Gammatone filter bank
Audio Toolbox / Filters
The Gammatone Filter Bank block decomposes a signal by passing it through a bank of gammatone filters equally spaced on the equivalent rectangular bandwidth (ERB) scale. Gammatone filter banks are designed to model the human auditory system.
Port_1— Audio input to filter bank
Audio input to the filter bank, specified as a scalar, vector, or matrix. If you specify the input as a matrix, the block treats the columns as independent audio channels. If you specify the input as a vector, the block treats the input as containing a single channel.
Port_1— Audio output from filter bank
Audio output from the filter bank, returned as a scalar, vector, matrix, or 3-D
array. The shape of output signal depends on the shape of input signal and
filters. If input is an M-by-N
matrix, then output is an M-by-Number of
filters-by-N array. If N is
1, then output is a matrix.
Frequency range (Hz)— Frequency range of filter bank
[50 8000](default) | two-element row vector of monotonically increasing values
Frequency range of the filter bank, specified as a two-element row vector of monotonically increasing values in Hz.
Number of filters— Number of filters
32(default) | positive integer
Number of filters in the filter bank, specified as a positive integer.
Inherit sample rate from input— Specify sample rate from input port
Select this parameter to specify the sample rate from the input port.
Input sample rate (Hz)— Input sample rate
16000(default) | positive integer
Input sample rate, specified as a positive integer in Hz.
To enable this parameter, set Inherit sample rate
from input port to
Bands as separate output port— Separate ports for each filter output
Select this parameter to separate ports for each filter output.
View Filter Response— Visualize filter bank responses
This button uses the
function to visualize gammatone filter bank responses.
Simulate using— Specify type of simulation to run
Interpreted execution(default) |
Type of simulation to run, specified as one of the following:
Interpreted execution –– Simulate model using the
MATLAB® interpreter. This option shortens startup time and has simulation
speed comparable to
Code generation. In this mode, you
can debug the source code of the block.
Code generation –– Simulate model using generated C
code. The first time you run a simulation, Simulink® generates C code for the block. The C code is reused for subsequent
simulations as long as the model does not change. This option requires additional
startup time but the speed of the subsequent simulations is faster than
A gammatone filter bank is often used as the front end of a cochlea simulation. A cochlea simulation transforms transforms complex sounds into a multichannel activity pattern like the one observed in the auditory nerve  .The Gammatone Filter Bank block follows the algorithm described in . The algorithm is an implementation of an idea proposed in . The design of the gammatone filter bank can be described in two parts: the filter shape (gammatone) and the frequency scale. The equivalent rectangular bandwidth (ERB) scale defines the relative spacing and bandwidth of the gammatone filters. The derivation of the ERB scale also provides an estimate of the auditory filter response that closely resembles the gammatone filter.
The block determines the ERB scale using the notched-noise masking method. This method involves a listening test wherein notched noise is centered on a tone. The power of the tone is tuned, and the audible threshold (the power required for the tone to be heard) is recorded. The experiment is repeated for different notch widths and center frequencies.
The notched-noise method assumes that the audible threshold corresponds to a constant signal-to-masker ratio at the output of the theoretical auditory filter. That is, the ratio of the power of the fc tone and the shaded area is constant. Therefore, the relationship between the audible threshold and 2Δf (the notch bandwidth) is linearly related to the relationship between the noise passed through the filter and 2Δf.
The derivative of the function relating Δf to the noise passed through the filter estimates the shape of the auditory filter. Because Δf has an inverse relationship with the noise power passed through the filter, the derivative of the function must be multiplied by –1. The resulting shape of the auditory filter is usually approximated as a roex filter.
The equivalent rectangular bandwidth of the auditory filter is defined as the width of a rectangular filter required to pass the same noise power as the auditory filter.
 defines ERB as a function of center frequency for young listeners with normal hearing and a moderate noise level:
The ERB scale (ERBs) is an extension of the relationship between ERB and the center frequency, derived by integrating the reciprocal of the ERB function:
To design a gammatone filter bank,  suggests distributing the center frequencies of the filters in proportion to their bandwidth. To accomplish this, Gammatone Filter Bank block defines the center frequencies as linearly spaced on the ERB scale, covering the specified frequency range with the desired number of filters. You can specify the frequency range and desired number of filters using the Frequency range (Hz) and Number of filters parameters.
The gammatone filter was introduced in . The continuous impulse response is:
a –– amplitude factor
t –– time in seconds
n –– filter order (set to four to model human hearing)
fc–– center frequency
b –– bandwidth, set to
ϕ –– phase factor
The gammatone filter is similar to the roex filter derived from the notched-noise experiment. The Gammatone Filter Bank block implements the digital filter as a cascade of four second-order sections, as described in .
 Slaney, Malcolm. "An Efficient Implementation of the Patterson-Holdworth Auditory Filter Bank." Apple Computer Technical Report 35, 1993.
 Patterson, R.D., K. Robinson, J. Holdsworth, D. Mckeown, C. Zhang, and M. Allerhand. "Complex Sounds and Auditory Images." Auditory Physiology and Perception. 1992, pp. 429–446.
 Aertsen, A. M. H. J., and P. I. M. Johannesma. "Spectro-temporal Receptive Fields of Auditory Neurons in the Grassfrog." Biological Cybernetics. Vol. 38, Issue 4, 1980, pp. 223–234.
 Glasberg, Brian R., and Brian CJ Moore. "Derivation of Auditory Filter Shapes from Notched-Noise Data." Hearing Research. Vol. 47. Issue 1-2, 1990, pp. 103–138.