pydrobert.speech.scales

Scaling functions

Scaling functions transform a scalar in the frequency domain to some other real domain (the “scale” domain). The scaling functions should be invertible. Their primary purpose is to define the bandwidths of filters in pydrobert.speech.filters.

class pydrobert.speech.scales.BarkScaling

Bases: ScalingFunction

Psychoacoustic scaling function

Based on a collection experiments briefly mentioned in [zwicker1961] involving masking to determine critical bands. The functional approximation to the scale is implemented with the formula from [traunmuller1990] (being honest, from Wikipedia):

\[\begin{split}s = \begin{cases} z + 0.15(2 - z) & \mbox{if }z < 2 \\ z + 0.22(z - 20.1) & \mbox{if }z > 20.1 \end{cases}\end{split}\]

where

\[z = 26.81f/(1960 + f) - 0.53\]

Where \(s\) is the scale and \(f\) is the frequency in Hertz.

aliases = {'bark'}

class pydrobert.speech.scales.LinearScaling(low_hz, slope_hz=1.0)

Bases: ScalingFunction

Linear scaling between high and low scales/frequencies

Parameters:

• low_hz (float) – The frequency (in Hertz) corresponding to scale 0.

• slope_hz (float) – The increase in scale corresponding to a 1 Hertz increase in frequency.

aliases = {'linear', 'uniform'}

low_hz

slop_hz

class pydrobert.speech.scales.MelScaling

Bases: ScalingFunction

Psychoacoustic scaling function

Based of the experiment in [stevens1937] wherein participants adjusted a second tone until it was half the pitch of the first. The functional approximation to the scale is implemented with the formula from [oshaughnessy1987] (being honest, from Wikipedia):

\[s = 1127 \ln \left(1 + \frac{f}{700} \right)\]

Where \(s\) is the scale and \(f\) is the frequency in Hertz.

aliases = {'mel'}

class pydrobert.speech.scales.OctaveScaling(low_hz)

Bases: ScalingFunction

Uniform scaling in log2 domain from low frequency

Parameters:

low_hz (float) – The positive frequency (in Hertz) corresponding to scale 0. Frequencies below this value should never be queried.

aliases = {'octave'}

low_hz

class pydrobert.speech.scales.ScalingFunction

Bases: AliasedFactory

Converts a frequency to some scale and back again

abstract hertz_to_scale(hertz)

Convert frequency (in Hertz) to scalar

abstract scale_to_hertz(scale)

Convert scale to frequency (in Hertz)