Signed serial-/parallel multiplication
Struggling with costly wide adders for signed multiplication on FPGAs? Markus Nentwig unpacks a neat bit-level trick that turns two's-complement signed-signed multiplication into a serial-parallel routine using only a one-bit wider adder. Learn how flipping sign bits and a small, controlled constant cancel lets you avoid full sign-extension, and get a parametrized Verilog RTL plus synthesis notes to try it yourself.
A Remarkable Bit of DFT Trivia
Rick Lyons highlights a surprising equality: the DFT's worst-case scalloping loss equals 2/π, the same probability that a toothpick crosses a floorboard seam in Buffon's needle problem when the toothpick equals board width. The post sketches the DFT bin-intersection derivation and connects the math to the classic probability puzzle, offering a playful insight that sharpens intuition about bin responses.
Understanding and Preventing Overflow (I Had Too Much to Add Last Night)
Integer overflow is stealthier than you think, and in embedded systems it can break control loops or corrupt data. Jason Sachs walks through the usual culprits, including addition, subtraction, multiplication, shifting and Q15 fixed-point traps, plus C-specific pitfalls such as undefined signed overflow and INT_MIN edge cases. He then lays out practical defenses: prefer fixed-width types, widen and saturate intermediates, enable wraparound where appropriate, and reason about modular congruence for compound arithmetic.
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.
Computing Translated Frequencies in Digitizing and Downsampling Analog Bandpass Signals
Textbooks rarely give ready formulas for tracking where individual spectral lines land after bandpass sampling or decimation. Rick Lyons provides three concise equations, with Matlab code, that compute translated frequencies for analog bandpass sampling, real digital downsampling, and complex downsampling. Practical examples show how to place the sampled image at fs/4 and how to translate a complex bandpass to baseband for efficient demodulation.
Goertzel Algorithm for a Non-integer Frequency Index
Rick Lyons demonstrates how to run the Goertzel algorithm with a non-integer frequency index k, letting you target DTFT frequencies that do not align with DFT bin centers. He interprets Rajmic and Sysel's generalization, provides a simple implementation, and presents a real-valued reformulation that reduces the final multiplies for real inputs. Example Matlab code is included to reproduce and adapt the technique.
Is It True That j is Equal to the Square Root of -1 ?
A viral YouTube video claimed that saying j equals the square root of negative one is wrong. Rick Lyons shows the apparent paradox comes from misusing square-root identities with negative arguments, not from the usual definition of j. He argues it is safer to define j by j^2 = -1 and illustrates how careless root operations produce contradictions in two appendices.
Signal Processing Contest in Python (PREVIEW): The Worst Encoder in the World
Jason Sachs previews a hands-on Python contest to find the best velocity estimator for a noisy, low-cost quadrature encoder. The post explains the Estimator API, submission constraints, and a 5 second, 10 kHz evaluation harness that uses a simulated "Lucky Wheel" encoder with realistic manufacturing timing errors. Jason also includes a simple baseline estimator and discusses the practical tradeoff between noise reduction and phase lag in velocity estimation.
A Table of Digital Frequency Notation
Rick Lyons compiles a compact, practical table that untangles the many algebraic frequency notations used in DSP. The reference lines up continuous and discrete sinusoid forms, shows the frequency variable names and units, and lists valid ranges and conversions like Ω = 2πf and normalized forms with fs. A printable PDF of the table is available for easy desk reference.
Shared-multiplier polyphase FIR filter
One multiplier and a dual-port RAM can implement an arbitrary m/n polyphase FIR resampler on an FPGA, Markus Nentwig demonstrates. The post focuses on practical implementation details, including a parametrized Verilog design, pipelined MAC control, and a Matlab testbench for verification. It shows how bank indexing and pipeline delay compensation let you multiplex many coefficient banks efficiently for resource-constrained FPGA designs.
Helping New Bloggers to Break the Ice: A New Ipad Pro for the Author with the Best Article!
Breaking the ice can be tough. Over the years, many individuals have asked to be given access to the blogging interface only to never post an article.
A Simplified Matlab Function for Power Spectral Density
Neil Robertson provides a tiny Matlab wrapper around pwelch that simplifies PSD computation by preselecting a Kaiser window, default overlap, and converting units from W/Hz to dBW/bin. Call psd_simple(x,nfft,fs) to get PdB and a frequency vector, with nfft controlling whether DFT averaging is used. The post includes examples showing the effect of averaging and explains the Kaiser window processing loss.
Signal Processing Contest in Python (PREVIEW): The Worst Encoder in the World
Jason Sachs previews a hands-on Python contest to find the best velocity estimator for a noisy, low-cost quadrature encoder. The post explains the Estimator API, submission constraints, and a 5 second, 10 kHz evaluation harness that uses a simulated "Lucky Wheel" encoder with realistic manufacturing timing errors. Jason also includes a simple baseline estimator and discusses the practical tradeoff between noise reduction and phase lag in velocity estimation.
Live Streaming from Embedded World!
Stephane Boucher will bring Embedded World to engineers who cannot attend, streaming high-quality HD video from the show floor. He plans to use a professional camera and a device that bonds three internet links to keep the stream stable, and he is coordinating live sessions with vendors and select talks. Read on to learn how to vote for the presentations you want streamed.
The Risk In Using Frequency Domain Curves To Evaluate Digital Integrator Performance
Frequency-response curves can be misleading when selecting a digital integrator, Rick Lyons shows, and he proves it with counterexamples using seven test signals. By comparing methods such as Simpson's 1/3 rule, Al-Alaoui, and Tick's rule on definite-integral tasks, Lyons demonstrates that a close match to the ideal frequency response does not guarantee accurate integrals, because input signal traits strongly affect results.
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.
Sinusoidal Frequency Estimation Based on Time-Domain Samples
Rick Lyons presents three time-domain algorithms for estimating the frequency of real and complex sinusoids from samples. He shows that the Real 3-Sample and Real 4-Sample estimators, while mathematically exact, fail in the presence of noise and can produce biased or invalid outputs. The Complex 2-Sample (Lank-Reed-Pollon) estimator is more robust but can be biased at low SNR and near 0 or Fs/2, so narrowband filtering is recommended.
Stereophonic Amplitude-Panning: A Derivation of the 'Tangent Law'
Rick Lyons presents a clear geometrical derivation of the stereophonic amplitude-panning Tangent Law, filling a gap left by common references. Using vector components and the equidistant speaker assumption to keep signals in phase, he arrives at the Tangent Law and isolates practical gain formulas gL and gR needed to place an apparent source at a desired panning angle. Engineers can apply Eqs. (12) and (14) directly.
Reducing IIR Filter Computational Workload
Rick Lyons demonstrates a simple, practical way to cut the multiply count for IIR lowpass and highpass filters by converting them into dual-path allpass structures. The conversion preserves the original magnitude response while drastically reducing multiplies per input sample, for example turning a 5th-order IIR that needs 11 multiplies into an equivalent allpass form needing only five. The linked PDF includes theory, implementation notes, a design example, and MATLAB code.
New Code Sharing Section & Reward Program for Contributors!
DSPRelated is launching a new code sharing section and looking for contributors to help seed it with useful DSP snippets. Stephane Boucher also introduces a pageview-based reward program, with payouts tied to unique visits so popular code can earn contributors up to $250. It is a practical push to build a high-quality library for the DSP community from the start.
scipy.signal calling all developers
SciPy’s signal-processing toolbox is at a crossroads, and Christopher Felton is urging developers to jump in. He points to active discussion on scipy-dev, the possibility of a separate scikit-signal effort, and the broad set of functions already in scipy.signal. If you work in DSP and like open-source software, this is a good moment to look at the package, and maybe help shape it.
Multilayer Perceptrons and Event Classification with data from CODEC using Scilab and Weka
For my first blog, I thought I would introduce the reader to Scilab [1] and Weka [2]. In order to illustrate how they work, I will put together a script in Scilab that will sample using the microphone and CODEC on your PC and save the waveform as a CSV file.
The Beginning of a New Chapter
After years of hesitation, Stephane Boucher and Jacob Beningo finally turned their virtual events into an in-person reality with the inaugural Signal Processing Summit and Embedded Systems Summit at the Sonesta Silicon Valley. The post captures the logistics, a last-minute travel scare during a US government shutdown, the joy of meeting speakers like Fred Harris, and practical lessons for future technical events. It closes by inviting community feedback and venue suggestions.
A Useful Source of Signal Processing Information
A surprisingly handy web tool turned up for finding signal processing material in PDF and PowerPoint form. Rick Lyons shows how a plain-looking site can surface lots of topic-specific documents, using FM demodulation as the example. If you often hunt for reference slides and papers, this is a quick source worth bookmarking.
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.
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.
"Neat" Rectangular to Polar Conversion Algorithm
Rick Lyons revisits a clever slide-rule era trick for estimating the magnitude of a complex number without computing a square root. He highlights a neat identity, prompted by a Jerry Avins post, that converts the sqrt problem into forward and inverse trigonometric operations plus ratios. The post invites readers to derive Eq. (2) and see why a seemingly complex idea is actually simple and practical.
Autocorrelation and the case of the missing fundamental
A short hands-on exploration shows why we perceive the fundamental pitch even when it's absent from the spectrum. Using saxophone recordings, high-pass filtering, and autocorrelation plots, the post demonstrates that the highest ACF peak often predicts perceived pitch rather than the strongest spectral line. The experiments also show that removing high harmonics eliminates the effect, and that autocorrelation is a useful but incomplete model of pitch perception.
A Remarkable Bit of DFT Trivia
Rick Lyons highlights a surprising equality: the DFT's worst-case scalloping loss equals 2/π, the same probability that a toothpick crosses a floorboard seam in Buffon's needle problem when the toothpick equals board width. The post sketches the DFT bin-intersection derivation and connects the math to the classic probability puzzle, offering a playful insight that sharpens intuition about bin responses.
A Wide-Notch Comb Filter
Traditional comb filters make very narrow stopband notches, which limits their ability to suppress broader interfering tones. Rick Lyons presents a linear-phase comb filter that produces wider stopband notches than the conventional design while preserving linear-phase behavior. The post also reviews the traditional cascaded recursive running-sum architecture, its co-located dual poles and zeros on the z-plane, and the placement of nulls at integer multiples of fs/D.
