Some Thoughts on Sampling
Sampling's 1/Ts amplitude factor is not a paradox but a consequence of axis scaling and impulse density, once you view the units correctly. This post walks through impulse trains in continuous and discrete time, uses DFT examples and Parseval's relation, and shows how downsampling and time scaling produce the familiar spectral replicas and their amplitudes. The geometry of the axes resolves the confusion.
Matlab Code to Synthesize Multiplierless FIR Filters
Learn how to build multiplierless FIR lowpass filters in Matlab using Canonic Signed-Digit coefficients. The post explains converting Parks-McClellan floating-point taps to scaled integers, then to exact CSD digits, and includes two m-files that search maintap scaling to minimize signed digits while preserving the filter response. Practical notes cover external gain compensation, the 2/3 full-scale CSD limit, and sensitivity to pass/stop edges.
Wavelets II - Vanishing Moments and Spectral Factorization
This post walks through how vanishing moments turn into concrete algebraic constraints on wavelet filter coefficients, and why that leads to Daubechies filters. It explains how a wavelet with A vanishing moments is orthogonal to all polynomials up to degree A minus one, and it shows how those continuous conditions become discrete sums like sum_k k^n h1(k)=0. Expect clear links between approximation power and filter length.
Fibonacci trick
Tim Wescott shares a compact, surprising trick linking Fibonacci numbers and difference equations. Start with any two consecutive Fibonacci numbers, negate the larger-magnitude one, and iterate the usual recurrence; after a few steps you'll arrive at the standard Fibonacci sequence or its negative. This behavior is specific to the Fibonacci recurrence and makes a great illustrative example for teaching linear recurrences.
The Power Spectrum
You can get absolute power from a DFT, not just relative spectra. In this post Neil Robertson shows how to convert FFT outputs into watts per bin using Parseval's theorem, how to form one-sided spectra, and how to normalize windows so power is preserved. Matlab examples demonstrate bin-centered and between-bin sinusoids, leakage, scalloping, and how to recover component power by summing bins.
New Comments System (please help me test it)
DSPRelated just got a practical upgrade, Stephane Boucher has released a new comments system built from his earlier forum work. It supports drag-and-drop or Insert Image uploads, MathML, TeX and ASCIImath rendered by MathJax, syntax-highlighted code via highlight.js, and in-place editing and deletion of comments. Improved email notifications alert authors and commenters to replies, and readers are invited to post test comments and report problems.
Wavelets I - From Filter Banks to the Dilation Equation
Starting from a practical cascaded FIR filter bank, this post derives the key equations behind the Fast Wavelet Transform. It shows how conjugate-quadrature analysis and synthesis filters give perfect reconstruction and how iterating the cascade produces the scaling function, leading to the dilation equation. DB4 coefficients are used as a concrete example and a linear-system trick yields exact integer-sample values of the scaling function.
The Real Star of Star Trek
Rick Lyons argues the real star of Star Trek is not an actor but the USS Enterprise, whose image drove much of the franchise's power. He traces the ship from two 1966 scale models through Smithsonian restoration, NASA naming influence, global architecture, and magazine art to show how an engineered prop became a worldwide cultural icon. The piece mixes nostalgia with concrete examples and a hands-on modeler lesson.
An s-Plane to z-Plane Mapping Example
A misleading online diagram prompted Rick Lyons to reexamine how s-plane points map to the z-plane. He spotted apparent errors in the original figure, drew a corrected mapping, and invites readers to inspect both diagrams and point out any remaining mistakes. The short post is a quick visual primer for engineers who rely on accurate s-plane to z-plane mappings in analysis and design.
Should DSP Undergraduate Students Study z-Transform Regions of Convergence?
Rick Lyons argues z-transform regions of convergence are mostly a classroom abstraction with little practical use for real-world DSP engineers. For all stable LTI impulse responses encountered in practice the ROC includes the unit circle, so DTFT and DFT exist and ROC analysis rarely affects implementation. He notes digital oscillators are a notable exception, and suggests reallocating classroom time to more practical engineering topics.
Complex Down-Conversion Amplitude Loss
Rick Lyons shows why a standard complex down-converter seems to halve amplitudes yet only imposes a -3 dB power loss. He walks through mixing math from an RF cosine to i and q paths, demonstrates that each path has peak A/2 but the complex output has half the average power, and offers practical guidance for software modeling and avoiding spectral interpretation traps.
Simple Concepts Explained: Fixed-Point
Fixed-point is the bridge between real-world values and integer arithmetic, and this post makes that bridge tangible with a hands-on ADC-to-gain example. It walks through mapping voltages to Q-format integers, choosing gain resolution in bits, and how multiplication adds bit growth and produces quantization error. Read it to build intuition for practical fixed-point choices when implementing DSP on FPGA or ASIC.
SEGGER's 25th Anniversary Video
Stephane Boucher spent a week at SEGGER's headquarters and distilled that visit into a tight, two-minute 25th anniversary video. The post highlights rising production value, thanks to softbox lighting and a two-camera setup that allows seamless wide-to-tight cuts and emotional close-ups. Stephane invites readers to watch full screen, leave feedback and thumbs-up on YouTube, and suggests future coverage like product launches or companies with happy engineers.
Simulink-Simulation of SSB demodulation
This post walks through Simulink models that implement SSB demodulation and modulation, using Richard Lyons' phasing method as a foundation. It shows practical models for simple carrier multiplication and for the phasing method with cosine and -sin paths plus Hilbert filtering, and it highlights sampling, decimation, filter choices, and delay alignment to make the techniques work in simulation.
The 2024 DSP Online Conference
The DSP Online Conference returns for a fourth year, running October 29–31, with a program designed for students, engineers, hobbyists, and experts. Organized into four tracks—general DSP theory, communications, audio, and DSP with deep learning—the event accepts short MicroTalks through two-hour Workshops and offers early-bird registration plus immediate archive access for registrants.
Python scipy.signal IIR Filter Design Cont.
Christopher Felton continues his practical tour of SciPy's iirdesign, moving beyond lowpass examples to show highpass, bandpass, and stopband designs with concise, code-focused explanations. He highlights how ellip and cheby2 let you tighten specifications for sharper transitions, and shows that the iirdesign workflow is consistent across filter types. Read for clear, reusable examples to produce IIR filter coefficients with scipy.signal.
An Efficient Lowpass Filter in Octave
Paul Lovell presents an efficient linear-phase lowpass FIR implemented in Octave, built as a Matrix IFIR with two matrix band-edge shaping stages followed by three recursive running-sum stages. The design reshapes input blocks into matrices to exploit interpolation structure and uses cumsum-based moving sums for speed. For a 200 Hz cutoff at 48 kHz the five-stage example ran about 15 times faster than a single-stage FIR.
Design IIR Band-Reject Filters
This post walks through designing IIR Butterworth band-reject filters and provides two MATLAB synthesis functions, br_synth1.m and br_synth2.m. br_synth1 accepts a null frequency plus an upper -3 dB frequency, while br_synth2 takes lower and upper -3 dB frequencies. The author demonstrates an example where a 2nd-order prototype yields a 4th-order H(z), prints b and a coefficients, and plots the response using freqz.
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.
Sonos, Shut Up and Take My Money! - Is Spatial Audio Finally Here?
Stephane bought a Sonos ERA 300 and discovered that spatial audio can finally feel convincing from a single wireless speaker, provided you set it up correctly. The trick is using Dolby Atmos tracks played inside the Sonos app, plus Sonos' calibration and a close listening position. The post shares setup tips, vivid listening impressions, and encouragement for more spatial mixes to come.
Are DSPs Dead ?
Jeff Brower argues that the science of digital signal processing is far from dead, but commercial DSP chips lost momentum when Texas Instruments refused to embrace server-centric AI and 5G markets. He traces how TI's embedded-only culture, halted multicore CPU roadmaps, and lack of server-class products pushed customers to GPUs and FPGAs. A comeback would demand PCIe cards, VM and container support, open-source engagement, and bold leadership.
Ancient History
The other day I was downloading an IDE for a new (to me) OS. When I went to compile some sample code, it failed. I went onto a forum, where I was told "if you read the release notes you'd know that the peripheral libraries are in a legacy download". Well damn! Looking back at my previous versions I realized I must have done that and forgotten about it. Everything changes, and keeping up with it takes time and effort.
When I first started with microprocessors we...
A Simpler Goertzel Algorithm
Rick Lyons presents a streamlined Goertzel algorithm that simplifies computing a single DFT bin by removing the textbook method's extra shift and zero-input steps. The proposed network changes the numerator so you run the main stage N times then perform one final output stage, making the implementation cleaner and slightly cheaper computationally. Rick also points out that common textbook forms differ from Gerald Goertzel's 1958 original.
Add the Hilbert Transformer to Your DSP Toolkit, Part 1
Learn how the Hilbert transformer creates a 90-degree phase-shifted quadrature component without down-conversion, and why it is simply a special FIR filter. Part 1 defines the transformer, derives its ideal frequency response H(ω)=j for ω<0 and -j for ω≥0, and walks through Matlab examples that demonstrate phase shifting and image attenuation for bandpass signals.
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.
Computing Translated Frequencies in Digitizing and Downsampling Analog Bandpass Signals
Textbooks rarely give ready formulas for tracking where individual spectral lines land after bandpass sampling or decimation. Rick Lyons provides three concise equations, with Matlab code, that compute translated frequencies for analog bandpass sampling, real digital downsampling, and complex downsampling. Practical examples show how to place the sampled image at fs/4 and how to translate a complex bandpass to baseband for efficient demodulation.
Complex Down-Conversion Amplitude Loss
Rick Lyons shows why a standard complex down-converter seems to halve amplitudes yet only imposes a -3 dB power loss. He walks through mixing math from an RF cosine to i and q paths, demonstrates that each path has peak A/2 but the complex output has half the average power, and offers practical guidance for software modeling and avoiding spectral interpretation traps.
What to See at Embedded World 2019
Skip the overwhelm at Embedded World 2019, Stephane Boucher lays out a practical preview of what to see and how to prioritize your time. The post helps embedded engineers focus on demos, vendor booths, and sessions that matter without getting lost on the show floor. Read it to plan a short, efficient visit that maximizes technical takeaways and networking opportunities.
Multimedia Processing with FFMPEG
FFMPEG is a set of libraries and a command line tool for encoding and decoding audio and video in many different formats. It is a free software project for manipulating/processing multimedia data. Many open source media players are based on FFMPEG libraries.
How the Cooley-Tukey FFT Algorithm Works | Part 1 - Repeating Calculations
The Fourier Transform is a powerful tool, used in many technologies, from audio processing to wireless communication. However, calculating the FT can be computationally expensive. The Cooley-Tukey Fast Fourier Transform (FFT) algorithm provides a significant speedup. It exploits the repetitive nature of calculations within the Discrete Fourier Transform (DFT), the mathematical foundation of the FT. By recognizing patterns in the DFT calculations and reusing intermediate results, the FFT vastly reduces the number of operations required. In this series of articles, we will look at how the Cooley-Tukey FFT algorithm works.
