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.
Model a Sigma-Delta DAC Plus RC Filter
Sigma-delta digital-to-analog converters (SD DAC’s) are often used for discrete-time signals with sample rate much higher than their bandwidth. For the simplest case, the DAC output is a single bit, so the only interface hardware required is a standard digital output buffer. Because of the high sample rate relative to signal bandwidth, a very simple DAC reconstruction filter suffices, often just a one-pole RC lowpass. In this article, I present a simple Matlab function that models the combination of a basic SD DAC and one-pole RC filter. This model allows easy evaluation of the overall performance for a given input signal and choice of sample rate, R, and C.
DAC Zero-Order Hold Models
This article provides two simple time-domain models of a DAC’s zero-order hold. These models will allow us to find time and frequency domain approximations of DAC outputs, and simulate analog filtering of those outputs. Developing the models is also a good way to learn about the DAC ZOH function.
Decimators Using Cascaded Multiplierless Half-band Filters
In my last post, I provided coefficients for several multiplierless half-band FIR filters. In the comment section, Rick Lyons mentioned that such filters would be useful in a multi-stage decimator. For such an application, any subsequent multipliers save on resources, since they operate at a fraction of the maximum sample frequency. We’ll examine the frequency response and aliasing of a multiplierless decimate-by-8 cascade in this article, and we’ll also discuss an interpolator cascade using the same half-band filters.
Frequency Formula for a Pure Complex Tone in a DTFT
The analytic formula for calculating the frequency of a pure complex tone from the bin values of a rectangularly windowed Discrete Time Fourier Transform (DTFT) is derived. Unlike the corresponding Discrete Fourier Transform (DFT) case, there is no extra degree of freedom and only one solution is possible.
Pentagon Construction Using Complex Numbers
A method for constructing a pentagon using a straight edge and a compass is deduced from the complex values of the Fifth Roots of Unity. Analytic values for the points are also derived.
Multiplierless Half-band Filters and Hilbert Transformers
This article provides coefficients of multiplierless Finite Impulse Response 7-tap, 11-tap, and 15-tap half-band filters and Hilbert Transformers. Since Hilbert transformer coefficients are simply related to half-band coefficients, multiplierless Hilbert transformers are easily derived from multiplierless half-bands.
Algebra's Laws of Powers and Roots: Handle With Care
Rick Lyons shows that familiar power and root rules from algebra can break down when exponents are complex. He tests common identities for two scenarios, real and fully complex exponents, with positive and negative mantissas, and compiles a table of cases that sometimes fail. The post includes MATLAB examples that reproduce counterexamples and a clear warning to numerically verify algebraic steps involving complex powers.
Access to 50+ Sessions From the DSP Online Conference
Registering for the 2023 DSP Online Conference gives you 10 months of unlimited access to 50+ on-demand DSP sessions, turning a single sign-up into a compact DSP library. Stephane highlights top-rated talks and workshops you can binge, including deep dives from fred harris and a three-hour control-loop workshop by Dan Boschen. The post points to must-watch recordings on resampling, polyphase filters, FIR design, beamforming, and more.
Interpolator Design: Get the Stopbands Right
In this article, I present a simple approach for designing interpolators that takes the guesswork out of determining the stopbands.
Digital Envelope Detection: The Good, the Bad, and the Ugly
Envelope detection sounds simple, but implementation choices change everything. Rick Lyons gathers common digital detectors, including half-wave, full-wave, square-law, Hilbert-based complex, and synchronous coherent designs, and explains how harmonics, filtering, and carrier recovery change results. He ranks detectors by output SNR from a representative simulation and offers practical tips on filter cutoff, Hilbert transformer bandwidth, and when a simple detector is good enough.
A Beginner's Guide to OFDM
Orthogonal Frequency Division Multiplexing made modern high-speed wireless practical by turning one fast serial bitstream into many slow parallel streams carried on orthogonal sinusoids. This beginner guide explains, with minimal math, how the iDFT/DFT pair builds OFDM, how spectral slicing makes each subcarrier effectively flat so equalization reduces to simple divisions, and why a cyclic prefix prevents inter-symbol interference.
Padé Delay is Okay Today
High-order Padé approximations for time delays break in surprising ways, but the failure is not magic. Jason Sachs walks through why coefficient-based transfer functions and companion-form state-space are numerically fragile, shows how to compute poles and zeros directly from the hypergeometric form with Newton iteration, and demonstrates building modal or block-diagonal state-space realizations to make high-order Padé delays practical while noting remaining limits.
A New Related Site!
The post announces the launch of MLRelated, a new Related site dedicated to machine learning and deep learning. It positions MLRelated as complementary to existing Related sites by highlighting cross-cutting interests: TinyML for embedded developers, machine/deep learning applications in signal processing, and FPGA-based AI/ML implementations. The new site debuts with a modest amount of content and is expected to expand rapidly through contributions from the Related community in the form of blogs, forum threads, and webinars. The author invites readers to report navigation errors, share feedback, and propose ideas to help steer MLRelated into a practical, community-driven resource for researchers and practitioners in ML and adjacent domains.
Adventures in Signal Processing with Python
Jason Sachs shows how PyLab (numpy, scipy, matplotlib) can handle many signal-processing and visualization tasks engineers usually reach for MATLAB to do. He walks through practical examples including PWM ripple, two pole RC filters, and symbolic math with SymPy, and shares real-world installation tips and trade-offs. The post closes with pointers to IPython and pandas to speed interactive analysis and data handling.
How the Cooley-Tukey FFT Algorithm Works | Part 4 - Twiddle Factors
The beauty of the FFT algorithm is that it does the same thing over and over again. It treats every stage of the calculation in exactly the same way. However, this. “one-size-fits-all” approach, although elegant and simple, causes a problem. It misaligns samples and introduces phase distortions during each stage of the algorithm. To overcome this, we need Twiddle Factors, little phase correction factors that push things back into their correct positions before continuing onto the next stage.
A Matlab Function for FIR Half-Band Filter Design
FIR Half-band filters are not difficult to design. In an earlier post [1], I showed how to design them using the window method. Here, I provide a short Matlab function halfband_synth that uses the Parks-McClellan algorithm (Matlab function firpm [2]) to synthesize half-band filters. Compared to the window method, this method uses fewer taps to achieve a given performance.
Handling Spectral Inversion in Baseband Processing
Spectral inversion often sneaks in during RF and IF mixing chains and can break downstream demodulation. Eric Jacobsen shows that at baseband you can correct inversion with three trivial, equivalent operations: invert Q, swap I and Q, or invert I, and he explains the math and geometric intuition behind each. The fixes work in modulators or demodulators and tolerate arbitrary phase offsets.
Digital PLL's -- Part 2
Neil Robertson builds a Z-domain model of a second-order digital PLL with a proportional-plus-integral loop filter, then derives closed-form formulas for KL and KI from the desired loop natural frequency and damping. The post explains the s → (z - 1)/Ts approximation, shows how to form the closed-loop IIR CL(z) for step and frequency responses, and highlights when the linear Z-domain model falls short of nonlinear acquisition behavior.
5G NR QC-LDPC Encoding Algorithm
Lyons Zhang breaks down the 5G NR QC-LDPC encoding structure, emphasizing the circulant permutation matrices and why QC-LDPC suits simple hardware. The post defines the Q(P) and Q(-1) notation, summarizes BG1 and BG2 dimensions and selection rules, and shows how the parity-check matrix is partitioned for practical encoder implementations.
The Exponential Nature of the Complex Unit Circle
Euler's equation links exponential scaling and rotation by translating a distance along the unit-circle circumference into a complex value. Cedron Dawg develops an intuitive geometric view, using integer and fractional powers of i to show how points, roots of unity, and multiplication behave as additive moves along that circumference. The article also connects this picture to radians and the conventional Taylor-series proof for broader perspective.
Python scipy.signal IIR Filtering: An Example
Christopher Felton walks through using scipy.signal IIR filters to demodulate PWM signals, using spectrum and spectrogram analysis to show what works and what does not. He demonstrates using filtfilt to avoid phase delay, compares a single narrow IIR to a very high order FIR, and shows how staged IIR filtering and multirate ideas give much better attenuation. Includes an FPGA-ready MyHDL PWM model.
Back from Embedded World 2019 - Funny Stories and Live-Streaming Woes
Stephane Boucher tried live-streaming multiple talks from Embedded World 2019 and turned a chaotic experiment into a useful set of lessons for embedded engineers. Between broken tripods, flaky venue WiFi, tricky German SIM purchases, and audio nightmares, he learned practical fixes for reliable streams and better video quality. Read this if you want candid, tactical advice on streaming hardware, connectivity, and on-site troubleshooting.
Design IIR Filters Using Cascaded Biquads
High-order IIR filters are numerically sensitive, especially at low cutoff frequencies. This article shows how to implement a Butterworth lowpass as a cascade of second-order biquads, deriving the per-section coefficient formulas and giving a Matlab biquad_synth example. It explains computing denominator coefficients from pole pairs, using b = [1 2 1] with K = sum(a)/4 for unity DC gain, and highlights reduced quantization sensitivity.
Digital PLL's -- Part 1
A hands-on introduction to time-domain digital phase-locked loops, Neil Robertson builds a simple DPLL model in MATLAB and walks through the NCO, phase detector, and PI loop filter implementations. The post uses phase-in-cycles arithmetic to show how the phase accumulator, detector wrapping, and loop filter interact, and it contrasts linear steady-state behavior with the nonlinear acquisition seen when initial frequency error is large. Part 2 will cover frequency-domain tuning of the loop gains.
Polyphase Filters and Filterbanks
Kyle walks through practical polyphase filtering and analysis filterbanks, complete with Python code using numpy, scipy and matplotlib. The post shows how splitting an FIR into M polyphase legs gives identical, more efficient decimation while avoiding aliasing, and it flags the subtle reordering, zero padding and FFT versus IDFT ordering issues that trip many implementers. Includes runnable reference code and links for deeper theory.
Free DSP Books on the Internet
Finding reliable DSP textbooks online is hit-or-miss. Rick Lyons assembled a curated list of over forty legally downloadable signal processing books, organized by topic from theory and communications to audio, image processing, and implementation. The post points to vendor manuals, MATLAB and algorithm resources, and clear copyright guidance so engineers can grab useful references without breaking licensing rules.
Design IIR Bandpass Filters
Designing Butterworth IIR bandpass filters is easier than it looks when you start from a lowpass prototype. This post walks through the s-domain lowpass-to-bandpass transform, bilinear digital mapping, and the bp_synth.m Matlab implementation that produces scaled numerator and denominator coefficients. Practical pole-zero intuition and Matlab examples help you verify magnitude and group-delay behavior for real sampling rates and bandwidths.
Delay estimation by FFT
Markus Nentwig presents a practical FFT-based algorithm to estimate and correct integer and fractional sample delays between two signals, returning a scaled, aligned replica and delay estimate. The method combines coarse cross-correlation with a phase-slope linear regression on weighted spectra to achieve subsample timing accuracy. The article also discusses accuracy limits, phase-unwrapping pitfalls, and how to use the error-vector spectrum to reveal distortion in lab measurements.
Understanding and Implementing the Sliding DFT
The Sliding DFT delivers exact DFT results with per-sample frequency updates, making real-time spectral processing far more efficient than repeatedly running an FFT. Eric Jacobsen walks through the derivation, presents the simple recursive update, and covers practical concerns such as initialization and fixed-point stability. Engineers building low-latency, low-power systems will appreciate the algorithm's computational and latency advantages.
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.
Who else is going to Sensors Expo in San Jose? Looking for roommate(s)!
Stephane Boucher is heading to Sensors Expo in San Jose for the first time, and he is bringing cameras to capture demos and build a highlights video. He is also looking for roommates for a roomy Airbnb near the convention center, plus local tips for making the most of a free day in the Bay Area. If you are attending, there is also a registration discount code and a VIP pass giveaway in the mix.
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.
Embedded World 2018 - More Videos!
Two cinematic videos from Embedded World 2018 turn the show floor into slow-motion, stabilized footage using a Zhiyun Crane gimbal and a Sony a6300. One is a SEGGER booth highlights piece featuring Rolf Segger and Axel Wolf, the other is a roaming montage with appearances from Jacob Beningo, Micheal Barr, and Alan Hawse. Stephane asks viewers to enable audio and share feedback.
Embedded World 2018 - The Interviews
Stephane Boucher brought video gear to Embedded World 2018 and teamed up with Jacob Beningo to capture concise vendor interviews that focus on real product news. The videos showcase Percepio's new Tracealyzer with a drone demo, Intrinsic ID's method for creating device-unique IDs from manufacturing variations, and SEGGER's broader toolset including embOS now certified by TÜV SÜD. Watch for short demos and expert explanations.
Finally got a drone!
Stephane Boucher finally bought a DJI Phantom 4 and found it does more than boost his video production value, it’s also hugely fun to fly. He used the drone for an aerial shot at SEGGER’s anniversary and for a beach project where kids drew a turtle while a separate camera captured a side timelapse. The post highlights creative shot combinations and a reminder to fly where it is legal.
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.
Went 280km/h (174mph) in a Porsche Panamera in Germany!
A week at SEGGER’s headquarters in Germany turned into more than a video shoot, it became a look inside a company that clearly runs on passion, trust, and a lot of teamwork. Stephane Boucher also gets an unforgettable autobahn ride in a Porsche Panamera, hitting 280 km/h along the way. Between interviews, B-roll, and a 25th anniversary celebration, he comes away impressed by both the people and the pace.
Going back to Germany!
A conference conversation turned into a return trip to Germany for Stephane Boucher, this time to visit SEGGER’s headquarters in Dusseldorf and produce videos. The post shares how a chance introduction at ESC Boston led to the invitation, and it teases coverage from SEGGER’s 25th anniversary celebration. He also invites local tips and customer questions before the trip.
ESC Boston's Videos are Now Up
Stephane Boucher shares the videos he produced from ESC Boston, including a short highlight montage, a booth video for DLOGIC, and full talk clips from the conference. He also reflects on what he learned shooting on the show floor, especially the challenge of getting engineers on camera. It’s a quick behind-the-scenes look at technical event videography, with a preview of his next stop in Germany.
