Signal Generators¶

pyminidsp provides stateless signal generators for creating test signals. No audio input or microphone source is needed — just specify the parameters and get a NumPy array back.

Sine wave¶

The fundamental test signal — a pure tone at a single frequency:

\[x[n] = A \sin(2\pi f \, n / f_s)\]

import pyminidsp as md

signal = md.sine_wave(44100, amplitude=1.0, freq=440.0, sample_rate=44100.0)

# Verify: the FFT peak should align with the expected frequency bin
mag = md.magnitude_spectrum(signal)

Listen — 440 Hz, 2 seconds:

Impulse (Kronecker delta)¶

A single spike at a given position, zeros everywhere else. The unit impulse (amplitude 1.0 at position 0) is the identity element of convolution and has a perfectly flat magnitude spectrum.

imp = md.impulse(1024, amplitude=1.0, position=0)

# Flat spectrum — all bins have equal magnitude
mag = md.magnitude_spectrum(imp)

Listen — impulse train (4 clicks at 0.5 s intervals):

Chirp (swept sine)¶

Two varieties:

Linear chirp — frequency sweeps at a constant rate. The instantaneous frequency traces a straight diagonal in the spectrogram.

# 1-second sweep from 200 Hz to 4 kHz at 16 kHz sample rate
chirp = md.chirp_linear(16000, amplitude=1.0, f_start=200.0,
                         f_end=4000.0, sample_rate=16000.0)

Logarithmic chirp — exponential sweep, spending equal time per octave. Ideal for measuring systems on a log-frequency axis.

# Full audible range sweep: 20 Hz to 20 kHz
chirp = md.chirp_log(44100, amplitude=1.0, f_start=20.0,
                      f_end=20000.0, sample_rate=44100.0)

Square wave¶

Alternates between +amplitude and −amplitude. Its Fourier series contains only odd harmonics (1f, 3f, 5f, …) with amplitudes decaying as 1/k — a textbook demonstration of the Gibbs phenomenon.

sq = md.square_wave(4096, amplitude=1.0, freq=440.0, sample_rate=44100.0)

Sawtooth wave¶

Ramps linearly from −amplitude to +amplitude each period. Contains all integer harmonics (1f, 2f, 3f, …) decaying as 1/k — richer harmonic content than the square wave’s odd-only series.

saw = md.sawtooth_wave(4096, amplitude=1.0, freq=440.0, sample_rate=44100.0)

White noise¶

Gaussian white noise has equal power at all frequencies — its PSD is approximately flat. Samples follow N(0, σ²) via the Box-Muller transform. A fixed seed gives reproducible output.

noise = md.white_noise(4096, amplitude=1.0, seed=42)

# Same seed → same output
noise2 = md.white_noise(4096, amplitude=1.0, seed=42)
assert (noise == noise2).all()

Shepard tone¶

See Shepard Tone for a dedicated guide on this auditory illusion.