Create Sound as gammatone...

A command to create a Sound as a gammatone.

## Settings

Name
  the name of the resulting Sound object.
Minimum time (s) and Maximum time (s)
  the start and end time of the resulting Sound.
Sampling frequency (Hz)
  the sampling frequency of the resulting Sound.
Gamma
  determines the exponent of the polynomial.
Frequency (Hz) and Bandwidth (Hz)
  determine the frequency and damping of the cosine wave in the gammatone.
Initial phase (radians)
  the initial phase of the cosine wave.
Addition factor (standard value: 0)
  determines the degree of asymmetry in the spectrum of the gammatone. The zero default value gives a gammatone. A value unequal to zero results in a so called gammachirp. A negative value is used in auditory filter modelling to guarantee the usual direction of filter asymmetry, which corresponds to an upward glide in instantaneous frequency.
Scale amplitudes
  determines whether the amplitudes will be scaled to fit in the range (-1, 1).

## Purpose

to create a Sound according to the following formula:

tγ–1 e–2π·bandwidth·t cos (2π·frequency·t + additionFactor·ln(t) + initialPhase),

The gammachirp function has a monotonically frequency-modulated carrier (the chirp) with instantaneous frequency

instantaneousFrequency(t) = frequency + additionFactor / (2·π·t)

and an envelope that is a gamma distribution function. It is a theoretically optimal auditory filter, in the sense that it leads to minimal uncertainty in the joint time and scale representation of auditory signal analysis.

For faithful modelling of the inner ear, Irino & Patterson (1997) conclude that a value of approximately 1.5 * ERB (frequency) is appropriate for bandwidth. ERB stands for equivalent rectangular bandwidth. Their formula for ERB is:

ERB(f) = 6.23 10–6 f2 + 93.39 10–3 f + 28.52.

To avoid aliasing in the chirp sound, a sound is only generated during times where the instantaneous frequency is greater than zero and smaller than the Nyquist frequency.

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