AudioGenerator

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`AudioGenerator`

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AudioGenerator[model]

generates one second of audio of a given model.

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AudioGenerator[model,t]

generates t seconds of audio.

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AudioGenerator[model,t,"type"]

generates audio samples of the specified "type".

Details and Options

AudioGenerator can generate different types of audio, including oscillators or noises.
Possible settings for model include:

	f	sample an arbitrary function f of time (in seconds)
	proc	generate samples from a random process proc
	tseries	generate samples from a TimeSeries tseries
	"model"	generate sample from a named function "model"

Silence:
"Silence" silence (zero) signal
Oscillators:

		{"Sin",freq,phase}	sine wave
		{"Triangle",freq,phase}	triangle wave
		{"Sawtooth",freq,phase}	sawtooth wave
		{"Square",freq,phase}	square wave
		{"Pulse",freq,phase,width}	rectangular wave using the duty cycle width
		{"Impulse",freq,phase}	impulse signal

By default, , , and are used.
The parameters freq, phase, and width can be a scalar value, a Quantity, an Audio object, a TimeSeries, or a pure function.
Noise:

		"White"	constant power spectral density
		"Pink"	power spectral density that follows
		"Brown"	power spectral density that follows
		"Blue"	power spectral density that follows
		{"Color",α}	power spectral density that follows with
		{"White",dist}	random noise with values sampled from dist
		"PeriodicRandomNoise"	sum of sinusoidal components with constant amplitude and random phase

Other:
AudioGenerator generates an audio object of "Real32" type. See the reference page for Audio for possible settings of "type".
AudioGenerator has the same options as Audio.

List of all options

Examples

open allclose all

Basic Examples (3)Summary of the most common use cases

Generate one second of sinusoidal audio:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-nryizk

Out[1]=1

Generate a signal from an arbitrary function:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-gevum

Out[1]=1

Generate two seconds of white noise:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-h34sdn

Out[1]=1

Scope (17)Survey of the scope of standard use cases

Basic Uses (2)

By default, 1 second of audio is generated:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-p7idou

Out[1]=1

Specify the duration:

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-oubtgl

Out[2]=2

Specify the duration as a time quantity:

In[3]:=3

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https://wolfram.com/xid/0d6g1v2jsu-zp1pw1

Out[3]=3

Specify the number of samples to generate:

In[4]:=4

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https://wolfram.com/xid/0d6g1v2jsu-pffqs5

Out[4]=4

By default, the generated audio is of "Real32" type:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-ugemm7

Out[1]=1

Specify a different data type:

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-9f755c

Out[2]=2

Model Specifications (15)

Oscillators (5)

Sinusoidal oscillator at 2000 Hz:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-bvty2t

Out[1]=1

Control the frequency of the sine wave with a function:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-60jwfy

Out[1]=1

Visualize the spectrogram:

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-mqt0d2

Out[2]=2

Control the frequency of the sine wave with another Audio object:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-0uk5q5

Out[1]=1

Visualize a spectrogram of the generated audio:

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-dql5y3

Out[2]=2

Control the frequency of the sine wave with a TimeSeries:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-xp8x8h

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-i0e3ks

Out[2]=2

Generate different oscillators:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-viyw23

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-sa9zor

Out[2]=2

Noise Generators (5)

Generate white noise:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-ldepvf

Out[1]=1

The values for the white noise can be sampled from a distribution:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-urq4x4

Out[1]=1

Generate different kinds of noises:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-kcrc5a

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-5bo60w

Out[2]=2

The spectra of pink, brown, and blue noises follow a distribution of f^-α, with α equal to 1, 2, and , respectively:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-2r2cwe

Out[1]=1

The spectrum of "PeriodicRandomNoise" is perfectly flat:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-7hot2x

Out[1]=1

Using Functions (1)

AudioGenerator supports functions of time:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-ogcpv9

Out[2]=2

Using Processes (2)

Generate audio from a noise process:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-45vg9v

Out[1]=1

Use an audio object generated from a random process to control the amplitude of a sinusoid:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-hithn1

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-e6p01c

Out[2]=2

Using TimeSeries (2)

Generate an audio object from a TimeSeries:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-9ghcqw

Out[1]=1

Generate an audio object from an irregular TimeSeries:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-b2ljxz

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-hbczrn

Out[2]=2

Options (1)Common values & functionality for each option

SampleRate (1)

By default, SampleRate->44100 is used:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-gde5vh

Out[1]=1

Specify a different sample rate:

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-l24l6a

Out[2]=2

Applications (8)Sample problems that can be solved with this function

Noise Applications (2)

Add noise to an audio object:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-7bnfk8

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-kqio3b

Out[2]=2

Use "PeriodicRandomNoise" to test the frequency response of a linear system:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-0aw60o

Out[1]=1

Audio Generation from Temporal Data (2)

Compare the stock price trends of two companies:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-qqo0jb

Resample and smooth the data:

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-u8x038

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0d6g1v2jsu-1yc4jk

Generate audio controlled by the two time series:

In[4]:=4

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https://wolfram.com/xid/0d6g1v2jsu-0yjigp

Out[4]=4

Use a list of TimeSeries to control the amplitudes of a list of harmonic sine waves:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-bpn3wn

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-c6lkp8

In[3]:=3

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https://wolfram.com/xid/0d6g1v2jsu-qmshp4

In[4]:=4

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https://wolfram.com/xid/0d6g1v2jsu-f34n0e

Out[4]=4

In[5]:=5

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https://wolfram.com/xid/0d6g1v2jsu-odbtli

Out[5]=5

Multi-Frequency Generation (3)

Generate a series of DTMF tones to simulate the dialing of a phone number:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-v2ke8y

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-0hrmdb

In[3]:=3

✖

https://wolfram.com/xid/0d6g1v2jsu-zu5cxk

In[4]:=4

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https://wolfram.com/xid/0d6g1v2jsu-lbftvg

Out[4]=4

Create a numeric keypad:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-mqpjw2

Out[1]=1

Create an auditory illusion:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-9jbfwp

Generate ramps to control frequencies and amplitudes of the oscillators:

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-jihk8

Out[2]=2

Create frequencies that will control the oscillators. The frequencies are exactly one octave apart from each other and increase exponentially, so that pitch increases linearly:

In[3]:=3

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https://wolfram.com/xid/0d6g1v2jsu-gg073k

Out[3]=3

Create amplitudes that will control the oscillators. Amplitudes go to 0 when the frequencies drop to the minimum value:

In[4]:=4

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https://wolfram.com/xid/0d6g1v2jsu-qhlvy3

Out[4]=4

Show the relation between frequency and amplitude of one oscillator:

In[5]:=5

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https://wolfram.com/xid/0d6g1v2jsu-svowlw

Out[5]=5

Combine a bank of oscillators using the created frequencies and amplitudes:

In[6]:=6

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https://wolfram.com/xid/0d6g1v2jsu-7w44uo

Out[6]=6

In[7]:=7

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https://wolfram.com/xid/0d6g1v2jsu-c4b5z8

Out[7]=7

Frequency and Amplitude Modulation (1)

Generation and reconstruction of an AM signal:

In[1]:=1

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https://wolfram.com/xid/0d6g1v2jsu-55w4o2

In[2]:=2

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https://wolfram.com/xid/0d6g1v2jsu-b8gc3w

Out[2]=2

Modulate the amplitude with a 22050 Hz sinusoid to shift the content at the high end of the spectrum. The result should be already inaudible for most people:

In[3]:=3