Design IIR Butterworth Filters Using 12 Lines of Code
Build a working lowpass IIR Butterworth filter from first principles in just 12 lines of Matlab using Neil Robertson's butter_synth.m. The post walks through the analog prototype poles, frequency pre-warping, bilinear transform pole mapping, adding N zeros at z = -1, and gain normalization so the result matches Matlab's built-in butter function. It's a compact, hands-on guide with clear formulas and code.
Feedback Controllers - Making Hardware with Firmware. Part 6. Self-Calibration Related.
Self-calibration is the missing piece that turns this mixed-signal hardware from a prototype into a usable instrument. In this installment, the author lays out how the board will measure itself, generate reference signals, and verify ADC and DAC behavior before the low-latency control firmware is built. The result is a practical framework for evaluation, production test, and routine self-test.
Simplest Calculation of Half-band Filter Coefficients
Half-band FIR filters put the cutoff at one-quarter of the sampling rate, and nearly half their coefficients are exactly zero, which makes them highly efficient for decimation-by-2 and interpolation-by-2. This post shows the straightforward window-method derivation of half-band coefficients from the ideal sinc impulse response, providing a clear, hands-on explanation for engineers learning filter design. It also points to equiripple options such as Matlab's firhalfband and a later Parks-McClellan implementation.
Feedback Controllers - Making Hardware with Firmware. Part 5. Some FPGA Aspects.
This installment digs into practical FPGA choices and board-level issues for a low-latency, floating-point feedback controller. It compares a Cyclone V implementation against an older SHARC-based design, quantifies the tradeoff between raw DSP resources and cycle latency, and calls out Gotchas found on the BeMicro CV A9 evaluation card. Engineers get concrete prompts for where to optimize: clocking, DSP-block use, I/O standards, and algorithm partitioning.
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.
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.
There and Back Again: Time of Flight Ranging between Two Wireless Nodes
Conventional timestamping seems too coarse for centimeter-level RF ranging, yet many products claim and deliver that precision. This post unpacks the fundamentals behind high-resolution wireless ranging, contrasting common RF approaches such as RSSI, ToA, PoA, TDoA, and AoA. It also explains how device timestamps and counter registers work, giving engineers a practical starting point for implementing or evaluating time-of-flight ranging systems.
Feedback Controllers - Making Hardware with Firmware. Part 4. Engineering of Evaluation Hardware
This installment follows the hardware from concept to first power-up for a low-latency feedback controller and arbitrary circuit emulator. It walks through the practical engineering steps, from requirements, block diagrams, and issue tracking to component selection, simulation, PCB planning, purchasing, and staged bring-up. The result is a realistic look at how careful due diligence and a few trade-offs turned a research idea into working evaluation hardware.
Online DSP Classes: Why Such a High Dropout Rate?
Rick Lyons digs into a startling statistic: online DSP courses reported a 97% dropout rate. He argues the main culprits are math-heavy curricula that overwhelm beginners and rigid, non-self-paced schedules that demand sustained 8-10+ hours per week. Rick urges course creators to rethink pacing and mathematical depth to improve completion rates and student engagement.
Two Bin Exact Frequency Formulas for a Pure Real Tone in a DFT
Cedron Dawg derives exact, closed-form frequency formulas that recover a pure real tone from just two DFT bins using a geometric vector approach. The method projects bin-derived vectors onto a plane orthogonal to a constraint vector to eliminate amplitude and phase, yielding an explicit cos(alpha) estimator; a small adjustment improves noise performance so the estimator rivals and slightly betters earlier two-bin methods.
Linear Feedback Shift Registers for the Uninitiated, Part XV: Error Detection and Correction
CRCs and Hamming codes look a lot less magical when you view them as redundancy with a purpose. Jason Sachs walks from parity bits and checksums into finite-field polynomial arithmetic, then shows how CRCs map cleanly onto LFSRs and how Hamming codes use syndromes to locate single-bit errors. It is a practical tour of error detection and correction, with enough worked examples to make the theory feel usable.
Impulse Response Approximation
A stepped-triangular impulse approximation represents an FIR low-pass using a cascade of recursive running-sum filters, offering big savings in computation. Christopher Felton outlines the quantization step that maps a true impulse into three stepped-triangular types and shows how the approximation is built from recursive running-sum and sparse-sum blocks. Inspect the frequency tradeoffs and decide if the efficiency gain is worth the approximation error.
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.
Coupled-Form 2nd-Order IIR Resonators: A Contradiction Resolved
Rick Lyons resolves a long-standing confusion about the coupled-form 2nd-order IIR resonator by deriving its correct z-domain transfer function and explaining why textbooks can appear to contradict pole plots. He shows that with infinite precision the coupled and standard denominators match, but finite-bit quantization of rcos(Θ) and rsin(Θ) changes the z^-2 coefficient and shifts pole positions. Read to learn the correct H(z) to predict quantized behavior and when the coupled form outperforms the standard design.
Learn About Transmission Lines Using a Discrete-Time Model
A simple discrete-time approach makes lossless transmission-line behavior easy to simulate and visualize. The post introduces MATLAB functions tline and wave_movie to model uniform lossless lines with resistive terminations, compute time and frequency responses, and animate travelling waves. A microstrip pulse example shows how reflections produce ringing and how source matching nearly eliminates it, making this a practical learning tool.
A Fast Real-Time Trapezoidal Rule Integrator
Rick Lyons presents a compact, recursive real-time Trapezoidal Rule integrator that computes N-sample discrete integration using only four arithmetic operations per input sample. The proposed network yields a finite-length, linear-phase impulse response with constant group delay (N-1)/2 and cuts substantial computation compared with a tapped-delay implementation, making it useful for speeding Romberg-based digital filters.
Simple Discrete-Time Modeling of Lossy LC Filters
Converting a lossy LC filter into a discrete-time impulse response lets you analyze mixed analog and DSP systems in one time domain. This post walks through computing the LC frequency response via chain (ABCD) parameters including resistive losses, enforcing the Hermitian symmetry required for a real IDFT, and using the IDFT to produce an asymmetrical FIR impulse response. A 5th-order Butterworth example illustrates insertion loss and impulse-shape effects.
Sensors Expo - Trip Report & My Best Video Yet!
Stephane Boucher turns a first-time Sensors Expo visit into a fun travelogue and a polished conference highlights video. He mixes candid trip anecdotes from Moncton to San Jose, electric-scooter discoveries, Santa Cruz detours, Airbnb tips, and on-the-floor expo footage. The post culminates in what he calls his best highlights reel yet, plus a follow-up video focused on embedded and IoT.
A Differentiator With a Difference
Rick Lyons presents a compact, practical FIR differentiator that combines central-difference noise attenuation with a much wider linear range. The proposed ydif(n) doubles the usable frequency range to about 0.34π (0.17fs), uses ±1/16 coefficients so multiplications become simple 4-bit right shifts, and has an exact three-sample group delay for easy synchronization with other signals.
60-Hz Noise and Baseline Drift Reduction in ECG Signal Processing
Rick Lyons shows a very efficient way to clean up ECGs when both baseline drift and 60 Hz power-line interference are getting in the way. He starts from a linear-phase DC removal filter, reshapes it into a notch filter that hits both 0 Hz and 60 Hz, and then tests it on a noisy real-world ECG. The payoff is a practical design that uses only two multiplications and five additions per sample.
The Discrete Fourier Transform as a Frequency Response
Neil Robertson shows that the discrete frequency response H(k) of an FIR filter is exactly the DFT of its impulse response h(n). He derives the continuous H(ω) and discrete H(k) using complex exponentials for a four-tap FIR, then replaces h(n) with x(n) to recover the general DFT formula. The post keeps the math simple and calls out topics left for separate treatment, such as windowing and phase.
Summary of ROC Rules
This is a very short guide on how to find all possible outcomes of a system where Region of Convergence (ROC) and the original signal is not known.
Reduced-Delay IIR Filters
Rick Lyons investigates a simple 2nd-order IIR modification that reduces passband group delay by just under one sample, inspired by Steve Maslen's reduced-delay concept. He walks through the conversion steps and compares z-plane, magnitude, and group-delay plots for Butterworth, elliptic, and Chebyshev prototypes, showing how zeros shift and stopband attenuation degrades. A linked PDF extends the study to 1st-, 3rd-, and 4th-order cases so you can follow the tradeoffs.
The Swiss Army Knife of Digital Networks
A single discrete-signal network can masquerade as a comb filter, a recursive section, or something much more versatile. Rick Lyons shows how this seven-coefficient structure can be reconfigured to realize a wide range of DSP functions, with tables of impulse responses, pole-zero plots, and frequency responses to illustrate each case. The full explanations live in the downloadable PDF, but the post gives a strong feel for why this is such a handy building block.
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.
Online DSP Classes: Why Such a High Dropout Rate?
Rick Lyons digs into a startling statistic: online DSP courses reported a 97% dropout rate. He argues the main culprits are math-heavy curricula that overwhelm beginners and rigid, non-self-paced schedules that demand sustained 8-10+ hours per week. Rick urges course creators to rethink pacing and mathematical depth to improve completion rates and student engagement.
Differentiating and integrating discrete signals
Think DSP's new chapter digs into discrete differentiation and integration, using first differences, convolution, and FFTs to compare time and frequency domain views. The author reproduces diff via convolution then explores cumsum as its inverse and runs into two puzzling mismatches: noisy FFT amplitude ratios for nonperiodic data, and a time-domain convolution that does not reproduce cumsum for a sawtooth despite matching frequency responses. The post includes IPython notebooks and invites troubleshooting.
Curse you, iPython Notebook!
Christopher Felton shares a cautionary tale about losing an ipython 0.12 notebook session after assuming the browser would save his interactive edits. He explains that notebooks at the time required clicking the top Save button to persist sessions, and autosave was not yet available. He recommends basing interactive work on scripts, saving often, and testing export behavior to avoid redoing text, LaTeX, and plots.
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.
A Fast Real-Time Trapezoidal Rule Integrator
Rick Lyons presents a compact, recursive real-time Trapezoidal Rule integrator that computes N-sample discrete integration using only four arithmetic operations per input sample. The proposed network yields a finite-length, linear-phase impulse response with constant group delay (N-1)/2 and cuts substantial computation compared with a tapped-delay implementation, making it useful for speeding Romberg-based digital filters.
