to fs/4 that way. It is a very common way to do the mix, and then take an...
It looks to me like the signal was generated at baseband at half the sample rate, then mixed up to fs/4 without sufficiently suppressing the nearest image. The...
I didn't see anything in my copy of Rick's book in App D about this, but usually in the frequency domain SNR estimation is done assuming constant noise spectral...
Yes, you need a way to measure it, and there are potentially a number of ways to do it depending on your system, the signal modulation, and the receiver architecture.e.g.,...
Az kaz mentioned, the mixer and signal sample rates need to match, so if you run the DDS at 1MHz and tune it accordingly the signal will need to be sampled at 1MHz. ...
Bit metrics are just some quantification of a characteristic of a bit, usually something reflective of the bit SNR or some quality or reliability metric of some...
I'm not sure your question really has much to do with polyphase structures. I'm also not sure your statements about anti-aliasing are strictly true about polyphase...
I suspect that one of the reasons the subtle tradeoffs don't get detailed treatment in papers/texts is because the implementation possibilities are so varied, and...
A resampling polyphase filter will do that job, but if the error is unknown how will you know what correction to apply?
Many of the matlab/octave filter functions use fast convolution once the length of the filter impulse response gets very large. You don't mention how long your...
This treats the theory, but no code examples. :(http://www.compdsp.com/presentations/Jacobsen/abin...
"Where do I even begin. Is the first equation saying that sin(2πf0ntₛ) produces the same value as sin(2πf0ntₛ + 2πm) the same value as sin(2π(f0 +...
Which edition of that book do you have? I'm looking at a first edition and the text description around the equations seems reasonably thorough to me. The...
As fred mentioned, you can decouple the symbol rate and the sample rate with a polyphase resampling filter. You will likely have to decouple the sample rate...
If the signal was properly sampled as a real signal, then the imaginary components are conceptually there, they're just zero-valued. If you want the simplest...
The simplest, and most accurate, method would be to just create the imaginary components for each collected sample and set them all to zero. Then do whatever...
I'll just concur with kaz that what he described is the way to do it: multiply the sum of the absolute values of the convolution coefficients with the max input...
Knowing the modulation lets you plan based on what else will be in the receiver. For a PSK signal there will be a phase detector and, if it is a coherent receiver,...
Much depends on the type of signal. Analog or digital? Single or multi-carrier? PSK? MSK? QAM? Something else? Coherent or differential?If...
The signal is not sufficently synchronized to recover the constellations. You need proper timing and phase lock, and how to do that will depend on the signal...
The mixing operation may be fewer computations than the Hilbert transformer, so you may want to look into it.I'm not sure what you mean in 2), but the complex tone...
It looks like you need the desired signal shifted to complex baseband, i.e., moved down 1kHz. Since the signal is already digitized, an easy way to do this is...
You'll also want to consider that each stage will have some insertion loss and Noise Figure, so cascading them like that might be costly from a performance perspective. ...
I complain about this in aviation as a lot of text-based messages, like METAR weather reports, NOTAMs, etc., etc., are still heavily abbreviated and cryptic, which...
FWIW, an alternative approach might be to use a 4096-pt DFT, but compute only the subcarriers of interest, i.e., a sparse DFT. This is pretty easy with a DFT,...
A few things:If I understand correctly, the symbol is 20us long. If you stretch a 400-pt DFT to cover the entire symbol the bins will be much wider (about 10x,...
OFDM symbols are pretty simply defined for the FFT size in order to recover the subcarriers with an FFT (one subcarrier per bin). If the FFT size is changed...
Yes, if the decimator isn't simply averaging the two frames in time, sample by sample, then the processes won't be equivalent. Decimation implies a filter is...
That's something that you should be able to evaluate in a simulation pretty easily, I'd think. Synchronization errors might affect one more than the other, and...
What I was getting as was that if the signal going into the FFT was the same signal used for determining symbol synchronization, then group delay won't matter because...
How is the frame time synchronization performed? If it does something like the typical cyclic prefix correlation with the end of the frame, and if the signal...
Yes, it is possible to model the behavior in C, Matlab, or just about any software language. Many professional design processes over the years have developed systems...
If it is not a decimating filter then it won't cause aliasing. Generally "noise" comes from external sources and not the filter, although if one isn't careful...
You're going to need to define or clarify what you mean by "reliable". Filter implementations are generally deterministic in that you'll know ahead of time exactly...
Others have already pointed out the phase differences between the chirp and and a sinc. Back when I did radar work we always called it "quadratic phase" rather...
The spectrogram is pretty easy to draw, i.e., a line in the time-frequency plane that shows the peak energy moving across the frequencies that the chirp occupies. ...
I think many of these kinds of abbreviations are left over from the days when saving time during handwriting, or saving money on typesetting, or saving money on...
I think that's the part that is just badly worded if not downright wrong. You're right that there are only two points that are zero, and they will only be sampled...
What makes you think it wouldn't be? If you provide some detail about your application and your concerns you might get better answers.
I don't have a copy of that text, but the part you show looks very poorly worded, indeed.Realize that 1/T is the magnitude of the slope of the two lines and the...
Inserting anything other than zeros prior to filtering in an interpolation process adds energy and information, and if it's not part of the original signal energy...
Not sure what you mean by upsampling by the filter length. A filter may be N symbols long, but with M samples per symbol the final length of the convolutional...
Consider what the frequency domain looks like when the signal is sampled only at the symbol rate, and if the spectrum were shaped what the alias behavior would be. ...
Since each receiver has to attain its own synchronization independently, each receiver must estimate and use its own frequency offset information.There may be...
Yes, that's useful. I do that in resampling loops and tracking loops where the output sampling instant is steered by the loop, i.e., the decimation ratio is...
Yes, you need synchronization so that the two channels can be added coherently, rather than potentially cancelling or distorting each other worse than just single-channel...
A synchronization block will have a number of components, and they have to be appropriate for the signal and situation. If you can break out the Timing Error...
This is often done with a Timing Error Detector, a timing loop filter, and a resampling filter. If the existing samples are spaced closely enough that you don't...
You seem to be describing an equalizer. If you can use one of the amps output as the reference, then just generate the error signal between the reference and...
It looks like you've already been pointed in the right direction, but I'll add that this confusion is often exacerbated by the casual use of the term "sinc" to describe...
Don't worry, stuff like this is brain-bending even for experienced guys.Generally the double-sided noise is just N, such that 2N = No, where the 2 accounts for the...
You may want to provide some more details to help understand the problem. Why can't you run a traditional FIR in real-time? i.e., why do you need to use OLA? ...
Do you need a stable clock or pulse running at the coded rate or can you just get away with framing and buffering? Alternatively, if the coded rate is a nice...
I'm not enough of a wavelet expert to comment specifically about implementation of that, other than to say that real-time processing of almost anything at 512Hz...
Under some conditions you can discern sidelobes from main lobes, but this generally means that that signal has to be made up of isolated tone(s). Since this...
I *think* I understand what you're doing, and I'll suggest that you need more than three samples per pulse to get the accuracy you're looking for. In order to...
Rayleigh fading channel models may be complex, (as are many channel models), but usually they are applied at baseband. In a simulation the upconverter and downverter...
This is what I mentioned early on: downconvert with a complex LO, i.e., multiply by cos/sin instead of just one of them. One product will be the real component,...
Yes, I noticed that in his plot. It should be equivalent to unfiltered (i.e., rectangular pulse) 8-PSK generated as a complex constellation and upconverted to...
Consider that any real-world signal transmitted from an antenna (or over a cable, or fiber or whatever), will be a bandpass signal with a carrier frequency of fc...
Downconvert to complex baseband. As you mentioned, if you downconvert with a complex-valued LO of exactly the carrier frequency, you will wind up with a complex-valued...
You can downconvert from real-valued to baseband digitally, i.e., after the single ADC.Edit: same in the modulator; upconvert to real-valued prior to the DAC.
Most digital communication texts have a lot of content describe PSK modulation and typical modulators and demodulators. Usually the waveform is processed, in...
You only need an SNR estimate from each input signal to do the combining rather than a full channel estimate if you want to do the combining first. You can use...
If you combine first before equalization, you have to train the equalizer on the combined signal, not either of the pre-combined signals.
If you do the combining first, you will get the SNR improvement of the combiner and will be equalizing on the combined channels. If you do the equalizing first,...
In my personal experience I've only ever needed IIR filters when I needed an LPF that had a very narrow bandwidth. They're very good for that since the complexity...
I'll +1 on some of what's been said before, and just point out that it's often a matter of implementation efficiency. Scaling by 1/sqrt(N) on both forward and...
There are lots of ways to do this, including linear interpolation, spline interpolation, etc. Also look into "multirate filtering" or similar topics such as...
It looks to me like you're just getting tripped up on definitions and terminology, which are pretty soft, anyway. Additionally, the time required for the cyclic...
I'll add a +1 that this isn't a trivial task if you want some degree of accuracy in the final jitter estimation. There are a number of tricks that you can do...
It can depend on the type of modulation and the type of fading, but generally robust algorithms will work in either (maybe that's just the definition of a robust...
Waveform compression has been around for a long time and is well-studied. Depending on your requirements you can look into all of the various audio compression...
If there is only one tone present, there are quite a few different algorithms that can interpolate the peak value, both direct and iterative. Here is a survey...
Any wifi product that is compliant with 802.11n or better will have MIMO. In other words, the multiple antennas will be used for a variety of combining and MIMO...
What do you mean by "enhance"? It's hard to recommend anything without knowing what you're trying to achieve.
Ah, I misunderstood. That happens a lot. ;)There were a lot of papers on non-uniform sampling probably ten years ago, and my impression on the gist of the...
If you are just collecting samples and doing some DSP stuff with them, like correlation, etc., is there really a need to resample to the other clock? I'm still...
What is the final end use of the signal? If you are just doing analysis or extracting information from it, then there's no need to insert the zero and generate...
Look into using Gnu Octave. It is generally compatible with Matlab (older stuff, anyway), is free, and has a decent GUI IDE.
No, that's not normal. Be careful about how you are measuring the signal and noise power in the receiver, as that is a common area for mistakes. Since you are...
It's just an element-by-element multiplication, so a structure with a counter or two and a multiplier is basically it. If the window function is symmetric, which...
The system is designed so that the fading will be flat for each subcarrier, so, in general, this restricts the subcarrier spacing. Once that is determined and...
The terminology that you're using, "header" and "tail", are ambiguous in this context. I think you need to clarify what you mean. By "header" do you mean a...
If you're really just interested in the magnitude of the energy in bins 1 and 3 and you know there isn't other interfering energy in those bins to corrupt the measurement,...
Generally AWGN is the appropriate model for thermal noise, and with the usual numeric ways of generating AWGN (which you should be able to find with some simple...
It should be easy to compute the total power in the input, then estimate the power in the tone from the amplitude estimate you determine, the noise power is then...
One of the beauties of the complex mix (rather than a real-valued mix) is that it translates all of the spectrum equally, so no image-rejection filters are needed.A...
How would you determine the frequency offset? Are there assumptions about your input signal you can exploit? However you detect the offset, you can adjust...
The input spectrum is just the spectrum of the input signal being processed. It can be shifted up or down in frequency by any arbitrary amount by multiplying...
Why not just mix the input spectrum up or down with e^jw to match the known offset? It accomplishes the same thing and you don't have to worry about orthogonality...
If you're using only a single example of possible channel impulse responses, then, yes, that can happen. Is this a free-space application, or...? Regardless,...
I think the first step is determining what "optimal" and "best" mean to you in the context of your project. Until you do that you have no way of assessing whether...
Yes, you don't have to maintain phase coherence, i.e., phase-lock. Differential coding allows there to be a small amount of phase rotation between symbols, due...
The differential modulation allows the data to be recovered without requiring phase coherence in the receiver. It does not mitigate interference of any kind,...
1) For an N-point DFT, the input can be "windowed". Even with a rectangular window the window will be N-points, or less if zero-padding is used.2-4) You need...
The FIR filter is not doing anything magic. The output will be the input with the frequencies attenuated by the filter suppressed. That is all. If the input...
What are you trying to accomplish with the FIR filter? The output of the FIR will be the input filtered by the FIRs frequency response. You've indicated a...
For bursty systems like WiFi or Zigbee, PER (Packet Error Rate) is usually used instead of BER, pretty much for the reason you illustrate. Characterizing PER provides...
There are a number of different crosstalk removal methods depending on what your signals are and how much processing you can do. If the crosstalk characteristic...
I'm not sure what you mean by "known preamble and unknown pilots", but be careful with the use of the preamble. In many standards the preamble is segmented into...
The relevance is to budget headroom to saturation in the Power Amplifier. A higher PAPR means a higher backoff from peak output is required to maintain linearity...
No, the coherence bandwidth has to do with the dynamic fading of the channel. It is a measure of how wide the fading regions are in the channel spectrum. They're...
I still have my cps to Hz conversion chart that my first manager gave me as a joke. One axis is logarithmic so it makes a nice curve.
Is the context of your question specific to a particular standard or device? "Rate Matching" may actually mean something different across different contexts,...
As gregladd pointed out, the aggregate response of the time window (considering both duration and shape) will result in a frequency response with a modified sinx/x...
You can do that but you'll lose performance as the SNR decreases or the multipath gets bad (e.g., more than one large peak). Usually with SS a "rake receiver"...
In general usage Zigbee range is not very far, 10-20m, so the expected delay spreads would be less than a chip period. If the delay spread is less than a symbol...
I might be missing something, but if you want the same effect as swapping speaker terminals, that's the same as multiplying by -1. i.e., a sign inversion will...
Actually that's backwards. The terminology is from the perspective of the channel, so Single Input Multiple Output means that there is a single transmit antenna...
Distortion is the difference between the shape of the waveform that went into the amplifier and what came out. If anything changes in the shape of the waveform,...
If an "ideal" amp is really "ideal" it doesn't add any distortion, amplitude or phase. Otherwise it wouldn't be very "ideal", I think. ;)The easy example to...
No worries, it was really just addressing your comment about where do non-linear amps get employment if they're not in a rock or metal band.
As John_G alluded, nonlinear (e.g., Class C) amps are often used in communications to increase transmit power efficiency. This requires using constant-envelope...
One point that hasn't yet been mentioned (aside from the excellent comments so far), is that TWTAs have historically often been run in saturation for efficiency,...
The unused subcarriers are the easiest to regenerate because they're always zero. So when you recreate the OFDM symbol, there is no energy in those subcarriers....
There is no signal in the unused subcarriers, ever, so any channel effects in the unused spectrum will be inconsequential to the signals in the occupied subcarriers.It's...
There often isn't any, since the "source" of the data is usually not known to the modem, or even the network. That makes it hard to apply source coding since...
To your example, if the input is x and the output is abc, you might puncture one of those to reduce the code rate to 1/2. e.g., the output of the encoder around...
What sampling rate you use for transmission, i.e., at the final DAC before the RF system, is an implementation decision. Some may choose to digitze at baseband,...
The initial waveform used to get synchronization is known as a "preamble", and right now you're using a chirp. One nice property of a chirp is that it has a good...
The definitions of coded bit and uncoded bit can get swapped. In the article I referenced Ec was specifically defined to represent the channel bits, which are...
Help me understand your question. If I understand correctly, you're asking what's the difference between:EbN0[db]=EbN0[db](old)−10log10(Rc)andCodedEbNo = UncodedEbNo...
If Eb is the energy per information bit, and Rb is the information bit rate, then that already takes into account any coding overhead or other overhead (e.g., framing).This...
The units of the products of the oscillator and detector gains should be something like 1/seconds. "Volts" are usually abstracted in a digital implementation,...
What are the units of the VCO gain when it is equal to 1? Which multiplier do you mean? Do you mean the phase detector? What are the units of the gain when...
I'll second Tim's statement that you need to be clear about what you mean. Anything you run in Matlab is digital. It may be a simulation of an analog system,...
In another thread you mentioned obtaining frequency from a locked digital PLL, and I explained how to do that very accurately using the Phase Increment Register...
Have you done a web search on "frequency estimation"? There are a number of techniques depending on what your unique constraints might be, but there's a lot of...
Yes, the NCO always has the basic value of the reference frequency in its Phase Increment Register (PIR). If your loop adjusts the PIR to steer the loop to lock...
In the zero-IF receiver the analog signal is mixed to baseband and two converters sample the I and Q streams with the signal centered about DC. The difficulty...
As has already been pointed out, there are some unsubstantiated grandiose claims on the linked site and the example code doesn't appear to do anything that would...
There are a number of things you can do depending on how much processing power you have available to you. This sounds like a good application for a sliding DFT,...
This presentation covers one way to address this:http://www.compdsp.com/presentations/Jacobsen/abin...Note that KoKd (or kpko in your notation) has no dependence...
There are two texts that come up a lot for this:Digital Communications Receivers, Synchronization, Channel Estimation, and Signal Processing, by Meyr and Moeneclaey, and,Synchronization...
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