Python scipy.signal IIR Filtering: An Example
Christopher Felton walks through using scipy.signal IIR filters to demodulate PWM signals, using spectrum and spectrogram analysis to show what works and what does not. He demonstrates using filtfilt to avoid phase delay, compares a single narrow IIR to a very high order FIR, and shows how staged IIR filtering and multirate ideas give much better attenuation. Includes an FPGA-ready MyHDL PWM model.
A Quadrature Signals Tutorial: Complex, But Not Complicated
Quadrature signals are essential in modern communications, yet complex numbers and the j operator intimidate many engineers. In this tutorial Rick Lyons uses phasor geometry, three-dimensional time and frequency plots, and practical I/Q sampling examples to demystify complex exponentials, negative frequency, and how to generate baseband complex signals. Read to get physical intuition and hands-on rules you can apply to modulation, demodulation, and DSP implementations.
Polyphase Filters and Filterbanks
Kyle walks through practical polyphase filtering and analysis filterbanks, complete with Python code using numpy, scipy and matplotlib. The post shows how splitting an FIR into M polyphase legs gives identical, more efficient decimation while avoiding aliasing, and it flags the subtle reordering, zero padding and FFT versus IDFT ordering issues that trip many implementers. Includes runnable reference code and links for deeper theory.
Beat Notes: An Interesting Observation
Rick Lyons overturns a common intuition about beat notes, showing that adding two nearby audio tones yields an average-frequency tone whose amplitude fluctuates, rather than a separate low-frequency sinusoid. He contrasts multiplication and summation of sines, provides simple trigonometric insight, and includes Matlab audio demos to explain why aircraft engine "whump" sounds are amplitude fluctuations of the average engine frequency.
DSPRelated Finally on Twitter!
After resisting social networks, Stephane Boucher announces DSPRelated's move to Twitter and a few site improvements. Users can now sign in once to access DSPRelated, FPGARelated and EmbeddedRelated with the same account, and the site will post updates from @dsprelated, @embeddedrelated and @fpgarelated. To encourage followers, Boucher will occasionally tweet links that award prizes to the first visitors.
Using the DFT as a Filter: Correcting a Misconception
Some sources claim the DFT, when used as a filter, shifts spectral energy down to DC. Rick Lyons shows that this is not true for consecutive DFT-bin outputs and explains the cause of the confusion: the FIR interpretation requires reversing the usual twiddle-factor order. He derives the DFT-bin frequency response, shows the bandpass center at 2πm/N, and explains when decimation does produce a translation to zero Hz.
The Little Fruit Market: The Beginning of the Digital Explosion
A small fruit market in Mountain View became an unlikely cradle for the modern electronics era. Rick Lyons recounts how William Shockley’s lab at 391 San Antonio prompted the Traitorous Eight to form Fairchild, seeding Silicon Valley and spawning an industry whose transistor production quickly dwarfed grains of rice. The post ties that history to the everyday ubiquity of semiconductor devices.
Noise shaping
Markus Nentwig presents a compact, practical introduction to noise shaping by treating quantization error as the first sample of a designed impulse response. He shows how to derive a noise shaper from a target spectrum, demonstrates the tradeoff between in-band noise reduction and total noise increase, and includes a Matlab example while highlighting clipping and stability caveats for sigma-delta contexts.
Two jobs
Stephane Boucher explains why EmbeddedRelated went quiet for a few months after a volunteer project demanded more of his time. He and his wife organized a clown-gymnastics show with 15 kids, sold more than 700 of 800 tickets, and raised $2,700 for the Tree of Hope. Now the shows are done and he plans to resume regular posting with new site features.
Coupled-Form 2nd-Order IIR Resonators: A Contradiction Resolved
Rick Lyons resolves a long-standing confusion about the coupled-form 2nd-order IIR resonator by deriving its correct z-domain transfer function and explaining why textbooks can appear to contradict pole plots. He shows that with infinite precision the coupled and standard denominators match, but finite-bit quantization of rcos(Θ) and rsin(Θ) changes the z^-2 coefficient and shifts pole positions. Read to learn the correct H(z) to predict quantized behavior and when the coupled form outperforms the standard design.
The Zeroing Sine Family of Window Functions
A previously unrecognized family of DFT window functions is introduced, built from products of shifted sines that deliberately zero out tail samples and control nonzero support. Cedron Dawg presents recursive and semi-root constructions, runnable code, and numerical examples, and shows that the odd-N member L=(N-1)/2 numerically matches a discrete Hermite-Gaussian DFT eigenvector. The post highlights practical properties, an even-N fix, and applications to spectrograms and tone decomposition.
A DSP Quiz Question
A short visual puzzle from Rick Lyons shows how a common plotting trick can fool even experienced DSP engineers. He presents a 3D circular plot that looks like a triangular window but is actually a 32-point hann window, then explains why the circular projection distorts the view. The post highlights the importance of checking equations and 2D plots before naming a window by sight.
Are DSPs Dead ?
Jeff Brower argues that the science of digital signal processing is far from dead, but commercial DSP chips lost momentum when Texas Instruments refused to embrace server-centric AI and 5G markets. He traces how TI's embedded-only culture, halted multicore CPU roadmaps, and lack of server-class products pushed customers to GPUs and FPGAs. A comeback would demand PCIe cards, VM and container support, open-source engagement, and bold leadership.
Polynomial calculations on an FIR filter engine, part 1
FIR filter blocks can be repurposed as fast polynomial evaluators, offering hardware acceleration for non-linear compensation, function approximation, and harmonic synthesis, but they require careful scaling and coefficient management. This article outlines when to use binomial or fitted polynomials, compares Horner's nested evaluation with the direct power-sum approach, and highlights precision and overflow pitfalls on fixed-point engines like the Cypress DFB.
Filter a Rectangular Pulse with no Ringing
You can filter a rectangular pulse with no ringing simply by using an FIR whose coefficients are all positive, and make them symmetric to get identical leading and trailing edges. This post walks through a MATLAB example that convolves a normalized Hanning window with a 32-sample rectangular pulse, showing that window length controls edge duration and that shorter windows widen the spectrum. It also notes this is not a QAM pulse-shaping solution.
Candan's Tweaks of Jacobsen's Frequency Approximation
Cedron Dawg shows how small tweaks to Jacobsen's three-bin frequency estimator turn a popular approximation into an exact formula, and how a modest cubic correction yields a near-exact, low-cost alternative. The article derives an arctan/tan exact recovery, relates it to Candan's 2011/2013 tweaks, and supplies reference C code and numerical tables so engineers can see when each formula is sufficient.
Python number crunching faster? Part I
Christopher Felton walks through simple benchmarks comparing raw Python, numpy, and PyPy for numeric workloads, and shares what surprised him about performance. He shows that idiomatic Python optimizations such as list comprehensions and built-ins plus the PyPy JIT can sometimes beat a numpy approach for small tests, and explains why native PyPy numpy progress matters for scientific users.
Deconvolution by least squares (Using the power of linear algebra in signal processing).
When we deal with our normal discrete signal processing operations, like FIR/IIR filtering, convolution, filter design, etc. we normally think of the signals as a constant stream of numbers that we put in a sequence
Embedded Toolbox: Programmer's Calculator
A tiny but powerful cross-platform tool, QCalc evaluates full C-syntax expressions so you can paste results straight into firmware. It handles bitwise ops, mixed hex/decimal/binary constants, and scientific math, and it automatically shows integer results in formatted hex and binary. The post explains key features, variable handling, error messages, and how to run qcalc.tcl with the wish Tk interpreter.
Resolving 'Can't initialize target CPU' on TI C6000 DSPs - Part 2
Mike Dunn walks through practical, low-level debugging to fix "Can't initialize target CPU" on TI C6000 DSPs using CCS 3.3, focusing on XDS510-class emulators. He demonstrates how to run xdsprobe to perform JTAG resets, read and interpret adapter and port error messages, and run JTAG IR/DR integrity tests. The article shows example outputs and a simple scope-based trace to locate signal faults.
Polar Coding Notes: Channel Combining and Channel Splitting
Lyons Zhang walks through the core algebra of polar coding, showing how channel combining builds the vector channel W_N from N copies of a binary-input DMC using the polar transform G_N = B_N F^{⊗n}. The notes then define channel splitting, derive the coordinate-channel transition probabilities from the chain rule, and present the recursive formulas that let you compute W_{2N}^{(2i-1)} and W_{2N}^{(2i)} from W_N^{(i)}.
Off-Topic: A Fluidic Model of the Universe
Cedron Dawg develops a Newtonian, fluidic model where space is a compressible "fluff" and particle motion is governed by a simple refractive steering equation. He shows how rho = ln n links index, permittivity and permeability to a gravity-like potential, derives a massive-particle steering law, and works through orbit and disk solutions that produce MOND-like effects while conflicting with General Relativity. The paper highlights concrete formulas and numerics to test the hypothesis.
Radio Frequency Distortion Part II: A power spectrum model
Markus Nentwig presents a power-spectrum model that predicts RF nonlinear distortion from spectral power values instead of time-domain signals. The model computes distortion as repeated convolutions with a frequency-reversed replica and uses an FFT/IFFT trick with real-valued arithmetic for very high efficiency, making it suitable for system-level simulations and interference-aware radios. It is accurate for OFDM-like, Gaussian-amplitude signals when spectral binning is sufficiently fine; narrowband cases require denser bins.
Least-squares magic bullets? The Moore-Penrose Pseudoinverse
Markus Nentwig walks through a practical way to remove power-line hum from measurements using the Moore-Penrose pseudoinverse. He builds a harmonic basis, computes pinv(basis) to get least-squares coefficients, and reconstructs and subtracts the hum, with a ready-to-run Matlab example. The post highlights limits and performance: basis-like signal components will be removed, and accuracy improves with the square root of sample count.
Filter a Rectangular Pulse with no Ringing
You can filter a rectangular pulse with no ringing simply by using an FIR whose coefficients are all positive, and make them symmetric to get identical leading and trailing edges. This post walks through a MATLAB example that convolves a normalized Hanning window with a 32-sample rectangular pulse, showing that window length controls edge duration and that shorter windows widen the spectrum. It also notes this is not a QAM pulse-shaping solution.
Compute Images/Aliases of CIC Interpolators/Decimators
CIC filters provide multiplier-free interpolation and decimation for large sample-rate changes, but their images and aliases can trip up designs. This post supplies two concise Matlab functions and hands-on examples to compute interpolator images and decimator aliases, showing spectra and freqz plots. Readers will learn how interpolation ratio and number of stages alter passband, stopband, and aliasing behavior.
Weighted least-squares FIR with shared coefficients
Markus Nentwig demonstrates how to design FIR filters that share coefficients across delay taps, allowing multiplier reuse and reduced implementation cost. He reimplements Lawson's iterative reweighted least-squares for complex-valued FIRs and provides Matlab/Octave code you can adapt for nonstandard constraints. The post explains iteration weight logic, the Toeplitz special-case with Levinson-Durbin, and practical trade-offs between multiplier count and stopband performance.
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.
New Discussion Group: DSP & FPGA
I have just created a new discussion group for engineers implementing DSP functions on FPGAs. The creation of this group has been on my todo list for a long time. If you want to join the group, send a blank email to: fpgadsp-subscribe@yahoogroups.com
As usual, it should take a few weeks before there are enough members for interesting discussions to get started.
There's No End to It -- Matlab Code Plots Frequency Response above the Unit Circle
If you want a fresh way to inspect a digital filter, this post introduces plotfil3d, a compact MATLAB function that wraps the magnitude response around the unit circle in the Z-plane so you can view it in 3D. It uses freqz to compute H(z) in dB for N points and accepts an optional azimuth to change the viewing angle; the code is provided in the appendix.
