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# compand

Source code mu-law or A-law compressor or expander

## Syntax

out = compand(in,param,v)
out = compand(in,Mu,v,'mu/compressor')
out = compand(in,Mu,v,'mu/expander')
out = compand(in,A,v,'A/compressor')
out = compand(in,A,v,'A/expander')

## Description

out = compand(in,param,v) implements a µ-law compressor for the input vector in. Mu specifies µ, and v is the input signal's maximum magnitude. out has the same dimensions and maximum magnitude as in.

out = compand(in,Mu,v,'mu/compressor') is the same as the syntax above.

out = compand(in,Mu,v,'mu/expander') implements a µ-law expander for the input vector in. Mu specifies µ and v is the input signal's maximum magnitude. out has the same dimensions and maximum magnitude as in.

out = compand(in,A,v,'A/compressor') implements an A-law compressor for the input vector in. The scalar A is the A-law parameter, and v is the input signal's maximum magnitude. out is a vector of the same length and maximum magnitude as in.

out = compand(in,A,v,'A/expander') implements an A-law expander for the input vector in. The scalar A is the A-law parameter, and v is the input signal's maximum magnitude. out is a vector of the same length and maximum magnitude as in.

 Note:   The prevailing parameters used in practice are µ= 255 and A = 87.6.

## Examples

The examples below illustrate the fact that compressors and expanders perform inverse operations.

```compressed = compand(1:5,87.6,5,'a/compressor')
expanded = compand(compressed,87.6,5,'a/expander')```

The output is

```compressed =

3.5296    4.1629    4.5333    4.7961    5.0000

expanded =

1.0000    2.0000    3.0000    4.0000    5.0000
```

expand all

### Algorithms

For a given signal x, the output of the µ-law compressor is

$y=\frac{V\mathrm{log}\left(1+\mu |x|/V\right)}{\mathrm{log}\left(1+\mu \right)}\mathrm{sgn}\left(x\right)$

where V is the maximum value of the signal x, µ is the µ-law parameter of the compander, log is the natural logarithm, and sgn is the signum function (sign in MATLAB).

The output of the A-law compressor is

where A is the A-law parameter of the compander and the other elements are as in the µ-law case.

## References

[1] Sklar, Bernard, Digital Communications: Fundamentals and Applications, Englewood Cliffs, NJ, Prentice-Hall, 1988.