minidsp_generators.c File Reference

Signal generators: sine, white noise, impulse, chirps, square, sawtooth waves, and Shepard tone. More...

#include "minidsp.h"

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Functions
void	MD_sine_wave (double *output, unsigned N, double amplitude, double freq, double sample_rate)
	Generate a sine wave.
void	MD_white_noise (double *output, unsigned N, double amplitude, unsigned seed)
	Generate Gaussian white noise.
void	MD_impulse (double *output, unsigned N, double amplitude, unsigned position)
	Generate a discrete impulse (Kronecker delta).
void	MD_chirp_linear (double *output, unsigned N, double amplitude, double f_start, double f_end, double sample_rate)
	Generate a linear chirp (swept sine with linearly increasing frequency).
void	MD_chirp_log (double *output, unsigned N, double amplitude, double f_start, double f_end, double sample_rate)
	Generate a logarithmic chirp (swept sine with exponentially increasing frequency).
void	MD_square_wave (double *output, unsigned N, double amplitude, double freq, double sample_rate)
	Generate a square wave.
void	MD_sawtooth_wave (double *output, unsigned N, double amplitude, double freq, double sample_rate)
	Generate a sawtooth wave.
void	MD_shepard_tone (double *output, unsigned N, double amplitude, double base_freq, double sample_rate, double rate_octaves_per_sec, unsigned num_octaves)
	Generate a Shepard tone — the auditory illusion of endlessly rising or falling pitch.

Detailed Description

Signal generators: sine, white noise, impulse, chirps, square, sawtooth waves, and Shepard tone.

Author

Chuck Wooters woote.nosp@m.rs@h.nosp@m.ey.co.nosp@m.m

Copyright

2013 International Computer Science Institute

Definition in file minidsp_generators.c.

Function Documentation

MD_chirp_linear()

void MD_chirp_linear	(	double *	output,
		unsigned	N,
		double	amplitude,
		double	f_start,
		double	f_end,
		double	sample_rate
	)

Generate a linear chirp (swept sine with linearly increasing frequency).

The instantaneous frequency sweeps linearly from f_start to f_end over N samples:

f(t) = f_start + (f_end - f_start) * t / T

where T = (N-1) / sample_rate is the sweep duration. The output is:

output[i] = amplitude * sin(2*pi * (f_start*t + 0.5*chirp_rate*t^2))

A linear chirp is the standard test signal for spectrograms – its instantaneous frequency traces a straight diagonal line in the time-frequency plane.

Parameters

output	Output buffer of length N (caller-allocated).
N	Number of samples to generate. Must be > 0.
amplitude	Peak amplitude of the chirp (e.g. 1.0).
f_start	Starting frequency in Hz.
f_end	Ending frequency in Hz.
sample_rate	Sampling rate in Hz. Must be > 0.

double sig[16000];
// 1-second linear chirp from 200 Hz to 4000 Hz at 16 kHz sample rate
MD_chirp_linear(sig, 16000, 1.0, 200.0, 4000.0, 16000.0);

Definition at line 77 of file minidsp_generators.c.

MD_chirp_log()

void MD_chirp_log	(	double *	output,
		unsigned	N,
		double	amplitude,
		double	f_start,
		double	f_end,
		double	sample_rate
	)

Generate a logarithmic chirp (swept sine with exponentially increasing frequency).

The instantaneous frequency sweeps exponentially from f_start to f_end over N samples:

f(t) = f_start * (f_end / f_start)^(t / T)

where T = (N-1) / sample_rate is the sweep duration. The output is:

output[i] = amplitude * sin(2*pi * f_start * T * (r^(t/T) - 1) / ln(r))

where r = f_end / f_start.

A logarithmic chirp spends equal time per octave, making it ideal for measuring systems whose behaviour is best described on a log-frequency axis (e.g. audio equaliser response).

Parameters

output	Output buffer of length N (caller-allocated).
N	Number of samples to generate. Must be > 0.
amplitude	Peak amplitude of the chirp (e.g. 1.0).
f_start	Starting frequency in Hz. Must be > 0.
f_end	Ending frequency in Hz. Must be > 0 and != f_start.
sample_rate	Sampling rate in Hz. Must be > 0.

double sig[44100];
// 1-second log chirp from 20 Hz to 20 kHz at 44.1 kHz sample rate
MD_chirp_log(sig, 44100, 1.0, 20.0, 20000.0, 44100.0);

Definition at line 99 of file minidsp_generators.c.

MD_impulse()

void MD_impulse	(	double *	output,
		unsigned	N,
		double	amplitude,
		unsigned	position
	)

Generate a discrete impulse (Kronecker delta).

Fills the output buffer with zeros except at position, where the value is set to amplitude. A unit impulse (amplitude 1.0 at position 0) is the identity element of convolution and has a perfectly flat magnitude spectrum.

Common uses:

• Measure a system's impulse response by feeding it through a filter.
• Verify that MD_magnitude_spectrum() returns a flat spectrum.
• Create delayed spikes for testing convolution and delay estimation.

Parameters

output	Output buffer of length N (caller-allocated).
N	Number of samples to generate. Must be > 0.
amplitude	Value of the impulse spike (e.g. 1.0 for unit impulse).
position	Sample index of the spike (0-based). Must be < N.

double sig[1024];
MD_impulse(sig, 1024, 1.0, 0);  // unit impulse at sample 0

Definition at line 68 of file minidsp_generators.c.

MD_sawtooth_wave()

void MD_sawtooth_wave	(	double *	output,
		unsigned	N,
		double	amplitude,
		double	freq,
		double	sample_rate
	)

Generate a sawtooth wave.

Fills the output buffer with a sawtooth wave that ramps linearly from −amplitude to +amplitude over each period:

\[ x[n] = A \left(\frac{\phi}{\pi} - 1\right) \]

where \(\phi = 2\pi f n / f_s \pmod{2\pi}\).

A sawtooth wave contains all integer harmonics (1f, 2f, 3f, …) whose amplitudes decay as 1/k — useful for demonstrating richer harmonic content compared to the square wave's odd-only series.

Parameters

output	Output buffer of length N (caller-allocated).
N	Number of samples to generate. Must be > 0.
amplitude	Peak amplitude of the sawtooth wave (e.g. 1.0).
freq	Frequency in Hz.
sample_rate	Sampling rate in Hz. Must be > 0.

double sig[1024];
MD_sawtooth_wave(sig, 1024, 1.0, 440.0, 44100.0);

Definition at line 145 of file minidsp_generators.c.

MD_shepard_tone()

void MD_shepard_tone	(	double *	output,
		unsigned	N,
		double	amplitude,
		double	base_freq,
		double	sample_rate,
		double	rate_octaves_per_sec,
		unsigned	num_octaves
	)

Generate a Shepard tone — the auditory illusion of endlessly rising or falling pitch.

A Shepard tone superimposes several sine waves spaced one octave apart. Each tone glides continuously upward (or downward) in pitch while a Gaussian spectral envelope — fixed in log-frequency space — fades tones in at one end and out at the other. The result is a sound that seems to rise (or fall) forever without ever actually leaving its frequency range.

Signal model. At time \(t = n / f_s\) the output sample is:

\[ x[n] \;=\; A_\mathrm{norm}\!\sum_k \underbrace{ \exp\!\Bigl(-\frac{d_k(t)^2}{2\sigma^2}\Bigr) }_{\text{Gaussian envelope}} \;\sin\!\bigl(\varphi_k(n)\bigr) \]

where the octave distance from the Gaussian centre is

\[ d_k(t) = k - c + R\,t, \qquad c = \frac{L-1}{2}, \qquad \sigma = \frac{L}{4} \]

and the instantaneous frequency of layer \(k\) is \(f_k(t) = f_\text{base}\cdot 2^{d_k(t)}\). The phase \(\varphi_k\) is accumulated sample-by-sample from \(f_k\) so that each tone glides smoothly. \(R\) is rate_octaves_per_sec and \(L\) is num_octaves. \(A_\mathrm{norm}\) scales the peak to amplitude.

The sum ranges over all integer indices \(k\) for which \(|d_k(t)|\) is within \(5\sigma\) at some point during the signal, ensuring enough layers are present to sustain the illusion for the full duration.

Parameters

output	Output buffer of length N (caller-allocated).
N	Number of samples to generate. Must be > 0.
amplitude	Peak amplitude of the output signal.
base_freq	Centre frequency of the Gaussian envelope in Hz. Typical values: 200–600 Hz.
sample_rate	Sampling rate in Hz. Must be > 0.
rate_octaves_per_sec	Glissando rate in octaves per second. Positive = rising, negative = falling, 0 = static chord.
num_octaves	Number of audible octave layers (width of the Gaussian bell). Typical values: 6–10. Must be > 0.

// 5 seconds of endlessly rising Shepard tone at 44.1 kHz
unsigned N = 5 * 44100;
double *sig = malloc(N * sizeof(double));
MD_shepard_tone(sig, N, 0.8, 440.0, 44100.0, 0.5, 8);
// sig[] now sounds like it rises forever
free(sig);

Definition at line 159 of file minidsp_generators.c.

MD_sine_wave()

void MD_sine_wave	(	double *	output,
		unsigned	N,
		double	amplitude,
		double	freq,
		double	sample_rate
	)

Generate a sine wave.

Fills output[i] = amplitude * sin(2π * freq * i / sample_rate) for i in [0, N).

This is the simplest test signal in DSP — a pure tone at a single frequency. Use it to verify filter responses, check FFT bin alignment, or provide a clean input for any processing chain.

Parameters

output	Output buffer of length N (caller-allocated).
N	Number of samples to generate. Must be > 0.
amplitude	Peak amplitude of the sine wave (e.g. 1.0).
freq	Frequency in Hz.
sample_rate	Sampling rate in Hz. Must be > 0.

double sig[1024];
MD_sine_wave(sig, 1024, 1.0, 440.0, 44100.0);  // 440 Hz A4 tone

Definition at line 15 of file minidsp_generators.c.

MD_square_wave()

void MD_square_wave	(	double *	output,
		unsigned	N,
		double	amplitude,
		double	freq,
		double	sample_rate
	)

Generate a square wave.

Fills the output buffer with a bipolar square wave that alternates between +amplitude and −amplitude at the given frequency:

\[ x[n] = \begin{cases} +A & 0 < \phi < \pi \\ -A & \pi < \phi < 2\pi \\ 0 & \phi = 0 \text{ or } \phi = \pi \end{cases} \]

where \(\phi = 2\pi f n / f_s \pmod{2\pi}\).

A square wave contains only odd harmonics (1f, 3f, 5f, …) whose amplitudes decay as 1/k — a classic demonstration of the Fourier series and the Gibbs phenomenon.

Parameters

output	Output buffer of length N (caller-allocated).
N	Number of samples to generate. Must be > 0.
amplitude	Peak amplitude of the square wave (e.g. 1.0).
freq	Frequency in Hz.
sample_rate	Sampling rate in Hz. Must be > 0.

double sig[1024];
MD_square_wave(sig, 1024, 1.0, 440.0, 44100.0);

Definition at line 126 of file minidsp_generators.c.

MD_white_noise()

void MD_white_noise	(	double *	output,
		unsigned	N,
		double	amplitude,
		unsigned	seed
	)

Generate Gaussian white noise.

Fills output with normally distributed random samples (mean 0, standard deviation amplitude) using the Box-Muller transform. White noise has equal energy at all frequencies – its power spectral density is approximately flat.

Use white noise to test filters, measure impulse responses, or as an additive noise source for SNR experiments.

Parameters

output	Output buffer of length N (caller-allocated).
N	Number of samples to generate. Must be > 0.
amplitude	Standard deviation of the noise (e.g. 1.0).
seed	Seed for the random number generator. Using the same seed produces the same output sequence, which is useful for reproducible tests.

double noise[4096];
MD_white_noise(noise, 4096, 1.0, 42);  // reproducible Gaussian noise

Definition at line 26 of file minidsp_generators.c.