Evaluate Window Functions for the Discrete Fourier Transform
Spectral leakage makes DFTs of continuous sinewaves misleading, and windowing is the practical workaround. This post supplies Matlab code to plot spectra of windowed sinewaves and compute figures of merit, so you can compare windows such as flattop and Chebyshev. See how sidelobe level, mainlobe bandwidth, processing loss, noise bandwidth, and scallop loss trade off to guide your window choice.
Feedback Controllers - Making Hardware with Firmware. Part 10. DSP/FPGAs Behaving Irrationally
A practical approach to emulating lossy transmission lines in real time, using pole-zero approximations to replace irrational s-domain behaviors and enable FPGA implementation. The author shows 8-pole/zero fits for Zo(s) and a 6-pole/zero plus delay for P(s), validated against LTSpice and MATLAB. Conversion to sampled-data Zo(z) and biquad implementations is detailed, along with issues in single-precision arithmetic and mitigations such as mixed sample rates and partial-fraction decomposition.
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.
Polar Coding Notes: Channel Combining and Channel Splitting
Lyons Zhang walks through the core algebra of polar coding, showing how channel combining builds the vector channel W_N from N copies of a binary-input DMC using the polar transform G_N = B_N F^{⊗n}. The notes then define channel splitting, derive the coordinate-channel transition probabilities from the chain rule, and present the recursive formulas that let you compute W_{2N}^{(2i-1)} and W_{2N}^{(2i)} from W_N^{(i)}.
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.
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.
Design a DAC sinx/x Corrector
Neil Robertson provides a compact Matlab function and coefficient tables for designing linear-phase FIR sinx/x correctors to undo the DAC sinc roll-off. The post explains the sinc_corr(ntaps,fmax,fs) call, shows worked examples with ntaps=5 and different fmax values, and demonstrates fixed-point quantization including a k=512 example and CSD digit guidance. Practical notes cover corrector gain and input back-off to avoid clipping.
Off Topic: Refraction in a Varying Medium
Cedron Dawg derives a compact vector differential equation for a point particle moving through a smoothly varying refractive medium using the Euler-Lagrange variational method. By introducing a log refractive index called "fluff density," the paper expresses acceleration purely in terms of the fluff gradient and velocity, then explores curvature, superposition, and point-source capture radii with simple closed-form results.
Feedback Controllers - Making Hardware with Firmware. Part 9. Closing the low-latency loop
This article demonstrates combining DSP and feedback-control on an Intel Cyclone floating-point FPGA to build low-latency closed-loop circuit emulators and controllers. Using a single floating-point biquad at 1.6 Msps, an IFFT multi-tone 4.096 ms capture for wideband measurement, and MATLAB references for verification, the author achieves sub-nanosecond timing insight and applies DSP phase compensation to cancel about 100 pF of PCB parasitics.
Project update-2 : Digital Filter Blocks in MyHDL and their integration in pyFDA
This update shows a working integration between Pyfda and MyHDL using a compact API that passes fixed-point coefficients, stimulus data, and returns simulated filter responses. It walks through two usage styles, constructor-based and setter-method-based, and demonstrates a Pyfda workflow from specs to MyHDL simulation and plotting. Future plans include HDL code generation and API extension as filters grow.
Generating Complex Baseband and Analytic Bandpass Signals
Rick Lyons gathers and compares practical methods for creating complex baseband and analytic bandpass signals in one compact reference. The post clarifies definitions, lists time and frequency domain techniques from quadrature sampling to FFT-based analytic generation, and notes implementation tradeoffs such as sample-rate constraints, Hilbert transformer use, and phase linearity concerns. Engineers get a quick Hit Parade of options and pointers to deeper references.
Some Observations on Comparing Efficiency in Communication Systems
Efficiency in wireless communications is a multidimensional tradeoff, not a single metric. Eric Jacobsen walks through how transmit power, channel bandwidth, and FEC choices interact, showing when to judge systems by Eb/No versus SNR and how to read bandwidth-efficiency plots. The piece highlights a practical "sweet spot" of FEC code rates where power, spectrum, and decoder complexity are balanced, helping engineers choose MCS sets wisely.
OpenCV for DSP/GPU, MSDN equivalent for CCS, and more
Porting OpenCV to DSPs could be a real business opportunity, but it is far from trivial, writes Shehrzad Qureshi. He highlights major obstacles: the engineering scale, mixed open-source licenses, and hard-to-parallelize primitives like connected components. He also criticizes Code Composer Studio's help system compared with MSDN, notes an ATI Stream talk, and announces a CUDA walkthrough on FFT-based image filtering.
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.
Spectral Flipping Around Signal Center Frequency
Most DSP engineers know that multiplying a real signal by (-1)^n inverts its spectrum about fs/4, but that trick fails when you need to flip around a specific carrier. Rick Lyons presents two practical techniques: a multirate upsample-by-two solution using paired lowpass filters and cosine mixing, and a computationally heavier complex-multiply plus real-part method attributed to Dirk Bell, both yielding the desired fcntr-centered flip.
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.
The Most Interesting FIR Filter Equation in the World: Why FIR Filters Can Be Linear Phase
Rick Lyons pulls back the curtain on a little-known coefficient constraint that makes complex-coefficient FIR filters exhibit linear phase. Rather than simple symmetry of real coefficients, the key is a conjugate-reflection relation involving the filter phase at DC, which collapses to ordinary symmetry for real taps. The post includes derivations, intuition using the inverse DTFT, and a Matlab example to verify the result.
Time Machine, Anyone?
Causal filters can look like time machines, but they do not break physics. Andor Bariska reproduces a classic electronic experiment in MATLAB, showing how a minimum-phase peaking filter and its FDLS biquad approximation produce negative group delay bands that make predictable, bandlimited signals appear to emerge early. The post walks through group delay, discretization, pulse and random-signal tests, and why unpredictability restores causality.
DSP Algorithm Implementation: A Comprehensive Approach
This post lays out a practical pathway for taking DSP algorithms from high level simulation to production hardware, comparing GPP, DSP, FPGA and ASIC platforms. It presents a stepwise methodology starting with nested loop programs, then exposing parallelism with data flow graphs, using SystemC transaction level modeling to bridge to Verilog or VHDL, and explains why that flow speeds design and simulation.
Python number crunching faster? Part I
Christopher Felton walks through simple benchmarks comparing raw Python, numpy, and PyPy for numeric workloads, and shares what surprised him about performance. He shows that idiomatic Python optimizations such as list comprehensions and built-ins plus the PyPy JIT can sometimes beat a numpy approach for small tests, and explains why native PyPy numpy progress matters for scientific users.
Data Types for Control & DSP
Control engineers often default to double precision, but Tim Wescott shows that choice can waste CPU cycles on embedded targets. He separates numeric representation into floating point, integer, and fixed-point, then walks through the tradeoffs, including quantization, overflow, and performance. A concrete PID example highlights why integrator precision and ADC scaling should drive your choice of data type rather than habit.
Demonstrating the Periodic Spectrum of a Sampled Signal Using the DFT
This post makes a basic DSP principle tangible by computing the DFT over an extended set of bins and plotting the results. It demonstrates that a sampled signal's spectrum repeats every sampling rate, explains the k-to-frequency mapping, and contrasts common bin ranges such as 0..N-1 and -N/2..N/2-1. The write-up also highlights symmetry for real sequences and recommends using the FFT for efficiency.
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.
Compute the Frequency Response of a Multistage Decimator
This post shows a practical way to compute the full frequency response of a multistage decimator by representing every stage at the input sample rate. The author walks through upsampling lower-rate FIR coefficients, convolving to form the overall impulse response, and taking a DFT, then demonstrates how aliasing and stopband placement affect the aliased components. Example Matlab code and plots illustrate each step.
Design of an anti-aliasing filter for a DAC
If you need a practical way to design an anti-aliasing filter for a DAC, this post delivers an Octave/Matlab script that numerically optimizes a Laplace-domain transfer function for linear phase and arbitrary magnitude. The routine models the DAC sample-and-hold sinc response, compensates group delay automatically, and can include an optional multiplierless FIR equalizer. An example shows a 5.4 dB objective improvement and reduced analog Q for easier implementation.
Part 11. Using -ve Latency DSP to Cancel Unwanted Delays in Sampled-Data Filters/Controllers
Negative-latency DSP can cancel ADC, FPGA/DSP, DAC and propagation delays to deliver near-zero unwanted latency filtering. Steve Maslen explains how to split a digital filter into a simple feed gain b0 and an advanced DF3 block that produces samples one sample early, then recombine them so sampled-data delays cancel. MATLAB c2d examples, a PID case study and FPGA test-bed results show the technique is practical and proven, with active IP noted.
An Astounding Digital Filter Design Application
Rick Lyons was astonished by the ASN Filter Designer, a hands-on filter design tool that makes tweaking frequency responses as simple as dragging markers with your mouse. The software updates magnitude plots, z-plane pole/zero locations, and filter coefficients in real time, and it also includes a signal analyzer plus a MATLAB-like scripting language for custom coefficient generation. The post links to a demo and user guides so you can try it yourself.
ADC Clock Jitter Model, Part 1 -- Deterministic Jitter
Clock jitter on ADC sample clocks corrupts high-frequency signals, and this post builds a practical MATLAB model to show exactly how deterministic (periodic) jitter maps into phase modulation and discrete sidebands. The author explains a parabolic-interpolation approach using twice-rate samples, demonstrates examples from single tones to pulses, and matches simulation spectra to closed-form sideband formulas so engineers can predict jitter effects.
Canonic Signed Digit (CSD) Representation of Integers
Canonic Signed Digit (CSD) encoding slashes the number of nonzero bits in integer coefficients, enabling multiplierless FIR filters implemented with shifts and adds. This post uses MATLAB code to demonstrate CSD rules, show how negative values work, and plot the distribution of signed digits as bit width changes. It finishes with practical techniques to minimize signed digits per coefficient for area and power efficient filter designs.
Correcting an Important Goertzel Filter Misconception
A common claim says the Goertzel algorithm is marginally stable and prone to numerical errors. Rick Lyons shows that the usual second-order Goertzel filter has conjugate poles exactly on the unit circle, so pole placement alone does not make it unstable. The practical limits are coefficient quantization, which reduces frequency precision, and accumulator overflow for very large N.
