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.
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.
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.
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.
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.
Linear Feedback Shift Registers for the Uninitiated, Part XIII: System Identification
Jason Sachs shows how the output of a linear feedback shift register can be used for active system identification, not just spread-spectrum testing. The article compares traditional sine-wave probing with LFSR-based PRBS methods, demonstrates a worked Ra-Rb-C example, and unpacks practical issues such as reflected pseudonoise, ADC quantization, sample counts, and noise-shaping tricks to improve estimates.
Project update-1 : Digital Filter Blocks in MyHDL and their integration in pyFDA
By week 5 the project delivered parameterized MyHDL implementations of multiple digital filter topologies and started integration with PyFDA. The post walks through a behavioral direct-form I FIR, cascaded second-order-section implementations for FIR and IIR using structural modeling, and a parallel IIR design that concatenates per-section outputs for final summation. All designs infer order and coefficients from PyFDA, with examples in the filter-blocks repository.
How to Find a Fast Floating-Point atan2 Approximation
This post shows how a compact, fast atan2 can be built from a Remez-derived arctangent approximation and a matching 3rd-order polynomial. It walks through using Boost's remez_minimax to recover coefficients 0.97239411 and -0.19194795, integrating the polynomial into an atan2 with quadrant reduction, and applying branch reduction, bit tricks, and SSE2 SIMD to cut runtime while keeping max error under about 0.005 radians.
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.
The Sampling Theorem - An Intuitive Approach
Scott Kurtz from DSPSoundWare.com has put together a video presentation that aims to give DSP engineers an intuitive grasp of the Sampling Theorem. The short, approachable video focuses on conceptual understanding of sampling and aliasing rather than mathematical formality. Watch the presentation on DSPRelated and share your reactions in the post comments to join the discussion.
[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.
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.
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.
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.
Engineering the Statistics
Statistical analysis can get messy fast when theory and MATLAB simulations refuse to agree. This post shares a graduate student’s hard-earned shortcuts for taming random variables, from deriving a CDF or moments to using Gaussian or Gamma approximations, and falling back on Chernoff bounds when the exact PDF stays out of reach.
[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.
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.
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.
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.
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.
Looking For a Second Toolbox? This One's For Sale
A battered blue toolbox once used by Steve Wozniak during Apple’s early days is now up for auction, complete with a self-adhesive label bearing his name. Rick Lyons notes the 13 x 7 x 5 inch steel box shows heavy wear and includes a three-section lid tray, it currently resides in Italy and is listed with an estimated price around $25,000, shippable to buyers.
