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...
How Discrete Signal Interpolation Improves D/A Conversion
This blog post is also available in pdf format. Download here.
Earlier this year, for the Linear Audio magazine, published in the Netherlands whose subscribers are technically-skilled hi-fi audio enthusiasts, I wrote an article on the fundamentals of interpolation as it's used to improve the performance of analog-to-digital conversion. Perhaps that article will be of some value to the subscribers of dsprelated.com. Here's what I wrote:
We encounter the process of digital-to-analog...
Weighted least-squares FIR with shared coefficients
FIR design with arbitrary routing between delay line and coefficient multipliers.
Includes a commented implementation of a generic IRLS FIR design algorithm.
Introduction: Reverse EngineeringWhile looking for numerical IIR filter optimization, a Matlab program in [1] for the design of FIR filters caught my attention. The equations looked familiar, sort of, but on closer examination the pieces refused to fit together. Without the references, it took about two evenings to sort out how it...
How Not to Reduce DFT Leakage
This blog describes a technique to reduce the effects of spectral leakage when using the discrete Fourier transform (DFT).
In late April 2012 there was a thread on the comp.dsp newsgroup discussing ways to reduce the spectral leakage problem encountered when using the DFT. One post in that thread caught my eye [1]. That post referred to a website presenting a paper describing a DFT leakage method that I'd never heard of before [2]. (Of course, not that I've heard...
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...
Instant CIC
Summary:
A floating point model for a CIC decimator, including the frequency response.
Description:
A CIC filter relies on a peculiarity of its fixed-point implementation: Normal operation involves repeated internal overflows that have no effect to the output signal, as they cancel in the following stage.
One way to put it intuitively is that only the speed (and rate of change) of every little "wheel" in the clockworks carries information, but its absolute position is...
Curse you, iPython Notebook!
First, I think ipython is great. I use it daily and always have an ipython terminal open. But just recently, I was showing off the ipython 0.12 notebook and in the process created a lengthy example while demonstrating the cool features of the ipython notebook. The example included LaTeX equations, plots, etc. Since the notebook session was on something of relevance I decided to clean up the session and use it for the beginning of a report.
Engineering the Statistics
Do you remember the probability course you took in undergrad? If you were like me, you would consider it one of those courses that you get out of confused. But maybe a time will come where you regret skipping class because of the lecturer's persisting attempts to scare you with mathematical involved nomenclature.As you might have guessed, I had this moment few months back where I had to go deep into statistical analysis. I learned things the hard way, or maybe it is the right way. I mean...
The History of CIC Filters: The Untold Story
If you have ever studied or designed a cascaded integrator-comb (CIC) lowpass filter then surely you've read Eugene Hogenauer's seminal 1981 IEEE paper where he first introduced the CIC filter to the signal processing world [1]. As it turns out, Hogenauer's famous paper was not the first formal document describing and proposing CIC filters. Here's the story.
In the Fall of 1979 Eugene Hogenauer was finalizing his development of the CIC filter, the filter now used in so many multirate signal...
scipy.signal calling all developers
There has been some chatter on the scipy-dev mailing list lately about enhancing the scipy.signal package. Unfortunately, there seems to be a split. Some are going off and starting a new package scikit-signal. The original developer, Travis Oliphant, appears to have strong interest in seeing the scipy.signal evovle. If you are interested in signal processing you should check out the mailing lists (
TI DSP Predictions
I think it might be interesting to blog a couple of "Texas Instruments DSP predictions". The following are just my opinion, they do not result in any way from inside / confidential information to which I'm privy in working closely with TI for many years. Of course I could be dead wrong, but at least I can say, "if they should occur, it would have a huge impact on the TI DSP developer community".
1) TI will offer real-time Linux running on their DSPs.
With Linux legal...
Improved Narrowband Lowpass IIR Filters
Here's a neat IIR filter trick. It's excerpted from the "DSP Tricks" chapter of the new 3rd edition of my book "Understanding Digital Signal Processing". Perhaps this trick will be of some value to the subscribers of dsprelated.com.
Due to their resistance to quantized-coefficient errors, traditional 2nd-order infinite impulse response (IIR) filters are the fundamental building blocks in computationally-efficient high-order IIR digital filter implementations. However, when used in...
Compressive Sensing - Recovery of Sparse Signals (Part 1)
The amount of data that is generated has been increasing at a substantial rate since the beginning of the digital revolution. The constraints on the sampling and reconstruction of digital signals are derived from the well-known Nyquist-Shannon sampling theorem...
DSP Related Math: Nice Animated GIFs
I was browsing the ECE subreddit lately and found that some of the most popular posts over the last few months have been animated GIFs helping understand some mathematical concepts. I thought there would be some value in aggregating the DSP related gifs on one page.
The relationship between sin, cos, and right triangles: Constructing a square wave with infinite series (see this...Exact Near Instantaneous Frequency Formulas Best at Peaks (Part 1)
Introduction
This is an article that is a another digression from trying to give a better understanding of the Discrete Fourier Transform (DFT). Although it is not as far off as the last blog article.
A new family of formulas for calculating the frequency of a single pure tone in a short interval in the time domain is presented. They are a generalization of Equation (1) from Rick Lyons' recent blog article titled "Sinusoidal Frequency Estimation Based on Time-Domain Samples"[1]. ...
Polar Coding Notes: A Simple Proof
For any B-DMC $W$, the channels $\{W_N^{(i)}\}$ polarize in the sense that, for any fixed $\delta \in (0, 1)$, as $N$ goes to infinity through powers of two, the fraction of indices $i \in \{1, \dots, N\}$ for which $I(W_N^{(i)}) \in (1 − \delta, 1]$ goes to $I(W)$ and the fraction for which $I(W_N^{(i)}) \in [0, \delta)$ goes to $1−I(W)^{[1]}$.
Mrs. Gerber’s Lemma
Mrs. Gerber’s Lemma provides a lower bound on the entropy of the modulo-$2$ sum of two binary random...
Instant CIC
Summary:
A floating point model for a CIC decimator, including the frequency response.
Description:
A CIC filter relies on a peculiarity of its fixed-point implementation: Normal operation involves repeated internal overflows that have no effect to the output signal, as they cancel in the following stage.
One way to put it intuitively is that only the speed (and rate of change) of every little "wheel" in the clockworks carries information, but its absolute position is...
Through the tube...
Hello all,
something completely different...
there was some recent discussion on the forum about modeling guitar amplifiers.I have been wondering for quite a while, whether the methods that I use to model radio frequency power amplifiers might also work for audio applications.
It's been a rainy day, so I found the time and energy for some experiments. Just for fun.
The device-under-test is a preamplifier with a single 12AX7 tube:
My good ol' Kurzweil (not in the picture) serves as "signal...
Resolving 'Can't initialize target CPU' on TI C6000 DSPs - Part 1
Introduction
Today I am going to discuss some of the basics that can help prevent errors that frustrate some users. The information is directed toward TI C6000 family DSPs, but much of it also applies to other TI DSPs. In many cases they represent the user's first involvement with using Code Composer Studio [CCS] and a target board. It has been my experience that the primary cause of the "Can't initialize target CPU" error message and similar messages like "Error connecting to...
Of Forests and Trees and DSP
When Stephane invited me to write a blog for dsprelated.com I immediately came up with a flood of ideas for highly detailed, technical, narrowly focused articles related to the intersection of DSP and control systems.
Then the USENET groups that I frequent received a spate of posts from people that were either asking about how to implement highly detailed, narrowly focused algorithms in ways that were either fundamental misapplications or were flawed because they were having problems...
Off Topic: Refraction in a Varying Medium
IntroductionThis article is another digression from a better understanding of the DFT. In fact, it is a digression from DSP altogether. However, since many of the readers here are Electrical Engineers and other folks who are very scientifically minded, I hope this article is of interest. A differential vector equation is derived for the trajectory of a point particle in a field of varying index of refraction. This applies to light, of course, but since it is a purely theoretical...
How the Cooley-Tukey FFT Algorithm Works | Part 3 - The Inner Butterfly
At the heart of the Cooley-Tukey FFT algorithm lies a butterfly, a simple yet powerful image that captures the recursive nature of how the FFT works. In this article we discover the butterfly’s role in transforming complex signals into their frequency components with efficiency and elegance. Starting with the 2-point DFT, we reveal how the FFT reuses repeated calculations to save time and resources. Using a divide-and-conquer approach, the algorithm breaks signals into smaller groups, processes them through interleaving butterfly diagrams, and reassembles the results step by step.
A Two Bin Exact Frequency Formula for a Pure Complex Tone in a DFT
IntroductionThis is an article to hopefully give a better understanding to the Discrete Fourier Transform (DFT) by deriving an exact formula for the frequency of a complex tone in a DFT. It is basically a parallel treatment to the real case given in Exact Frequency Formula for a Pure Real Tone in a DFT. Since a real signal is the sum of two complex signals, the frequency formula for a single complex tone signal is a lot less complicated than for the real case.
Theoretical...A Matlab Function for FIR Half-Band Filter Design
FIR Half-band filters are not difficult to design. In an earlier post [1], I showed how to design them using the window method. Here, I provide a short Matlab function halfband_synth that uses the Parks-McClellan algorithm (Matlab function firpm [2]) to synthesize half-band filters. Compared to the window method, this method uses fewer taps to achieve a given performance.
Three Bin Exact Frequency Formulas for a Pure Complex Tone in a DFT
IntroductionThis is an article to hopefully give a better understanding to the Discrete Fourier Transform (DFT) by deriving exact formulas for the frequency of a complex tone in a DFT. This time it is three bin versions. Although the problem is similar to the two bin version in my previous blog article "A Two Bin Exact Frequency Formula for a Pure Complex Tone in a DFT"[1], a slightly different approach is taken using linear algebra concepts. Because of an extra degree of freedom...
OpenCV for DSP/GPU, MSDN equivalent for CCS, and more
A great business opportunity might await anyone brave enough to attempt a port of the OpenCV (Open Computer Vision) library to a DSP platform. OpenCV is the lingua franca of "industrial grade" image processing, and it's my sense that the DSP imaging libraries out there pale in comparison to the breadth of features offered by OpenCV. When writing my book for example, I fielded multiple inquiries about making an OpenCV port a centerpiece of the text. Two problems arise,...
Approximating the area of a chirp by fitting a polynomial
Once in a while we need to estimate the area of a dataset in which we are interested. This area could give us, for example, force (mass vs acceleration) or electric power (electric current vs charge).
Accelerating Matlab DSP Code on the GPU
Intrigued by GPUs, I've spent a few days testing out Jacket, an interface that lets you accelerate MATLAB (my favorite, if frustrating language) on NVIDIA GPUs. It's definitely got some caveats. But it was really easy to accelerate my code. And the results were impressive. So I thought I'd put up a few simple DSP-related benchmarks I created and ran on my laptop (a Macbook Air with NVIDIA GeForce 9400M graphics card). The m-files for the two functions I benchmarked (2D FFT and 2D...
DFT Bin Value Formulas for Pure Complex Tones
IntroductionThis is an article to hopefully give a better understanding to the Discrete Fourier Transform (DFT) by deriving an analytical formula for the DFT of pure complex tones and an alternative variation. It is basically a parallel treatment to the real case given in DFT Bin Value Formulas for Pure Real Tones. In order to understand how a multiple tone signal acts in a DFT it is necessary to first understand how a single pure tone acts. Since a DFT is a linear transform, the...
Project Report : Digital Filter Blocks in MyHDL and their integration in pyFDA
The Google Summer of Code 2018 is now in its final stages, and I’d like to take a moment to look back at what goals were accomplished, what remains to be completed and what I have learnt.
The project overview was discussed in the previous blog posts. However this post serves as a guide to anyone who wishes to learn about the project or carry it forward. Hence I will go over the project details again.
Project overviewThe project “Digital Filter Blocks in MyHDL and PyFDA integration" aims...
