Oscilloscope Dreams
My coworkers and I recently needed a new oscilloscope. I thought I would share some of the features I look for when purchasing one.
When I was in college in the early 1990's, our oscilloscopes looked like this:
Now the cathode ray tubes have almost all been replaced by digital storage scopes with color LCD screens, and they look like these:
Oscilloscopes are basically just fancy expensive boxes for graphing voltage vs. time. They span a wide range of features and prices:...
[Book Review] Numpy 1.5 Beginner's Guide
Full Disclosure: The publisher of this book, PACKT, was soliciting reviewers. I volunteered to review the book and the publisher sent me an e-version of the book.
IntroductionThe following is a review of "Numpy 1.5 Beginner's Guide", "Learn by doing: less theory, more results" by Ivan Idris. As the title suggests this book is for a beginner. Either someone who is new to numerical computing with high-level languages (HLL) or someone who is new to the Python...
Design study: 1:64 interpolating pulse shaping FIR
This article is the documentation to a code snippet that originated from a discussion on comp.dsp.
The task is to design a root-raised cosine filter with a rolloff of a=0.15 that interpolates to 64x the symbol rate at the input.
The code snippet shows a solution that is relatively straightforward to design and achieves reasonably good efficiency using only FIR filters.
Motivation: “simple solutions?”Accurate Measurement of a Sinusoid's Peak Amplitude Based on FFT Data
There are two code snippets associated with this blog post:
and
Testing the Flat-Top Windowing Function
This blog discusses an accurate method of estimating time-domain sinewave peak amplitudes based on fast Fourier transform (FFT) data. Such an operation sounds simple, but the scalloping loss characteristic of FFTs complicates the process. We eliminate that complication by...
Generating Complex Baseband and Analytic Bandpass Signals
There are so many different time- and frequency-domain methods for generating complex baseband and analytic bandpass signals that I had trouble keeping those techniques straight in my mind. Thus, for my own benefit, I created a kind of reference table showing those methods. I present that table for your viewing pleasure in this blog.
For clarity, I define a complex baseband signal as follows: derived from an input analog xbp(t)bandpass signal whose spectrum is shown in Figure 1(a), or...
Why is Fourier transform broken
Every engineer who took a basic signal processing course is familiar with the Gibbs phenomenon, however, not all know why it occurs, I mean really why!
The answer lies in the mathematical background that is almost always skipped in signal processing courses. Moreover, from my experience at least, many textbooks present the theory, e.g. the Fourier transform, as infallible and no discussion of the limitation of the topic is given.
The short answer is that the metric space of continuous...
Python number crunching faster? Part I
Everyone has their favorite computing platform, regardless if it is Matlab, Octave, Scilab, Mathematica, Mathcad, etc. I have been using Python and the common numerical and scientific packages available. Personally, I have found this to be very useful in my work. Lately there has been some chatter on speeding up Python.
From another project I follow, MyHDL, I was introduced to the Python JIT compiler,
More free Ebooks
I found this website that contains loads of free, high quality, ebooks and journals as well. There is 176 ebooks under electrical engineering heading. I found books suitable for engineers, researcher, and hobbiest as well.
Here is the link for it:
To be more useful here are few MATLAB books:
http://www.intechopen.com/books/show/title/applications-of-matlab-in-science-and-engineering
Bank-switched Farrow resampler
Bank-switched Farrow resampler SummaryA modification of the Farrow structure with reduced computational complexity.Compared to a conventional design, the impulse response is broken into a higher number of segments. Interpolation accuracy is achieved with a lower polynomial order, requiring fewer multiplications per output sample at the expense of a higher overall number of coefficients.
Example codeThis code snippet provides a Matlab / Octave implementation.And
Impulse Response Approximation
Recently, I stumbled upon a stepped-triangular (ST) approximation that can be implemented as a cascade of recursive running sum (RRS) filters. The following is a short introduction to the stepped-triangular approximation.The stepped-triangular approximation was introduced by Jovanovic-Dolecek and Mitra [1] as a quantized approximation of a low-pass filter (LPF). Figure 1 shows an example of the approximation.
[Figure 1: Stepped Approximation of a LPF...
The Sampling Theorem - An Intuitive Approach
Scott Kurtz from DSPSoundWare.com has put together a video presentation that aims to help DSPers gain a better intuitive understanding of the Sampling Theorem. Feel free to have a look and share your thoughts by commenting this blog post.
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...Phase and Amplitude Calculation for a Pure Complex Tone in a DFT
Introduction
This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by deriving exact formulas to calculate the phase and amplitude of a pure complex tone from a DFT bin value and knowing the frequency. This is a much simpler problem to solve than the corresponding case for a pure real tone which I covered in an earlier blog article[1]. In the noiseless single tone case, these equations will be exact. In the presence of noise or other tones...
Computing an FFT of Complex-Valued Data Using a Real-Only FFT Algorithm
Someone recently asked me if I knew of a way to compute a fast Fourier transform (FFT) of complex-valued input samples using an FFT algorithm that accepts only real-valued input data. Knowing of no way to do this, I rifled through my library of hardcopy FFT articles looking for help. I found nothing useful that could be applied to this problem.
After some thinking, I believe I have a solution to this problem. Here is my idea:
Let's say our original input data is the complex-valued sequence...
DSP Algorithm Implementation: A Comprehensive Approach
As DSP engineers, ultimately we are required to design and implement specific DSP algorithms. The first step is to make a choice on which algorithm to use, e.g. for filtering should we use FIR or IIR. Then we can go a little bit deeper into the, high level, implementation details, e.g. use the symmetry in FIR filter to reduce complexity. When the algorithm is clear, the first step is to test and simulate the algorithm in a high level language like MATLAB.
After we reach confidence in...
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.
Correlation without pre-whitening is often misleading
White Lies
Correlation, as one of the first tools DSP users add to their tool box, can automate locating a known signal within a second (usually larger) signal. The expected result of a correlation is a nice sharp peak at the location of the known signal and few, if any, extraneous peaks.
A little thought will show this to be incorrect: correlating a signal with itself is only guaranteed to give a sharp peak if the signal's samples are uncorrelated --- for example if the signal is composed...
Multiplying Two Binary Numbers
I just encountered what I think is an interesting technique for multiplying two integer numbers. Perhaps some of the readers here will also find it interesting.
Here's the technique: assume we want to multiply 18 times 17. We start by writing 18 and 17, side-by-side in column A and column B, as shown at the top of Figure 1. Next we divide the 18 at the top of column A by two, retaining only the integer part of the division, and double the 17 at the top of column B. The results of those two...
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) =...
New Video: Parametric Oscillations
I just posted this last night. It's kinda off-topic from the mission of the channel, but I realized that it had been months since I'd posted a video, and having an excuse to build on helped keep me on track.
The Discrete Fourier Transform of Symmetric Sequences
Symmetric sequences arise often in digital signal processing. Examples include symmetric pulses, window functions, and the coefficients of most finite-impulse response (FIR) filters, not to mention the cosine function. Examining symmetric sequences can give us some insights into the Discrete Fourier Transform (DFT). An even-symmetric sequence is centered at n = 0 and xeven(n) = xeven(-n). The DFT of xeven(n) is real. Most often, signals we encounter start at n = 0, so they are not strictly speaking even-symmetric. We’ll look at the relationship between the DFT’s of such sequences and those of true even-symmetric sequences.
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 Complex Variable Detective Story – A Disconnect Between Theory and Implementation
Recently I was in the middle of a pencil-and-paper analysis of a digital 5-tap FIR filter having complex-valued coefficients and I encountered a surprising and thought-provoking problem. So that you can avoid the algebra difficulty I encountered, please read on.
A Surprising Algebra Puzzle
I wanted to derive the H(ω) equation for the frequency response of my FIR digital filter whose complex coefficients were h0, h1, h2, h3, and h4. I could then test the validity of my H(ω)...
Phase and Amplitude Calculation for a Pure Complex Tone in a DFT using Multiple Bins
IntroductionThis is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by deriving exact formulas to calculate the phase and amplitude of a pure complex tone from several DFT bin values and knowing the frequency. This article is functionally an extension of my prior article "Phase and Amplitude Calculation for a Pure Complex Tone in a DFT"[1] which used only one bin for a complex tone, but it is actually much more similar to my approach for real...
More free Ebooks
I found this website that contains loads of free, high quality, ebooks and journals as well. There is 176 ebooks under electrical engineering heading. I found books suitable for engineers, researcher, and hobbiest as well.
Here is the link for it:
To be more useful here are few MATLAB books:
http://www.intechopen.com/books/show/title/applications-of-matlab-in-science-and-engineering
The Phase Vocoder Transform
1 Introduction
I would like to look at the phase vocoder in a fairly ``abstract'' way today. The purpose of this is to discuss a method for measuring the quality of various phase vocoder algorithms, and building off a proposed measure used in [2]. There will be a bit of time spent in the domain of continuous mathematics, thus defining a phase vocoder function or map rather than an algorithm. We will be using geometric visualizations when possible while pointing out certain group theory...
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...
Two Bin Exact Frequency Formulas for a Pure Real Tone in a DFT
IntroductionThis is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by deriving exact formulas for the frequency of a real tone in a DFT. This time it is a two bin version. The approach taken is a vector based one similar to the approach used in "Three Bin Exact Frequency Formulas for a Pure Complex Tone in a DFT"[1]. The real valued formula presented in this article actually preceded, and was the basis for the complex three bin...
The Sampling Theorem - An Intuitive Approach
Scott Kurtz from DSPSoundWare.com has put together a video presentation that aims to help DSPers gain a better intuitive understanding of the Sampling Theorem. Feel free to have a look and share your thoughts by commenting this blog post.
Candan's Tweaks of Jacobsen's Frequency Approximation
IntroductionThis is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by explaining how a tweak to a well known frequency approximation formula makes it better, and another tweak makes it exact. The first tweak is shown to be the first of a pattern and a novel approximation formula is made from the second. It only requires a few extra calculations beyond the original approximation to come up with an approximation suitable for most...
