# hz2erb

Convert from hertz to equivalent rectangular bandwidth (ERB) scale

## Syntax

``erb = hz2erb(hz)``

## Description

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````erb = hz2erb(hz)` converts values in hertz to values on the ERB frequency scale.```

## 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 in Hz, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: `single` | `double`

## Output Arguments

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Output frequency on the ERB scale, returned as a scalar, vector, matrix, or multidimensional array the same size as `hz`.

Data Types: `single` | `double`

## Algorithms

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

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

## 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.