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A technical notebook about signals and machines

sinusoidal.space

Visual essays about how continuous phenomena become samples, spectra, tensors and computation—and what gets lost along the way.

signals → representations → models → efficient computation

Featured essays

The Fourier transform, made visible

Compose a signal, then inspect the magnitude and phase that describe it.

Transforms · Signals

Aliasing is everywhere

See why different continuous signals can become identical after sampling.

Sampling · Machine learning

Convolution: FIR filters → CNNs → fast computation

Follow one operation across filtering, learned kernels and frequency space.

Convolution · Models

Sinusoidal positional encodings, from first principles

Build a vector representation of position from paired periodic coordinates.

Representations · Machine learning

Building a GPU STFT pipeline

Map a time–frequency transform from equations to buffers and execution.

GPU computing · Performance

Open the lab

All experiments

Fourier composer

Build tones and inspect their discrete spectrum.

Aliasing explorer

Fold a source frequency around the Nyquist boundary.

Sliding convolution

Inspect each multiply–accumulate in a filter.

Position encoding matrix

Explore frequency bands across position and dimension.

What this is

Signal processing and machine learning are often taught in separate rooms. This notebook follows the representations that connect them: from physical variation to samples, from samples to useful coordinates, and from those coordinates to algorithms that must run on real hardware.