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.
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
I am working on the 11th and probably final chapter of Think DSP, which follows material my colleague Siddhartan Govindasamy developed for a class at Olin College. He introduces amplitude modulation as a clever way to sneak up on the Nyquist–Shannon sampling theorem.
Most of the code for the chapter is done: you can check it out in this IPython notebook. I haven't written the text yet, but I'll outline it here, and paste in the key figures.
Convolution...
Differentiating and integrating discrete signals
Think DSP's new chapter digs into discrete differentiation and integration, using first differences, convolution, and FFTs to compare time and frequency domain views. The author reproduces diff via convolution then explores cumsum as its inverse and runs into two puzzling mismatches: noisy FFT amplitude ratios for nonperiodic data, and a time-domain convolution that does not reproduce cumsum for a sawtooth despite matching frequency responses. The post includes IPython notebooks and invites troubleshooting.
Bayes meets Fourier
Joseph Fourier never met Thomas Bayes—Fourier was born in 1768, seven years after Bayes died. But recently I have been exploring connections between the Bayes filter and the Fourier transform.
By "Bayes filter", I don't mean spam filtering using a Bayesian classifier, but rather recursive Bayesian estimation, which is used in robotics and other domains to estimate the state of a system that evolves over time, for example, the position of a moving robot. My interest in...
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
I am working on the 11th and probably final chapter of Think DSP, which follows material my colleague Siddhartan Govindasamy developed for a class at Olin College. He introduces amplitude modulation as a clever way to sneak up on the Nyquist–Shannon sampling theorem.
Most of the code for the chapter is done: you can check it out in this IPython notebook. I haven't written the text yet, but I'll outline it here, and paste in the key figures.
Convolution...
Differentiating and integrating discrete signals
Think DSP's new chapter digs into discrete differentiation and integration, using first differences, convolution, and FFTs to compare time and frequency domain views. The author reproduces diff via convolution then explores cumsum as its inverse and runs into two puzzling mismatches: noisy FFT amplitude ratios for nonperiodic data, and a time-domain convolution that does not reproduce cumsum for a sawtooth despite matching frequency responses. The post includes IPython notebooks and invites troubleshooting.
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.
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.
Bayes meets Fourier
Joseph Fourier never met Thomas Bayes—Fourier was born in 1768, seven years after Bayes died. But recently I have been exploring connections between the Bayes filter and the Fourier transform.
By "Bayes filter", I don't mean spam filtering using a Bayesian classifier, but rather recursive Bayesian estimation, which is used in robotics and other domains to estimate the state of a system that evolves over time, for example, the position of a moving robot. My interest in...
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
I am working on the 11th and probably final chapter of Think DSP, which follows material my colleague Siddhartan Govindasamy developed for a class at Olin College. He introduces amplitude modulation as a clever way to sneak up on the Nyquist–Shannon sampling theorem.
Most of the code for the chapter is done: you can check it out in this IPython notebook. I haven't written the text yet, but I'll outline it here, and paste in the key figures.
Convolution...
Differentiating and integrating discrete signals
Think DSP's new chapter digs into discrete differentiation and integration, using first differences, convolution, and FFTs to compare time and frequency domain views. The author reproduces diff via convolution then explores cumsum as its inverse and runs into two puzzling mismatches: noisy FFT amplitude ratios for nonperiodic data, and a time-domain convolution that does not reproduce cumsum for a sawtooth despite matching frequency responses. The post includes IPython notebooks and invites troubleshooting.
Bayes meets Fourier
Joseph Fourier never met Thomas Bayes—Fourier was born in 1768, seven years after Bayes died. But recently I have been exploring connections between the Bayes filter and the Fourier transform.
By "Bayes filter", I don't mean spam filtering using a Bayesian classifier, but rather recursive Bayesian estimation, which is used in robotics and other domains to estimate the state of a system that evolves over time, for example, the position of a moving robot. My interest in...
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.
