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.
Harmonic Notch Filter
A practical, DSP-friendly recipe for scrubbing 60 Hz power-line hum and its harmonics from noisy ECG and EEG recordings is presented, using IIR notch filters built from second-order all-pass sections. The post derives how to set all-pass phase to place notches and compute biquad coefficients by solving a simple 2x2 system, then shows C code and precomputed coefficients for cascading the first eight odd harmonics at a 2 kHz sample rate. Engineers get a compact, editable implementation with explicit control over notch bandwidth.
A Useful Source of Signal Processing Information
I just discovered a useful web-based source of signal processing information that was new to me. I thought I'd share what I learned with the subscribers here on DSPRelated.com.
The Home page of the web site that I found doesn't look at all like it would be useful to us DSP fanatics. But if you enter some signal processing topic of interest, say, "FM demodulation" (without the quotation marks) into the 'Search' box at the top of the web page
and click the red 'SEARCH...
3 Good News
Stephane Boucher reports three quick wins for the EmbeddedRelated community: two sponsors have seeded a $1,000 rewards pool, the site now serves all pages over HTTPS, and the new forums have their first active discussions. If you want a share of the sponsor-funded rewards, jump into the forums and check the Vendors Directory for opportunities. Stay tuned for more updates.
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.
The New Forum is LIVE!
After months of hard word, I am very excited to introduce to you the new forum interface.
Here are the key features:
1- Easily add images to a post by drag & dropping the images in the editor
2- Easily attach files to a post by drag & dropping the files in the editor
3- Add latex equations to a post and they will be rendered with Mathjax (tutorial)
4- Add a code snippet and surround the code with
Autocorrelation and the case of the missing fundamental
A short hands-on exploration shows why we perceive the fundamental pitch even when it's absent from the spectrum. Using saxophone recordings, high-pass filtering, and autocorrelation plots, the post demonstrates that the highest ACF peak often predicts perceived pitch rather than the strongest spectral line. The experiments also show that removing high harmonics eliminates the effect, and that autocorrelation is a useful but incomplete model of pitch perception.
Generating pink noise
This post implements a stochastic Voss-McCartney pink-noise generator in Python, tackling why incremental per-sample algorithms do not map well to NumPy batch operations. It presents a practical NumPy/Pandas approach that uses geometric-distributed update events and pandas' fillna for column-wise zero-order hold to make batch generation efficient. The generated noise shows a power-spectrum slope near -1, matching expected 1/f behavior.
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...
Dealing With Fixed Point Fractions
Fixed-point fractional math is easy to botch, and this post lays out pragmatic ways to avoid those mistakes. It clarifies the difference between integer and fractional overflow, shows how Q notation helps track binary-point scaling, and explains why multiplies add sign bits that may require shifting. Read for concrete FPGA strategies: keeping bit growth, selective shifts, or aggressive normalization, plus testing tips.
Exponential Smoothing with a Wrinkle
Cedron Dawg shows how pairing forward and backward exponential smoothing produces exact, frequency-dependent dampening for sinusoids while canceling time-domain lag. The average of the two passes scales the tone by a closed-form factor, and their difference acts like a first-derivative with a quarter-cycle phase shift. The post derives the analytic dampening formulas, compares them to the derivative, and includes a Python demo for DFT preprocessing.
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.
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.
Off-Topic: A Fluidic Model of the Universe
Cedron Dawg develops a Newtonian, fluidic model where space is a compressible "fluff" and particle motion is governed by a simple refractive steering equation. He shows how rho = ln n links index, permittivity and permeability to a gravity-like potential, derives a massive-particle steering law, and works through orbit and disk solutions that produce MOND-like effects while conflicting with General Relativity. The paper highlights concrete formulas and numerics to test the hypothesis.
Make Hardware Great Again
US weakness in 5G and the coming AI race stems from a deeper problem, hardware decline and lack of CPU innovation. Jeff Brower argues that the software-only narrative has hollowed out semiconductor leadership, leaving only a few chipmakers and blocking vital R&D. He calls for targeted government action, funding for neural-net chips, and an industrial Hardhattan Project to rebuild CPU and hardware capabilities.
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.
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.
FIR sideways (interpolator polyphase decomposition)
Markus Nentwig presents a compact way to implement a symmetric FIR interpolator by rethinking the usual tapped delay line. The 1:3 polyphase example uses separate delay lines per coefficient to skip multiplies on known zeros and exploit symmetry, cutting multiplications substantially; a Matlab/Octave demo and notes on ASIC-friendly implementation are included to help evaluate real-world cost tradeoffs.
Do Multirate Systems Have Transfer Functions?
Multirate systems can fool you into thinking standard z-domain analysis always applies. Rick Lyons shows why CIC decimation and Hogenauer implementations do not have a single z-domain transfer function from the input to the downsampled output, because downsampling breaks the one-to-one frequency mapping of LTI systems. Use the cascaded-subfilter H(z) up to the decimation point, then explicitly account for aliasing when predicting the decimated spectrum.
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.
Feedback Controllers - Making Hardware with Firmware. Part 3. Sampled Data Aspects
This article digs into practical sampled-data issues you must address when building feedback controllers for circuit emulation. It highlights a common MATLAB versus Simulink discrepancy caused by DAC holding, explains why FOH (ramp-invariant) c2d conversion matters, and surveys latency, bit depth, filter and precision trade-offs. It also lists candidate ADCs, DACs and FPGAs used in a real evaluation platform to guide hardware choices.
Modeling a Continuous-Time System with Matlab
Neil Robertson demonstrates a practical workflow for converting a continuous-time transfer function H(s) into an exact discrete-time H(z) using Matlab's impinvar. He walks through a 3rd-order Butterworth example, shows how to match impulse and step responses, and compares frequency response and group delay so engineers can see where the discrete model stays accurate and when sampling-rate limits cause departure.
Feedback Controllers - Making Hardware with Firmware. Part 4. Engineering of Evaluation Hardware
Following on from the previous abstract descriptions of an arbitrary circuit emulation application for low-latency feedback controllers, we now come to some aspects in the hardware engineering of an evaluation design from concept to first power-up. In due course a complete specification along with application examples will be maintained on the project website.- Part 1: Introduction
- Part 2:...
The Little Fruit Market: The Beginning of the Digital Explosion
A small fruit market in Mountain View became an unlikely cradle for the modern electronics era. Rick Lyons recounts how William Shockley’s lab at 391 San Antonio prompted the Traitorous Eight to form Fairchild, seeding Silicon Valley and spawning an industry whose transistor production quickly dwarfed grains of rice. The post ties that history to the everyday ubiquity of semiconductor devices.
Exponential Smoothing with a Wrinkle
Cedron Dawg shows how pairing forward and backward exponential smoothing produces exact, frequency-dependent dampening for sinusoids while canceling time-domain lag. The average of the two passes scales the tone by a closed-form factor, and their difference acts like a first-derivative with a quarter-cycle phase shift. The post derives the analytic dampening formulas, compares them to the derivative, and includes a Python demo for DFT preprocessing.
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.
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.
A New Contender in the Quadrature Oscillator Race
Rick Lyons highlights a compact quadrature oscillator introduced by A. David Levine and Martin Vicanek, offering guaranteed stability, accurate low-frequency tuning, and modest computational cost. The post walks through the simple u, v, w recurrences used for software implementation. Appendices provide transfer functions and an algebraic stability proof for engineers who want formal verification before deployment.
Premium Forum?
Stephane Boucher proposes a paid "premium" forum for DSPRelated that would redistribute membership fees to the community s top contributors via voting. The plan frames the $20/year fee as an incentive mechanism, not a revenue stream, with monthly payouts to the most appreciated posters. Boucher invites reader feedback to decide whether to implement the idea or pursue alternatives.
Filtering Noise: The Basics (Part 1)
How do you pull signals out of random noise? This post builds intuition from first principles for discrete-time white Gaussian noise and shows how simple linear FIR filtering (averaging) reduces noise. You’ll get derivations for the output mean, variance and autocorrelation, learn why the uniform moving-average minimizes noise under a unity-DC constraint, and why its sinc spectrum can be problematic. Part 1 of a short series.
