How to Find a Fast Floating-Point atan2 Approximation
This post shows how a compact, fast atan2 can be built from a Remez-derived arctangent approximation and a matching 3rd-order polynomial. It walks through using Boost's remez_minimax to recover coefficients 0.97239411 and -0.19194795, integrating the polynomial into an atan2 with quadrant reduction, and applying branch reduction, bit tricks, and SSE2 SIMD to cut runtime while keeping max error under about 0.005 radians.
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.
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.
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.
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.
Amplitude modulation and the sampling theorem
Amplitude modulation turns out to be a neat way to build intuition for the Nyquist-Shannon sampling theorem. In this draft chapter from Think DSP, the author shows how multiplying by a carrier shifts spectra, why sampling creates repeated copies in frequency, and how low-pass filtering can recover the original signal when those copies do not overlap.
Multilayer Perceptrons and Event Classification with data from CODEC using Scilab and Weka
For my first blog, I thought I would introduce the reader to Scilab [1] and Weka [2]. In order to illustrate how they work, I will put together a script in Scilab that will sample using the microphone and CODEC on your PC and save the waveform as a CSV file.
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.
Beat Notes: An Interesting Observation
Rick Lyons overturns a common intuition about beat notes, showing that adding two nearby audio tones yields an average-frequency tone whose amplitude fluctuates, rather than a separate low-frequency sinusoid. He contrasts multiplication and summation of sines, provides simple trigonometric insight, and includes Matlab audio demos to explain why aircraft engine "whump" sounds are amplitude fluctuations of the average engine frequency.
Amplitude modulation and the sampling theorem
Amplitude modulation turns out to be a neat way to build intuition for the Nyquist-Shannon sampling theorem. In this draft chapter from Think DSP, the author shows how multiplying by a carrier shifts spectra, why sampling creates repeated copies in frequency, and how low-pass filtering can recover the original signal when those copies do not overlap.
Beat Notes: An Interesting Observation
Rick Lyons overturns a common intuition about beat notes, showing that adding two nearby audio tones yields an average-frequency tone whose amplitude fluctuates, rather than a separate low-frequency sinusoid. He contrasts multiplication and summation of sines, provides simple trigonometric insight, and includes Matlab audio demos to explain why aircraft engine "whump" sounds are amplitude fluctuations of the average engine frequency.
The Phase Vocoder Transform
Treating the phase vocoder as a continuous transform, this post frames PV(x,α,β) as a bijection on signal space and derives the domain constraints needed for an inverse mapping. It uses geometric intuition and group-theory analogies to explain negative and zero scalings, then brings the idea back to DSP to show how aliasing and phase artifacts appear. The Laroche and Dolson consistency measure D_M plus MATLAB experiments are used to compare classic and identity phase-locking reconstructions.
Overview of my Articles
Cedron presents a guided tour of his DSPRelated articles that teach the discrete Fourier transform through derivations, numerical examples, and sample code. The collection centers on novel "bin value" formulas and exact frequency estimators for complex and real tones, with methods for phase and amplitude recovery and iterative multitone resolution. The overview also points to a zeroing-sine window family and an integer pseudo-differentiator for efficient peak and zero-crossing detection.
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.
In Search of The Fourth Wave
While working on Think DSP the presenter ran into a curious spectral pattern: sawtooth waves have all harmonics with amplitudes that scale like 1/f, square waves keep only odd harmonics with 1/f, and triangle waves keep odd harmonics with 1/f^2. That observation motivates a simple question: is there a basic waveform that has all integer harmonics but a 1/f^2 rolloff? The talk walks through four solution approaches, a fifth idea from the audience, and links to a runnable Colab notebook.
Exploring Human Hearing Range
Audacity makes it simple to explore the limits of human hearing by generating and inspecting single-tone audio. This post walks through creating a 9 kHz sine tone, noticing the default 44,100 Hz sample rate, and verifying the result with Audacity's Plot Spectrum tool. Follow the steps and use low playback volume to safely try higher or lower test frequencies yourself.
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.
A Markov View of the Phase Vocoder Part 2
This post builds a Markov-chain transition graph to guide phase vocoder time-frequency decisions, using spectral correlation data from a Bach violin sonata. It shows how FFT size and the time-stretch factor alpha change bin-to-bin correlations, proposes an inverse-square plus log-boundary probability model for transitions, and demonstrates practical limits and implementation choices with accompanying MATLAB code.
Components in Audio recognition - Part 1
This post introduces the core components of an audio recognition system, framed against how the human auditory system naturally familiarizes and retrieves tunes. Prabindh Sundareson outlines the three building blocks: an archive store, an analysis and fingerprinting engine that groups tracks, and a front-end that accepts queries and places samples into groups. He previews upcoming posts that will dig into implementations and tradeoffs.
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.
Multilayer Perceptrons and Event Classification with data from CODEC using Scilab and Weka
For my first blog, I thought I would introduce the reader to Scilab [1] and Weka [2]. In order to illustrate how they work, I will put together a script in Scilab that will sample using the microphone and CODEC on your PC and save the waveform as a CSV file.
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.
Overview of my Articles
Cedron presents a guided tour of his DSPRelated articles that teach the discrete Fourier transform through derivations, numerical examples, and sample code. The collection centers on novel "bin value" formulas and exact frequency estimators for complex and real tones, with methods for phase and amplitude recovery and iterative multitone resolution. The overview also points to a zeroing-sine window family and an integer pseudo-differentiator for efficient peak and zero-crossing detection.
Fitting Filters to Measured Amplitude Response Data Using invfreqz in Matlab
This post is a redirect notice for a code snippet now hosted elsewhere. If you were looking for the invfreqz example on fitting a filter to measured amplitude response data, this page simply points you to the new location and asks you to update your bookmark.
The Phase Vocoder Transform
Treating the phase vocoder as a continuous transform, this post frames PV(x,α,β) as a bijection on signal space and derives the domain constraints needed for an inverse mapping. It uses geometric intuition and group-theory analogies to explain negative and zero scalings, then brings the idea back to DSP to show how aliasing and phase artifacts appear. The Laroche and Dolson consistency measure D_M plus MATLAB experiments are used to compare classic and identity phase-locking reconstructions.
In Search of The Fourth Wave
While working on Think DSP the presenter ran into a curious spectral pattern: sawtooth waves have all harmonics with amplitudes that scale like 1/f, square waves keep only odd harmonics with 1/f, and triangle waves keep odd harmonics with 1/f^2. That observation motivates a simple question: is there a basic waveform that has all integer harmonics but a 1/f^2 rolloff? The talk walks through four solution approaches, a fifth idea from the audience, and links to a runnable Colab notebook.
Through the tube...
Markus Nentwig explores whether RF power amplifier modeling tricks work for audio tube preamps by modeling a 12AX7 preamp in Matlab. He records input and output with a two-channel reference, fits a simple Wiener-type model, and compares the modeled output to the real tube sound. The model explains over 99 percent of output power and leaves only small residual distortion to investigate further.
Exploring Human Hearing Range
Audacity makes it simple to explore the limits of human hearing by generating and inspecting single-tone audio. This post walks through creating a 9 kHz sine tone, noticing the default 44,100 Hz sample rate, and verifying the result with Audacity's Plot Spectrum tool. Follow the steps and use low playback volume to safely try higher or lower test frequencies yourself.
Digging into an Audio Signal and the DSP Process Pipeline
Zooming into an audio waveform can be misleading if you rely on only one view. This post compares Audacity with a simple C++ WAV reader and shows how the same samples can look like zero in a GUI, while the raw data reveals a small nonzero value. It is a practical reminder that multiple tools help you inspect and verify signal data more accurately.
