Determination of the transfer function of passive networks with MATLAB Functions
With MATLAB functions, the transfer function of passive networks can be determined relatively easily. The method is explained using the example of a passive low-pass filter of the sixth order, which is shown in Fig.1
Fig.1 Passive low-pass filter of the sixth order
If one tried, as would be logical, to calculate the transfer function starting from the input, it would be quite complicated. On the other hand, if you start from the output, the determination of this function is simple...
A DSP Quiz Question
Here's a DSP Quiz Question that I hope you find mildly interesting
BACKGROUND
Due to the periodic natures an N-point discrete Fourier transform (DFT) sequence and that sequence’s inverse DFT, it is occasionally reasonable to graphically plot either of those sequences as a 3-dimensional (3D) circular plot. For example, Figure 1(a) shows a length-32 x(n) sequence with its 3D circular plot given in Figure 1(b).
HERE'S THE QUIZ QUESTION:
I was reading a paper by an audio DSP engineer where the...The Discrete Fourier Transform and the Need for Window Functions
The Discrete Fourier Transform (DFT) is used to find the frequency spectrum of a discrete-time signal. A computationally efficient version called the Fast Fourier Transform (FFT) is normally used to calculate the DFT. But, as many have found to their dismay, the FFT, when used alone, usually does not provide an accurate spectrum. The reason is a phenomenon called spectral leakage.
Spectral leakage can be reduced drastically by using a window function in conjunction...
The 2021 DSP Online Conference
The 2021 DSP Online Conference is just around the corner and this year again, the program is packed with opportunities for DSP engineers to refresh their DSP skills and learn a few new tricks along the way.
By registering for the conference, not only will you have full access to all talks, workshops, and Q&A sessions at this year's event, but you'll also gain instant access to all talks from last year's...
Modeling Anti-Alias Filters
Digitizing a signal using an Analog to Digital Converter (ADC) usually requires an anti-alias filter, as shown in Figure 1a. In this post, we’ll develop models of lowpass Butterworth and Chebyshev anti-alias filters, and compute the time domain and frequency domain output of the ADC for an example input signal. We’ll also model aliasing of Gaussian noise. I hope the examples make the textbook explanations of aliasing seem a little more real. Of course, modeling of...
In Search of The Fourth Wave
Last year I participated in the first DSP Related online conference, where I presented a short talk called "In Search of The Fourth Wave". It's based on a small mystery I encountered when I was working on Think DSP. As you might know:
A sawtooth wave contains harmonics at integer multiples of the fundamental frequency, and their amplitudes drop off in proportion to 1/f. A square wave contains only odd multiples of the fundamental, but they also drop off...Sampling bandpass signals
Sampling bandpass signals 1.1 IntroductionIt is known [1], [3] that bandpass signals can be sampled with a sampling frequency which is lower than the sampling frequency according to the sampling theorem.
Fig. 1 shows an example of how the spectrum of a bandpass signal sampled with $f_s$ (Fig. 1a) arises in the baseband with $−f_s / 2 ≤ f < f_s/2$. The bandpass signal is assumed to have a center frequency $f_c = (f_{max} + f_{min})/2$ and bandwidth $\Delta f...
Digital Filter Instructions from IKEA?
Swedish “Bygglek” = build and play. Swedish “Bygglek” = build and play.
Swedish “Bygglek” = build and play. Swedish “Bygglek” = build and play.
Swedish “Bygglek” = build and play. Swedish “Bygglek” = build and play.
Swedish “Bygglek” = build and play. Swedish “Bygglek” = build and play.
Swedish “Bygglek” = build and play. Swedish “Bygglek” = build and...
Simulink-Simulation of SSB demodulation
≥≥≥ Simulink-Simulation of SSB demodulation or modulation from the article “Understanding the ‘Phasing Method’ of Single Sideband Demodulation” by Richard Lyons Josef HoffmannThe article “Understanding the ‘Phasing Method’ of Single Sideband Demodulation” by Richard Lyons is a very good description of this topic. The block representation from the figures are clear and easy to understand. They are predestined for a simulation in Simulink. The simulation can help...
Setting Carrier to Noise Ratio in Simulations
When simulating digital receivers, we often want to check performance with added Gaussian noise. In this article, I’ll derive the simple equations for the rms noise level needed to produce a desired carrier to noise ratio (CNR or C/N). I also provide a short Matlab function to generate a noise vector of the desired level for a given signal vector.
Definition of C/NThe Carrier to noise ratio is defined as the ratio of average signal power to noise power for a modulated...
Understanding the 'Phasing Method' of Single Sideband Demodulation
There are four ways to demodulate a transmitted single sideband (SSB) signal. Those four methods are:
- synchronous detection,
- phasing method,
- Weaver method, and
- filtering method.
Here we review synchronous detection in preparation for explaining, in detail, how the phasing method works. This blog contains lots of preliminary information, so if you're already familiar with SSB signals you might want to scroll down to the 'SSB DEMODULATION BY SYNCHRONOUS DETECTION'...
Design IIR Filters Using Cascaded Biquads
This article shows how to implement a Butterworth IIR lowpass filter as a cascade of second-order IIR filters, or biquads. We’ll derive how to calculate the coefficients of the biquads and do some examples using a Matlab function biquad_synth provided in the Appendix. Although we’ll be designing Butterworth filters, the approach applies to any all-pole lowpass filter (Chebyshev, Bessel, etc). As we’ll see, the cascaded-biquad design is less sensitive to coefficient...
Design IIR Bandpass Filters
In this post, I present a method to design Butterworth IIR bandpass filters. My previous post [1] covered lowpass IIR filter design, and provided a Matlab function to design them. Here, we’ll do the same thing for IIR bandpass filters, with a Matlab function bp_synth.m. Here is an example function call for a bandpass filter based on a 3rd order lowpass prototype:
N= 3; % order of prototype LPF fcenter= 22.5; % Hz center frequency, Hz bw= 5; ...Simplest Calculation of Half-band Filter Coefficients
Half-band filters are lowpass FIR filters with cut-off frequency of one-quarter of sampling frequency fs and odd symmetry about fs/4 [1]*. And it so happens that almost half of the coefficients are zero. The passband and stopband bandwiths are equal, making these filters useful for decimation-by-2 and interpolation-by-2. Since the zero coefficients make them computationally efficient, these filters are ubiquitous in DSP systems.
Here we will compute half-band...
A Fast Guaranteed-Stable Sliding DFT Algorithm
This blog presents a most computationally-efficient guaranteed-stable real-time sliding discrete Fourier transform (SDFT) algorithm. The phrase “real-time” means the network computes one spectral output sample, equal to a single-bin output of an N‑point discrete Fourier transform (DFT), for each input signal sample.
Proposed Guaranteed Stable SDFT
My proposed guaranteed stable SDFT, whose development is given in [1], is shown in Figure 1(a). The output sequence Xk(n) is an N-point...
Ten Little Algorithms, Part 2: The Single-Pole Low-Pass Filter
Other articles in this series:
- Part 1: Russian Peasant Multiplication
- Part 3: Welford's Method (And Friends)
- Part 4: Topological Sort
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection
I’m writing this article in a room with a bunch of other people talking, and while sometimes I wish they would just SHUT UP, it would be...
Design IIR Butterworth Filters Using 12 Lines of Code
While there are plenty of canned functions to design Butterworth IIR filters [1], it’s instructive and not that complicated to design them from scratch. You can do it in 12 lines of Matlab code. In this article, we’ll create a Matlab function butter_synth.m to design lowpass Butterworth filters of any order. Here is an example function call for a 5th order filter:
N= 5 % Filter order fc= 10; % Hz cutoff freq fs= 100; % Hz sample freq [b,a]=...Understanding and Implementing the Sliding DFT
Introduction
In 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...
Return of the Delta-Sigma Modulators, Part 1: Modulation
About a decade ago, I wrote two articles:
- Modulation Alternatives for the Software Engineer (November 2011)
- Isolated Sigma-Delta Modulators, Rah Rah Rah! (April 2013)
Each of these are about delta-sigma modulation, but they’re short and sweet, and not very in-depth. And the 2013 article was really more about analog-to-digital converters. So we’re going to revisit the subject, this time with a lot more technical depth — in fact, I’ve had to split this...
A New Related Site!
We are delighted to announce the launch of the very first new Related site in 15 years! The new site will be dedicated to the trendy and quickly growing field of Machine Learning and will be called - drum roll please - MLRelated.com.
We think MLRelated fits perfectly well within the “Related” family, with:
- the fast growth of TinyML, which is a topic of great interest to the EmbeddedRelated community
- the use of Machine/Deep Learning in Signal Processing applications, which is of...
Free DSP Books on the Internet
While surfing the "net" I have occasionally encountered signal processing books whose chapters could be downloaded to my computer. I started keeping a list of those books and, over the years, that list has grown to over forty books. Perhaps the list will be of interest to you.
Please know, all of the listed books are copyrighted. The copyright holders have graciously provided their books free of charge for downloading for individual use, but multiple copies must not be made or printed. As...
Polyphase Filters and Filterbanks
ALONG CAME POLY
Polyphase filtering is a computationally efficient structure for applying resampling and filtering to a signal. Most digital filters can be applied in a polyphase format, and it is also possible to create efficient resampling filterbanks using the same theories.
This post will walk through a reference implementation of both the downsampling polyphase filter and a downsampling polyphase filterbank using scipy, numpy, matplotlib, and python. It should also highlight some of...
A Beginner's Guide to OFDM
In the recent past, high data rate wireless communications is often considered synonymous to an Orthogonal Frequency Division Multiplexing (OFDM) system. OFDM is a special case of multi-carrier communication as opposed to a conventional single-carrier system.
The concepts on which OFDM is based are so simple that almost everyone in the wireless community is a technical expert in this subject. However, I have always felt an absence of a really simple guide on how OFDM works which can...
Python scipy.signal IIR Filter Design
Introduction
The following is an introduction on how to design an infinite impulse response (IIR) filters using the Python scipy.signal package. This post, mainly, covers how to use the scipy.signal package and is not a thorough introduction to IIR filter design. For complete coverage of IIR filter design and structure see one of the references.
Filter SpecificationBefore providing some examples lets review the specifications for a filter design. A filter...
Delay estimation by FFT
Given x=sig(t) and y=ref(t), returns [c, ref(t+delta), delta)] = fitSignal(y, x);:Estimates and corrects delay and scaling factor between two signals Code snippet
This article relates to the Matlab / Octave code snippet: Delay estimation with subsample resolution It explains the algorithm and the design decisions behind it.
IntroductionThere are many DSP-related problems, where an unknown timing between two signals needs to be determined and corrected, for example, radar, sonar,...
How to Find a Fast Floating-Point atan2 Approximation
Context Over a short period of time, I came across nearly identical approximations of the two parameter arctangent function, atan2, developed by different companies, in different countries, and even in different decades. Fascinated with how the coefficients used in these approximations were derived, I set out to find them. This atan2 implementation is based around a rational approximation of arctangent on the domain -1 to 1:
$$ atan(z) \approx \dfrac{z}{1.0 +...
Design IIR Bandpass Filters
In this post, I present a method to design Butterworth IIR bandpass filters. My previous post [1] covered lowpass IIR filter design, and provided a Matlab function to design them. Here, we’ll do the same thing for IIR bandpass filters, with a Matlab function bp_synth.m. Here is an example function call for a bandpass filter based on a 3rd order lowpass prototype:
N= 3; % order of prototype LPF fcenter= 22.5; % Hz center frequency, Hz bw= 5; ...Design IIR Filters Using Cascaded Biquads
This article shows how to implement a Butterworth IIR lowpass filter as a cascade of second-order IIR filters, or biquads. We’ll derive how to calculate the coefficients of the biquads and do some examples using a Matlab function biquad_synth provided in the Appendix. Although we’ll be designing Butterworth filters, the approach applies to any all-pole lowpass filter (Chebyshev, Bessel, etc). As we’ll see, the cascaded-biquad design is less sensitive to coefficient...
Back from Embedded World 2019 - Funny Stories and Live-Streaming Woes
When the idea of live-streaming parts of Embedded World came to me, I got so excited that I knew I had to make it happen. I perceived the opportunity as a win-win-win-win.
- win #1 - Engineers who could not make it to Embedded World would be able to sample the huge event,
- win #2 - The organisation behind EW would benefit from the extra exposure
- win #3 - Lecturers and vendors who would be live-streamed would reach a (much) larger audience
- win #4 - I would get...
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...
