Who else is going to Sensors Expo in San Jose? Looking for roommate(s)!
This will be my first time attending this show and I must say that I am excited. I am bringing with me my cameras and other video equipment with the intention to capture as much footage as possible and produce a (hopefully) fun to watch 'highlights' video. I will also try to film as many demos as possible and share them with you.
I enjoy going to shows like this one as it gives me the opportunity to get out of my home-office (from where I manage and run the *Related sites) and actually...
Digital PLL’s, Part 3 – Phase Lock an NCO to an External Clock
Sometimes you may need to phase-lock a numerically controlled oscillator (NCO) to an external clock that is not related to the system clocks of your ASIC or FPGA. This situation is shown in Figure 1. Assuming your system has an analog-to-digital converter (ADC) available, you can sync to the external clock using the scheme shown in Figure 2. This time-domain PLL model is similar to the one presented in Part 1 of this series on digital PLL’s [1]. In that PLL, we...
Project introduction: Digital Filter Blocks in MyHDL and their integration in pyFDA
Hi everyone! After a lot of hesitation and several failed attempts, I have finally entered the world of blogging. A little about myself : My name is Sriyash Caculo and I’m a third year undergrad student at BITS Pilani K.K. Birla Goa Campus pursuing a major in Electronics and Instrumentation engineering. Being an electronics engineer, I developed an interest in Digital Signal Processing and its implementation on hardware.
This blog-post is the first of many to come for the...
Two Easy Ways To Test Multistage CIC Decimation Filters
This blog presents two very easy ways to test the performance of multistage cascaded integrator-comb (CIC) decimation filters [1]. Anyone implementing CIC filters should take note of the following proposed CIC filter test methods.
Introduction
Figure 1 presents a multistage decimate by D CIC filter where the number of stages is S = 3. The '↓D' operation represents downsampling by integer D (discard all but every Dth sample), n is the input time index, and m is the output time index.
ADC Clock Jitter Model, Part 2 – Random Jitter
In Part 1, I presented a Matlab function to model an ADC with jitter on the sample clock, and applied it to examples with deterministic jitter. Now we’ll investigate an ADC with random clock jitter, by using a filtered or unfiltered Gaussian sequence as the jitter source. What we are calling jitter can also be called time jitter, phase jitter, or phase noise. It’s all the same phenomenon. Typically, we call it jitter when we have a time-domain representation,...
Take Control of Noise with Spectral Averaging
Most engineers have seen the moment-to-moment fluctuations that are common with instantaneous measurements of a supposedly steady spectrum. You can see these fluctuations in magnitude and phase for each frequency bin of your spectrogram. Although major variations are certainly reason for concern, recall that we don’t live in an ideal, noise-free world. After verifying the integrity of your measurement setup by checking connections, sensors, wiring, and the like, you might conclude that the...
Linear Feedback Shift Registers for the Uninitiated, Part XIV: Gold Codes
Last time we looked at some techniques using LFSR output for system identification, making use of the peculiar autocorrelation properties of pseudorandom bit sequences (PRBS) derived from an LFSR.
This time we’re going to jump back to the field of communications, to look at an invention called Gold codes and why a single maximum-length PRBS isn’t enough to save the world using spread-spectrum technology. We have to cover two little side discussions before we can get into Gold...
FFT Interpolation Based on FFT Samples: A Detective Story With a Surprise Ending
This blog presents several interesting things I recently learned regarding the estimation of a spectral value located at a frequency lying between previously computed FFT spectral samples. My curiosity about this FFT interpolation process was triggered by reading a spectrum analysis paper written by three astronomers [1].
My fixation on one equation in that paper led to the creation of this blog.
Background
The notion of FFT interpolation is straightforward to describe. That is, for example,...
ADC Clock Jitter Model, Part 1 – Deterministic Jitter
Analog to digital converters (ADC’s) have several imperfections that affect communications signals, including thermal noise, differential nonlinearity, and sample clock jitter [1, 2]. As shown in Figure 1, the ADC has a sample/hold function that is clocked by a sample clock. Jitter on the sample clock causes the sampling instants to vary from the ideal sample time. This transfers the jitter from the sample clock to the input signal.
In this article, I present a Matlab...
Crowdfunding Articles?
Many of you have the knowledge and talent to write technical articles that would benefit the EE community. What is missing for most of you though, and very understandably so, is the time and motivation to do it.
But what if you could make some money to compensate for your time spent on writing the article(s)? Would some of you find the motivation and make the time?
I am thinking of implementing a system/mechanism that would allow the EE community to...
Plotting Discrete-Time Signals
A discrete-time sinusoid can have frequency up to just shy of half the sample frequency. But if you try to plot the sinusoid, the result is not always recognizable. For example, if you plot a 9 Hz sinusoid sampled at 100 Hz, you get the result shown in the top of Figure 1, which looks like a sine. But if you plot a 35 Hz sinusoid sampled at 100 Hz, you get the bottom graph, which does not look like a sine when you connect the dots. We typically want the plot of a...
Using the DFT as a Filter: Correcting a Misconception
I have read, in some of the literature of DSP, that when the discrete Fourier transform (DFT) is used as a filter the process of performing a DFT causes an input signal's spectrum to be frequency translated down to zero Hz (DC). I can understand why someone might say that, but I challenge that statement as being incorrect. Here are my thoughts.
Using the DFT as a Filter It may seem strange to think of the DFT as being used as a filter but there are a number of applications where this is...
Demonstrating the Periodic Spectrum of a Sampled Signal Using the DFT
One of the basic DSP principles states that a sampled time signal has a periodic spectrum with period equal to the sample rate. The derivation of can be found in textbooks [1,2]. You can also demonstrate this principle numerically using the Discrete Fourier Transform (DFT).
The DFT of the sampled signal x(n) is defined as:
$$X(k)=\sum_{n=0}^{N-1}x(n)e^{-j2\pi kn/N} \qquad (1)$$
Where
X(k) = discrete frequency spectrum of time sequence x(n)
Two jobs
For those of you following closely embeddedrelated and the other related sites, you might have noticed that I have been less active for the last couple of months, and I will use this blog post to explain why. The main reason is that I got myself involved into a project that ended up using a better part of my cpu than I originally thought it would.
edit - video of the event:
I currently have two jobs: one as an electrical/dsp engineer recycled as a web publisher and the other...
Overview of my Articles
Introduction
This article is a summary of all the articles I've written here at DspRelated. The main focus has always been an increased understanding of the Discrete Fourier Transform (DFT). The references are grouped by topic and ordered in a reasonable reading order. All the articles are meant to teach math, or give examples of math, in context within a specific application. Many of the articles also have sample programs which demonstrate the equations derived in the articles. My...
Data Types for Control & DSP
There's a lot of information out there on what data types to use for digital signal processing, but there's also a lot of confusion, so the topic bears repeating.
I recently posted an entry on PID control. In that article I glossed over the data types used by showing "double" in all of my example code. Numerically, this should work for most control problems, but it can be an extravagant use of processor resources. There ought to be a better way to determine what precision you need...
A Fast Real-Time Trapezoidal Rule Integrator
This blog presents a computationally-efficient network for computing real‑time discrete integration using the Trapezoidal Rule.
Background
While studying what is called "N-sample Romberg integration" I noticed that such an integration process requires the computation of many individual smaller‑sized integrations using the Trapezoidal Rule integration method [1]. My goal was to create a computationally‑fast real‑time Trapezoidal Rule integration network to increase the processing...
Compute Modulation Error Ratio (MER) for QAM
This post defines the Modulation Error Ratio (MER) for QAM signals, and shows how to compute it. As we’ll see, in the absence of impairments other than noise, the MER tracks the signal’s Carrier-to-Noise Ratio (over a limited range). A Matlab script at the end of the PDF version of this post computes MER for a simplified QAM-64 system.
Figure 1 is a simplified block diagram of a QAM system. The transmitter includes a source of QAM symbols, a root-Nyquist...
The 2024 DSP Online Conference
We are very excited to announce that the DSP Online Conference is back this year for a fourth year in a row and will take place October 29, 30 and 31.
Unlike traditional DSP conferences, where most talks are highly specialized and tailored to researchers, our conference is designed to be accessible to a broader audience of DSP enthusiasts, from students and practicing engineers to hobbyists and DSP experts.
For this year's edition, we are aiming to provide a program that will be organized...
A New Contender in the Quadrature Oscillator Race
This blog advocates a relatively new and interesting quadrature oscillator developed by A. David Levine in 2009 and independently by Martin Vicanek in 2015 [1]. That oscillator is shown in Figure 1.
The time domain equations describing the Figure 1 oscillator are
w(n) =...
Half-band filter on Xilinx FPGA
1. DSP48 Slice in Xilinx FPGA
There are many DSP48 Slices in most Xilinx® FPGAs, one DSP48 slice in Spartan6® FPGA is shown in Figure 1, the structure may different depending on the device, but broadly similar.
Figure 1: A whole DSP48A1 Slice in Spartan6 (www.xilinx.com)
2. Symmetric Systolic Half-band FIRFigure 2: Symmetric Systolic Half-band FIR Filter
3. Two-channel Symmetric Systolic Half-band FIRFigure 3: 2-Channel...
Compute Modulation Error Ratio (MER) for QAM
This post defines the Modulation Error Ratio (MER) for QAM signals, and shows how to compute it. As we’ll see, in the absence of impairments other than noise, the MER tracks the signal’s Carrier-to-Noise Ratio (over a limited range). A Matlab script at the end of the PDF version of this post computes MER for a simplified QAM-64 system.
Figure 1 is a simplified block diagram of a QAM system. The transmitter includes a source of QAM symbols, a root-Nyquist...
Demonstrating the Periodic Spectrum of a Sampled Signal Using the DFT
One of the basic DSP principles states that a sampled time signal has a periodic spectrum with period equal to the sample rate. The derivation of can be found in textbooks [1,2]. You can also demonstrate this principle numerically using the Discrete Fourier Transform (DFT).
The DFT of the sampled signal x(n) is defined as:
$$X(k)=\sum_{n=0}^{N-1}x(n)e^{-j2\pi kn/N} \qquad (1)$$
Where
X(k) = discrete frequency spectrum of time sequence x(n)
Amplitude modulation and the sampling theorem
I am working on the 11th and probably final chapter of Think DSP, which follows material my colleague Siddhartan Govindasamy developed for a class at Olin College. He introduces amplitude modulation as a clever way to sneak up on the Nyquist–Shannon sampling theorem.
Most of the code for the chapter is done: you can check it out in this IPython notebook. I haven't written the text yet, but I'll outline it here, and paste in the key figures.
Convolution...
Data Types for Control & DSP
There's a lot of information out there on what data types to use for digital signal processing, but there's also a lot of confusion, so the topic bears repeating.
I recently posted an entry on PID control. In that article I glossed over the data types used by showing "double" in all of my example code. Numerically, this should work for most control problems, but it can be an extravagant use of processor resources. There ought to be a better way to determine what precision you need...
New Comments System (please help me test it)
I thought it would take me a day or two to implement, it took almost two weeks...
But here it is, the new comments systems for blogs, heavily inspired by the forum system I developed earlier this year.
Which means that:
- You can easily add images, either by drag and drop or through the 'Insert Image' button
- You can add MathML, TeX and ASCIImath equations and they will be rendered with Mathjax
- You can add code snippets and they will be highlighted with highlights.js
- You can edit...
Wavelets I - From Filter Banks to the Dilation Equation
This is the first in what I hope will be a series of posts about wavelets, particularly about the Fast Wavelet Transform (FWT). The FWT is extremely useful in practice and also very interesting from a theoretical point of view. Of course there are already plenty of resources, but I found them tending to be either simple implementation guides that do not touch on the many interesting and sometimes crucial connections. Or they are highly mathematical and definition-heavy, for a...
Design IIR Band-Reject Filters
In this post, I show how to design IIR Butterworth band-reject filters, and provide two Matlab functions for band-reject filter synthesis. Earlier posts covered IIR Butterworth lowpass [1] and bandpass [2] filters. Here, the function br_synth1.m designs band-reject filters based on null frequency and upper -3 dB frequency, while br_synth2.m designs them based on lower and upper -3 dB frequencies. I’ll discuss the differences between the two approaches later in this...
Frequency Translation by Way of Lowpass FIR Filtering
Some weeks ago a question appeared on the dsp.related Forum regarding the notion of translating a signal down in frequency and lowpass filtering in a single operation [1]. It is possible to implement such a process by embedding a discrete cosine sequence's values within the coefficients of a traditional lowpass FIR filter. I first learned about this process from Reference [2]. Here's the story.
Traditional Frequency Translation Prior To FilteringThink about the process shown in...
5G NR QC-LDPC Encoding Algorithm
3GPP 5G has been focused on structured LDPC codes known as quasi-cyclic low-density parity-check (QC-LDPC) codes, which exhibit advantages over other types of LDPC codes with respect to the hardware implementations of encoding and decoding using simple shift registers and logic circuits.
5G NR QC-LDPC Circulant Permutation MatrixA circular permutation matrix ${\bf I}(P_{i,j})$ of size $Z_c \times Z_c$ is obtained by circularly shifting the identity matrix $\bf I$ of...
