# erb2hz

Convert from equivalent rectangular bandwidth (ERB) scale to hertz

## Description

example

hz = erb2hz(erb) converts values on the ERB frequency scale to values in hertz.

## Examples

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Set two bounding frequencies in Hz and then convert them to the ERB scale.

b = hz2erb([20,8000]);

Generate a row vector of 32 values uniformly spaced on the ERB scale.

erbVect = linspace(b(1),b(2),32);

Convert the row vector of values into equivalent frequencies in Hz.

hzVect = erb2hz(erbVect);

Plot the two vectors for comparison. As ERB values increase linearly, Hz values increase exponentially.

plot(erbVect,hzVect,'o')
title('ERB vs Hz')
xlabel('ERB')
ylabel('Hz')
grid on

## Input Arguments

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Input frequency on the equivalent rectangular band (ERB) scale, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: single | double

## Output Arguments

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Output frequency in Hz, returned as a scalar, vector, matrix, or multidimensional array the same size as erb.

Data Types: single | double

## Algorithms

The frequency conversion from the ERB scale to Hz uses the following formula:

$\begin{array}{l}hz=\frac{{10}^{\frac{erb}{A}}-1}{0.00437}\\ \text{where}\\ A=\frac{1000{\mathrm{log}}_{e}\left(10\right)}{\left(24.7\right)\left(4.37\right)}\end{array}$

## References

[1] Glasberg, Brian R., and Brian C. J. Moore. "Derivation of Auditory Filter Shapes from Notched-Noise Data." Hearing Research. Vol. 47, Issues 1–2, 1990, pp. 103–138.