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.
50,000th Member Announced!
DSPRelated just crossed a major milestone, 50,000 registered members, and Stephane Boucher celebrates the anniversary by spotlighting the lucky winner, Charlie Tsai, an assistant professor in Taiwan. The post also looks back at more than a decade of community growth and thanks the contributors, authors, and sponsors who helped make the site a go-to DSP resource. It closes with a promise of big improvements ahead in 2010.
Unit Testing for Embedded Algorithms
Unit testing is a best practice for embedded algorithm development, and Anthony Ricke shows how to apply it to DSP code so host and target behave identically. He demonstrates writing unit tests, stubbing Blackfin fixed-point functions in the workstation, and using test-driven development to safely port and optimize an average-calculation example. The SourceForge examples make the approach practical to adopt.
Almost 50,000 Members!
DSPRelated is about to hit a big milestone, and Stephane Boucher marks the moment with a playful giveaway announcement. The post jokes about a BMW prize for the 50,000th registered member, then reveals the real reward, a copy of Rick Lyons’ Understanding Digital Signal Processing. It is a lighthearted community update built around a membership milestone and a bit of fun.
Deesspee #5
Peter Kootsookos's Deesspee #5 is a very short micro-post simply titled "Computers". It acts as a minimalist flag in the Deesspee series pointing readers toward the computing topic on DSPRelated; click through to view the original entry and any context or discussion. This compact post is useful if you track the author's brief topic markers or short-format updates.
Using Mason's Rule to Analyze DSP Networks
When algebra gets messy, Rick Lyons shows how Mason's Rule cuts through the tedium to produce z-domain transfer functions for even nested-feedback DSP networks. The post gives a clear step-by-step procedure, definitions, and worked examples including a biquad, a DC-bias remover, and a complex multi-loop network. It also points to a public MATLAB routine to automate the bookkeeping.
DSPRelated faster than ever!
Stephane Boucher moved DSPRelated's static assets to Amazon CloudFront to shrink page load times worldwide. Images, JavaScript and CSS are now served from the nearest CloudFront edge server, reducing latency especially for readers in Europe and Asia. If you visit regularly, you should notice the speedup, and the author asks readers to report their load-time experience in the comments.
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.
Simultaneously Computing a Forward FFT and an Inverse FFT Using a Single FFT
Rick Lyons presents a compact seven-step algorithm to compute a forward FFT and an inverse FFT at the same time using a single radix-2 complex FFT. The method builds intermediate sequences v(n) and z(n), exploits conjugate symmetry, and requires only one N-point FFT plus about 2N additions or subtractions. A clear MATLAB implementation accompanies the explanation so you can try it immediately.
Multiplierless Exponential Averaging
Rick Lyons shows how to implement exponential averaging without multiplies by exploiting a rearranged leaky-integrator form and binary shifts. He demonstrates reducing the standard two-multiply averager to a single-multiply form, then eliminating the multiply entirely when the weighting α equals reciprocals or differences of reciprocals of powers of two. The post catalogs practical α choices for fixed-point filters and flags quantization as an open issue.
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.
Ten Little Algorithms, Part 6: Green’s Theorem and Swept-Area Detection
Jason shows how Green's Theorem becomes a practical, low-cost method to detect real-time rotation from two orthogonal sensors by accumulating swept area. The post derives a compact discrete integrator S[n] = S[n-1] + (x[n]*(y[n]-y[n-1]) - y[n]*(x[n]-x[n-1]))/2, compares integer and floating implementations, and analyzes noise scaling and sampling rate tradeoffs. Includes Python demos and threshold guidance.
A New Contender in the Quadrature Oscillator Race
Rick Lyons highlights a compact quadrature oscillator introduced by A. David Levine and Martin Vicanek, offering guaranteed stability, accurate low-frequency tuning, and modest computational cost. The post walks through the simple u, v, w recurrences used for software implementation. Appendices provide transfer functions and an algebraic stability proof for engineers who want formal verification before deployment.
An Alternative Form of the Pure Real Tone DFT Bin Value Formula
Cedron Dawg derives an alternative exact formula for DFT bin values of a pure real tone, sacrificing algebraic simplicity for better numerical behavior near integer-valued frequencies. By rewriting cosine differences as products of sines and shifting to a delta frame of reference, the derivation avoids catastrophic cancellation and preserves precision for near-integer tones. The analysis also shows the integer-frequency case is a degenerate limit that yields the familiar M/2 e^{iφ} bin value.
Unit Testing for Embedded Algorithms
Unit testing is a best practice for embedded algorithm development, and Anthony Ricke shows how to apply it to DSP code so host and target behave identically. He demonstrates writing unit tests, stubbing Blackfin fixed-point functions in the workstation, and using test-driven development to safely port and optimize an average-calculation example. The SourceForge examples make the approach practical to adopt.
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.
Digging into an Audio Signal and the DSP Process Pipeline
Zooming into an audio waveform can be misleading if you rely on only one view. This post compares Audacity with a simple C++ WAV reader and shows how the same samples can look like zero in a GUI, while the raw data reveals a small nonzero value. It is a practical reminder that multiple tools help you inspect and verify signal data more accurately.
Frequency Formula for a Pure Complex Tone in a DTFT
The analytic formula for calculating the frequency of a pure complex tone from the bin values of a rectangularly windowed Discrete Time Fourier Transform (DTFT) is derived. Unlike the corresponding Discrete Fourier Transform (DFT) case, there is no extra degree of freedom and only one solution is possible.
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.
We are famous!!
A quick bit of DSPRelated pride, the IEEE Signal Processing eNewsletter mentioned the site’s blog section in a roundup of social media resources for DSP. The post shares the moment the author heard the news and points readers to the original mention. It is short, but it captures a nice sign that the community is paying attention.
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.
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.
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.
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.
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.
Do you like the new Comments System?
Stephane Boucher has just rolled out a new comments system for the DSPRelated blogs and wants feedback from readers. He’s asking the community to try it out, share thoughts, and help shake out any issues before it gets expanded to the code snippets and papers sections.
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.
A Lesson In Engineering Humility
Rick Lyons revisits a remarkable 1948 Bell Labs project that implemented a 12-channel telephone PCM transmission system without using transistors. The original two-paper PDF shows how engineers converted analog audio into 7-bit serial pulse-code streams sampled at 8000 samples per second, and Lyons calls studying that work a true lesson in engineering humility. He places the papers alongside 1948 milestones such as Shannon's theory and early transistor developments.
TI goes the Open Source way!
TI has started opening parts of its toolchain by releasing a free standalone compiler for its C54x line, announced through Googles Summer of Code. Praveen Raghavan points out the bundle includes a compiler, optimizer, assembler, and linker but no debugger, and shows why this can enable open-source codec work on DM320-based OSD projects. The post calls for industry and academia to collaborate on improving compilers.
Exploring Human Hearing Range
Audacity makes it simple to explore the limits of human hearing by generating and inspecting single-tone audio. This post walks through creating a 9 kHz sine tone, noticing the default 44,100 Hz sample rate, and verifying the result with Audacity's Plot Spectrum tool. Follow the steps and use low playback volume to safely try higher or lower test frequencies yourself.
