Improved Narrowband Lowpass IIR Filters
Rick Lyons presents a practical trick from his DSP book that makes narrowband lowpass IIR filters usable in fixed-point systems. By replacing unit delays with M-length delay lines to form an interpolated-IIR, pole radii and angles are transformed so desired poles fall into quantizer-friendly locations without wider coefficient words or extra multiplies. A following CIC image-reject stage removes replicated passbands to meet tight stopband specs.
A multiuser waterfilling algorithm
Markus Nentwig shares a compact, heuristic multiuser waterfilling algorithm with ready-to-run C code, designed for practical radio resource allocation. The approach uses round-robin user handling, per-user power budgets and a mode switch between fixed-power and waterfilling distributions, and it is easy to extend for constraints or QoS tweaks. The implementation is suboptimal by design, fast, and requires verification before production use.
Code Snippets Section Now LIVE
A new code-sharing section on DSPRelated is now live, giving engineers a central place to browse and share DSP code snippets. Take a few minutes to rate and comment on snippets you can judge, or apply to become a contributor and upload your own examples. You can also learn about the contributor reward program and send feedback to help the community grow, says Stephane Boucher.
Discrete Wavelet Transform Filter Bank Implementation (part 1)
David Valencia walks through a practical implementation of discrete wavelet transform filter banks, focusing on cascading branches and efficient equivalent filters. He contrasts DWT and DFT resolution behavior and shows how cascading the low-pass branch sharpens frequency division while the high-pass path remains unchanged. Code pointers and a preview of formfilters() demonstrate how to compute only the needed samples by combining filters with upsampling.
Personal presentation and greetings
David Valencia joins DSPRelated from Mexico City and brings hands-on DSP projects and code. He plans to share Spectrum Digital DSK6713 examples covering GPIO control, external memory, and expansion port access, with MATLAB, C and TI DSP C implementations. Expect wavelet transform filter bank code, and occasional FPGA and CPLD notes. Stay tuned for practical, hardware-focused DSP resources.
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.
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.
Fitting Filters to Measured Amplitude Response Data Using invfreqz in Matlab
This post is a redirect notice for a code snippet now hosted elsewhere. If you were looking for the invfreqz example on fitting a filter to measured amplitude response data, this page simply points you to the new location and asks you to update your bookmark.
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.
Understanding Radio Frequency Distortion
Markus Nentwig breaks down how analog RF nonlinearities appear in a complex baseband model so you can simulate and predistort real transmitters. The article shows that even-order terms vanish in-band under narrowband assumptions, while odd-order products collapse to |BB(t)|^(n-1) BB(t) and do not depend on the carrier frequency. It also explains bandwidth scaling and includes a MATLAB example plus measured PA coefficients.
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 Recipe for a Basic Trigonometry Table
Cedron Dawg walks through building a degree-based sine and cosine table from first principles, showing both recursive and multiplicative complex-tone generators. The article highlights simple drift-correction tricks such as mitigated squaring and compact normalization, gives series methods to compute one-degree and half-degree values, and includes practical C code that ties the table to DFT usage and frequency estimation.
Matlab Programming Contest
Love puzzles or want to sharpen your MATLAB skills? Christopher Felton highlights MathWorks' biannual MATLAB programming contest, a week-long set of clever algorithm challenges that require only base MATLAB. Whether you're experienced or new, you can compete, compare solutions, or simply study others' code when later phases disclose submissions. No toolboxes or mex files allowed, so it's a pure programming playground for learning and bragging rights.
Coefficients of Cascaded Discrete-Time Systems
Multiplying discrete-time transfer functions is just polynomial multiplication, and polynomial multiplication is convolution. Neil Robertson shows that the numerator and denominator coefficients of cascaded systems come from convolving the individual coefficient vectors, then demonstrates the idea with MATLAB code and a 2nd-order IIR cascade that yields a 4th-order response. The approach makes computing time and frequency responses straightforward.
Constrained Integer Behavior
Overflow and underflow are not always bugs, they can be useful in DSP when fixed-width integers wrap during processing. Christopher Felton demonstrates with moving-average (recursive-windowed-averager) and CIC filter examples how 2's complement wraparound in MyHDL's modbv cancels between an integrator and a comb via pole-zero cancellation. He also covers fixed-point resizing choices, saturation versus wrap, and how rounding error can accumulate.
Somewhat Off Topic: Deciphering Transistor Terminology
Rick Lyons unpacks a small linguistic mystery in electronics, revealing why the transistor's middle terminal is called the "base". He traces the name to the 1949 Bell Labs "semiconductor triode", where the device sat on a metal base plate described as a large-area low-resistance contact, and notes that later transistor sandwich designs kept the name for historical reasons. The post includes original references and a few trivia nuggets.
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.
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.
DSP Related Math: Nice Animated GIFs
Stephane Boucher collected a compact set of animated GIFs that make common DSP math click visually. He spotted popular posts on the ECE subreddit and aggregated DSP-focused GIFs in one place to speed intuition and teaching. Examples include the relationship between sin and cos with right triangles, constructing a square wave from an infinite series, and the continuous Fourier transform pair of the rect and sinc functions.
A Markov View of the Phase Vocoder Part 2
This post builds a Markov-chain transition graph to guide phase vocoder time-frequency decisions, using spectral correlation data from a Bach violin sonata. It shows how FFT size and the time-stretch factor alpha change bin-to-bin correlations, proposes an inverse-square plus log-boundary probability model for transitions, and demonstrates practical limits and implementation choices with accompanying MATLAB code.
RF in Slow Motion: Sonifying a Wi-Fi 7 Packet
What would a 160 MHz OFDM waveform up in the 5 GHz U-NII band sound like if scaled to audio frequencies to keep the same wavelength (acoustic vs RF)?
A Lesson in Statistics Using Random Sequences
Statistics may come naturally to some people, but it is a difficult subject for many of us. Using simulations helps to remove some of the mystery of statistics. Luckily, it is trivial to produce a pseudo-random Gaussian or uniform sequence: a single command in Matlab (or Python) does it. In this article, I try to explain a few concepts using Gaussian and uniform random sequences generated in Matlab. First, we’ll generate a Gaussian sequence, calculate its variance, and plot a histogram and probability density function (PDF). Next, we’ll simulate the roll of a single die to illustrate a uniform distribution. Then we’ll simulate rolling two dice and finally, as an illustration of the Central Limit Theorem, we’ll sum the total when rolling several dice to obtain an approximately Gaussian distribution.
State Space Representation and the State of Engineering Thinking
State space is common in control, but it shows up much less often in signal processing. This post argues that the difference is really about engineering priorities: for many DSP problems, transfer functions are enough, while state space becomes valuable when internal behavior matters, like filter scaling or Kalman filtering. It is a short, practical look at why engineers choose one model over the other.
SDR: Does it makes sense? Part 1/2
Software-defined radio is still a question mark for deployment, but Praveen Raghavan argues the economics are starting to line up. He points to rising process costs, especially as devices move toward FinFET technologies, and notes that consumer products usually need only a couple of wireless standards at once. That makes multi-standard silicon look more practical than ever, and he tees up the next question, what should actually be software definable?
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.
DSP Papers, Articles, Theses, etc
Stephane Boucher invites the DSP community to help expand DSPRelated's Papers and Theses repository, which currently lists just over 100 documents. He asks contributors to find and submit recent DSP PDFs, ideally from the last ten years, and notes that each approved submission enters the submitter into a draw for Michael Parker's Digital Signal Processing 101; the draw is planned for early April.
Implementing a full-duplex UART using the TMS320VC33 serial port
You can convert the TMS320VC33's synchronous serial port into a full-duplex UART in software by using DR0/DX0, on-chip timers, and an external interrupt. Manuel Herrera walks through an interrupt-driven 9600 baud, 8N1 asynchronous receiver/transmitter, explains receiver gating by start bit detection, and includes a schematic plus a complete assembly listing with timer values tied to a 150 MHz clock. Adjust timing for different clock rates.
Through the tube...
Markus Nentwig explores whether RF power amplifier modeling tricks work for audio tube preamps by modeling a 12AX7 preamp in Matlab. He records input and output with a two-channel reference, fits a simple Wiener-type model, and compares the modeled output to the real tube sound. The model explains over 99 percent of output power and leaves only small residual distortion to investigate further.
Of Forests and Trees and DSP
Too often DSP engineers fixate on algorithms and miss the rest of the product. Tim Wescott uses the humble Korg CA-20 chromatic tuner to show that a great algorithm alone does not make a usable device, you also need good data acquisition, adequate processing, sensible precision, a usable UI, and appropriate casing and cost. The post gives practical do's and don'ts for system-level DSP design.
Exact Near Instantaneous Frequency Formulas Best at Zero Crossings
Cedron Dawg derives time-domain formulas that yield near-instantaneous frequency estimates optimized for zero crossings of pure tones. Complementing his earlier peak-optimized results, these difference-ratio formulas work for real and complex signals, produce four-sample estimators similar to Turners, and cancel amplitude terms, making them attractive low-latency options for clean tones while warning they degrade in noise and at peaks.
