Computing FFT Twiddle Factors
Rick Lyons gives two compact algorithms to compute individual twiddle factors for radix-2 DIF and DIT FFTs, handy when you need only a subset of outputs such as in pruned FFTs. He explains stage indexing, provides closed-form formulas including the bit-reversal step for DIT, and walks through N=8 examples so you can implement the twiddle-angle calculations directly.
Knowledge Mine for Embedded Systems
A little-known interactive portal makes learning embedded systems surprisingly practical and visual. The site is organized into four main areas: embedded systems design, design lifecycle, design methods, and design tools. Each section uses clickable system block diagrams so you can jump from a block, for example a MAC unit, to a focused page with detailed explanations. It’s a handy, ready reference for DSP and embedded engineers.
Hidden Linear Algebra in DSP
Linear algebra is hiding in plain sight inside many DSP techniques, not just abstract theory. By treating linear systems as matrix operators y = A x you reveal Toeplitz structure in LTI systems, connect to covariance matrices, and gain geometric intuition via eigenvalues and eigenvectors. This matrix viewpoint complements convolution-based thinking and offers practical tools for filter and channel analysis.
Accelerating Matlab DSP Code on the GPU
Seth Benton spent a few days testing Jacket to accelerate MATLAB on NVIDIA GPUs, and found it surprisingly easy to speed up DSP code. He ran 2D FFT and interp2 benchmarks on a MacBook Air with a GeForce 9400M, seeing impressive speedups for large images while hitting GPU memory and precision limits at high sizes. The post shares practical tips on casting to GPU types, minimizing CPU-GPU transfers, and when GPU acceleration is most useful.
Googling: a now-required skill
Finding the right DSP answer often starts with finding the right search term, not the right textbook. Seth Benton shares the web resources he leans on, from comp.dsp and the MATLAB File Exchange to Google tricks like related searches and the tilde operator. It is a practical reminder that better keywords can cut straight through the rabbit hole.
OpenCV for DSP/GPU, MSDN equivalent for CCS, and more
Porting OpenCV to DSPs could be a real business opportunity, but it is far from trivial, writes Shehrzad Qureshi. He highlights major obstacles: the engineering scale, mixed open-source licenses, and hard-to-parallelize primitives like connected components. He also criticizes Code Composer Studio's help system compared with MSDN, notes an ATI Stream talk, and announces a CUDA walkthrough on FFT-based image filtering.
Computing an FFT of Complex-Valued Data Using a Real-Only FFT Algorithm
Rick Lyons shows a compact trick to get an N-point complex FFT using only real-input FFT routines by transforming the real and imaginary parts separately and recombining their outputs. The post presents a one-line recombination formula, Xc(m) = real[Xr(m)] - imag[Xi(m)] + j{imag[Xr(m)] + real[Xi(m)]}, and an algebraic derivation based on the two-real-in-one-complex FFT identity. Useful for systems that only provide real-only FFTs.
Random GPGPU Musings
Shehrzad Qureshi argues that general-purpose GPU computing is poised to reshape engineering workloads, and contrasts Nvidia's CUDA ecosystem with ATI's Stream and OpenCL. He points out that GPU architectures and programming models are similar across vendors, but Nvidia's head start in sample code and developer community gives CUDA a practical advantage. Read for a concise industry perspective on choosing a GPGPU platform.
GPGPU DSP
Shehrzad Qureshi kicks off his DSP blog by championing GPGPU, focusing on Nvidia's CUDA and real-product experience. He argues that with CPU clock speeds stalled, large-scale parallelism on GPUs is the practical path forward for many signal-processing tasks. The post traces GPGPU history from shader 'hacks' to modern APIs and previews future posts comparing CUDA vs OpenCL, Intel's Larrabee, and Nvidia Fermi.
Some Thoughts on a German Mathematician
Rick Lyons revisits the remarkable career of Carl Friedrich Gauss, mixing memorable anecdotes with technical highlights. The post links Gauss’s work on the Gaussian curve, complex-plane representation, orbit prediction, and early telegraph experiments to ideas familiar to DSP engineers, and notes historical evidence that he developed trigonometric series before Fourier. It’s a short, engaging reminder of Gauss’s broad influence.
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.
Evaluate Noise Performance of Discrete-Time Differentiators
Differentiators can be wildly different at rejecting noise, even when they share the same usable bandwidth. Neil Robertson introduces the Differentiator Noise Power Ratio, a practical Gaussian-noise metric and a compact formula that uses the filter coefficients to quantify output noise and SNR loss. The post also gives MATLAB guidance for designing and comparing FIR differentiators so you can pick or build filters with much better noise performance.
The Signal Processing Summit 2025 - Registrations Now Open!
Stephane Boucher announces that registration is open for the inaugural Signal Processing Summit, October 14-16, 2025 at the Sonesta Silicon Valley. This three-day, engineer-focused event promises practical insights from leading DSP experts and tight networking in an intimate 70-seat setting. Register early to save $200 with the Early Bird rate and lock in a discounted Sonesta room before the block fills.
The Phase Vocoder Transform
Treating the phase vocoder as a continuous transform, this post frames PV(x,α,β) as a bijection on signal space and derives the domain constraints needed for an inverse mapping. It uses geometric intuition and group-theory analogies to explain negative and zero scalings, then brings the idea back to DSP to show how aliasing and phase artifacts appear. The Laroche and Dolson consistency measure D_M plus MATLAB experiments are used to compare classic and identity phase-locking reconstructions.
3 Good News
Stephane Boucher reports three quick wins for the EmbeddedRelated community: two sponsors have seeded a $1,000 rewards pool, the site now serves all pages over HTTPS, and the new forums have their first active discussions. If you want a share of the sponsor-funded rewards, jump into the forums and check the Vendors Directory for opportunities. Stay tuned for more updates.
Make Hardware Great Again
US weakness in 5G and the coming AI race stems from a deeper problem, hardware decline and lack of CPU innovation. Jeff Brower argues that the software-only narrative has hollowed out semiconductor leadership, leaving only a few chipmakers and blocking vital R&D. He calls for targeted government action, funding for neural-net chips, and an industrial Hardhattan Project to rebuild CPU and hardware capabilities.
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.
Crowdfunding Articles?
Technical writers in the embedded world often have the expertise, but not always the time or incentive to turn it into a post. Stephane Boucher explores a crowdfunding model for technical articles, where readers would pledge small amounts to back promising abstracts before the writing begins. It is an interesting attempt to create more high quality EE content by paying authors upfront.
Components in Audio recognition - Part 1
This post introduces the core components of an audio recognition system, framed against how the human auditory system naturally familiarizes and retrieves tunes. Prabindh Sundareson outlines the three building blocks: an archive store, an analysis and fingerprinting engine that groups tracks, and a front-end that accepts queries and places samples into groups. He previews upcoming posts that will dig into implementations and tradeoffs.
Project Report : Digital Filter Blocks in MyHDL and their integration in pyFDA
This Summer of Code project shows how to move from Python filter design to synthesizable HDL by building a MyHDL "filter-blocks" package and connecting it to PyFDA. The author implemented direct form I FIR and IIR blocks, added an API, tests, tutorials, and PyFDA export to VHDL and Verilog. The report also highlights practical fixed-point design choices and remaining work such as second-order sections.
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.
[Book Review] Numpy 1.5 Beginner's Guide
Christopher Felton's review gives a pragmatic take on Ivan Idris's Numpy 1.5 Beginner's Guide, praising its hands-on, exercise-driven approach while flagging several shortcomings. He finds the book a useful starting point for newcomers to Python numerical computing thanks to practical examples and a chapter on testing, but warns the title, incomplete installation guidance, and some factual errors may mislead readers.
Polar Coding Notes: A Simple Proof
Lyons Zhang presents a compact, elementary derivation of channel polarization for binary-input discrete memoryless channels. The note leverages Mrs. Gerber's Lemma to bound conditional entropies and follows the Alsan-Telatar averaging argument to show mediocre channels vanish. The proof sidesteps martingale convergence and recovers the standard result that the fraction of good channels approaches the channel capacity.
The Nature of Circles
Averaging angles the usual way can produce nonsense: the mean of 0 and 359 degrees is not 179.5 when working with circular data. Peter Kootsookos shows the correct approach using vectorial or phasor averaging, converting angles to unit complex numbers and taking the argument of their sum. The short post points to directional statistics and a related IEEE paper for deeper details.
Smaller DFTs from bigger DFTs
A neat DFT puzzle turns into a tour of three useful spectral tricks. Given only an N point DFT black box, the post shows how to recover the N/2 point DFT of a shorter sequence by zero padding, zero interlacing, or repeating the data. Along the way, it highlights why some methods smooth the spectrum, why others replicate it, and how these operations relate to FFT fundamentals.
Update to a Narrow Bandpass Filter in Octave or Matlab
Paul Lovell presents an updated, compact Octave/Matlab implementation of a narrow bandpass FIR that runs about four times faster and uses float32 to cut processing cost. The design combines a single matrix IFIR stage with three moving-sum (RRS) stages per baseband, auto-calculates the IFIR expansion factor, and adds easier parameter setup plus WAV I/O and FFT plots. A TensorFlow Colab demo is also provided.
Microprocessor Family Tree
Rick Lyons shares a compact, nostalgic microprocessor family tree that highlights early integrated circuits and his fondness for the Intel 8080. The post invites engineers to spot classic chips they remember, pairing brief commentary with a scanned image from Creative Computing, June 1985, copied without permission. It’s a short historical snapshot for anyone interested in vintage CPU lineage.
Signal Processing Summit - Cancellation Policy
The post announces a flexible cancellation policy for the inaugural Signal Processing Summit, an intimate DSP event limited to 70 seats and scheduled in Silicon Valley this October. It explains refundable options designed to give attendees confidence when registering early: a full refund minus a $95 processing fee for cancellations before the end of September, a 50% refund for cancellations in October before October 6, and no refunds after that date. The policy is positioned to help prospective attendees lock in the Early Bird rate, secure discounted hotel accommodations, and plan travel with reduced risk. The announcement frames the policy as a way to remove barriers to commitment and encourages readers who have been undecided to register now and attend the Summit.
Improved Three Bin Exact Frequency Formula for a Pure Real Tone in a DFT
Cedron Dawg extends his two-bin exact frequency formulas to a three-bin DFT estimator for a pure real tone, and presents the derivation in computational order for practical use. The method splits complex bin values into real and imaginary parts, forms vectors A, B, and C, applies a sqrt(2) variance rescaling, and computes frequency via a projection-based closed form. Numerical tests compare the new formula to prior work and show improved accuracy when the tone lies between bins.
Finding the Best Optimum
Optimization is seductive but often misleading, especially when mathematical models don't match messy reality. Tim Wescott shares stories from circuits and communications to show how chasing the theoretical global optimum can waste time and money. He recommends framing 'best' in practical terms, validating models, and optimizing for cost and impact so products ship on time and actually work in the real world.
