music.amplitude_modulation

music.amplitude_modulation(carrier_freq=200.0, modulation_freq=10.0, modulation_depth=1.0, duration=2.0, waveform_table=array([0., 0.0003835, 0.00076699, ..., -0.00115049, -0.00076699, -0.0003835], shape=(16384,)), modulation_waveform_table=array([0., 0.0003835, 0.00076699, ..., -0.00115049, -0.00076699, -0.0003835], shape=(16384,)), number_of_samples=0, sample_rate=44100)[source]

Sinusoidally modulate a carrier: sstim-v:techAmplitudeModulation.

A carrier tone whose amplitude is sinusoidally modulated at a target rate; the canonical stimulus for evoking auditory steady-state responses at the modulation frequency [2].

Parameters:
carrier_freqscalar

The frequency of the carrier, in Hertz.

modulation_freqscalar

The rate at which its amplitude is modulated, in Hertz.

modulation_depthscalar

How deep the modulation goes, in [0, 1]. At 1 the envelope reaches zero once per modulation period; at 0 the carrier is left alone.

durationscalar

The duration in seconds.

waveform_tablearray_like

The table the carrier is looked up in.

modulation_waveform_tablearray_like

The table the modulator is looked up in, so the modulation need not be sinusoidal.

number_of_samplesinteger

The number of samples of the sound, taken instead of duration when it is given.

sample_rateinteger

The sampling frequency in Hertz.

Returns:
ndarray

A mono sequence of PCM samples.

Raises:
ValueError

If modulation_depth is outside [0, 1], where the envelope would go negative and invert the carrier’s phase rather than deepening the modulation.

Parameters:

  • carrier_freq (float)

  • modulation_freq (float)

  • modulation_depth (float)

  • duration (float)

  • waveform_table (ArrayLike)

  • modulation_waveform_table (ArrayLike)

  • number_of_samples (int)

  • sample_rate (int)

Return type:

NDArray[float64]

See also

monaural_beats

an equivalent envelope arising from two tones rather than imposed on one.

Notes

The modulation is physically present, and it is the modulation rate rather than the carrier that sets the frequency of the evoked response, which is the whole point of the stimulus.

References

[1]

Fabbri, Renato, et al. “Musical elements in the discrete-time representation of sound.” arXiv preprint arXiv:abs/1412.6853 (2017)

[2]

SSTIM, techAmplitudeModulation. https://w3id.org/sstim/vocab#techAmplitudeModulation

Examples

>>> stimulus = amplitude_modulation(carrier_freq=200,
...                                 modulation_freq=40)
>>> stimulus.ndim
1