alawcompress

A-law compressor.

Syntax

use sigenc
output = alawcompress(input)
output = alawcompress(input, a)

Description

alawcompress(input,a) compresses signal input with A-law method using parameter a. The signal is assumed to be in [-1,1]; values outside this range are clipped. input can be a real array of any size and dimension. The default value of a is 87.6.

The compressor and its inverse, the expander, are static, nonlinear filters used to improve the signal-noise ratio of quantized signals. The compressor should be used before quantization (or on a signal represented with a higher precision).

See also

alawexpand, ulawcompress

alawexpand

A-law expander.

Syntax

use sigenc
output = alawexpand(input)
output = alawexpand(input, a)

Description

alawexpand(input,a) expands signal input with A-law method using parameter a. input can be a real array of any size and dimension. The default value of a is 87.6.

See also

alawcompress, ulawexpand

dpcmdeco

Differential pulse code modulation decoding.

Syntax

use sigenc
output = dpcmdeco(i, codebook, predictor)

Description

dpcmdeco(i,codebook,predictor) reconstructs a signal encoded with differential pulse code modulation. It performs the opposite of dpcmenco.

See also

dpcmenco, dpcmopt

dpcmenco

Differential pulse code modulation encoding.

Syntax

use sigenc
i = dpcmenco(input, codebook, partition, predictor)

Description

dpcmenco(input,codebook,partition,predictor) quantizes the signal in vector input with differential pulse code modulation. It predicts the future response with the finite-impulse response filter given by polynomial predictor, and it quantizes the residual error with codebook and partition like quantiz. The output i is an array of codes with the same size and dimension as input.

The prediction y*(k) for sample k s

y*(k) = sum predictor(i+1) * yq(k-i) for i = 1,2,...,length(predictor)-1

where yq(k) is the quantized (reconstructed) signal. The predictor must be strictly causal: predictor(0) must be zero. To encode the difference between in(k) and yq(k-1), predictor=[0,1]. Note that there is no drift between the reconstructed signal and the input, contrary to the case where the input is differentiated, quantized, and integrated.

Example

use sigenc
t = 0:0.1:10;
x = sin(t);
codebook = -.1:.01:.1;
partition = -.0:.01:.09;
predictor = [0, 1];
i = dpcmenco(x, codebook, partition, predictor);
y = dpcmdeco(i, codebook, predictor);

See also

quantiz, dpcmdeco, dpcmopt

dpcmopt

Differential pulse code modulation decoding.

Syntax

use sigenc
(predictor, codebook, partition) = dpcmopt(in, order, n)
(predictor, codebook, partition) = dpcmopt(in, order, codebook0)
(predictor, codebook, partition) = dpcmopt(in, predictor, ...)
(predictor, codebook, partition) = dpcmopt(..., tol)
predictor = dpcmopt(in, order)

Description

dpcmopt(in,order,n) gives the optimal predictor of order order, codebook of size n and partition to encode the signal in vector in with differential pulse code modulation. The result can be used with dpcmenco to encode signals with similar properties. If the second input argument is a vector, it is used as the predictor and not optimized further; its first element must be zero. If the third input argument is a vector, it is used as an initial guess for the codebook, which has the same length. An optional fourth input argument provides the tolerance (the default is 1e-7).

If only the predictor is required, only the input and the predictor order must be supplied as input arguments.

See also

dpcmenco, dpcmdeco, lloyds

lloyds

Optimal quantization.

Syntax

use sigenc
(partition, codebook) = lloyds(input, n)
(partition, codebook) = lloyds(input, codebook0)
(partition, codebook) = lloyds(..., tol)

Description

lloyds(input,n) computes the optimal partition and codebook for quantizing signal input with n codes, using the Lloyds algorithm.

If the second input argument is a vector, lloyds(input,codebook0) uses codebook0 as an initial guess for the codebook. The result has the same length.

A third argument can be used to specify the tolerance used as the stopping criterion of the optimization loop. The default is 1e-7.

Example

We start from a suboptimal partition and compute the distortion:

use sigenc
partition = [-1, 0, 1];
codebook = [-2, -0.5, 0.5, 2];
in = -5:0.6:3;
(i, out, dist) = quantiz(in, partition, codebook);
dist
  2.1421

The partition is optimized with lloyds, and the same signal is quantized again. The distortion is reduced.

(partition_opt, codebook_opt) = lloyds(in, codebook)
  partition_opt =
       -2.9  -0.5   1.3
  codebook_opt =
    -4.1  -1.7   0.4   2.2
(i, out, dist) = quantiz(in, partition_opt, codebook_opt);
dist
  1.0543

See also

quantiz, dpcmopt

quantiz

Table-based signal quantization.

Syntax

use sigenc
i = quantiz(input, partition)
(i, output, distortion) = quantiz(input, partition, codebook)

Description

quantiz(input,partition) quantizes signal input using partition as boundaries between different ranges. Range from -inf to partition(1) corresponds to code 0, range from partition(1) to partition(2) corresponds to code 1, and so on. input may be a real array of any size and dimension; partition must be a sorted vector. The output i is an array of codes with the same size and dimension as input.

quantiz(input,partition,codebook) uses codebook as a look-up table to convert back from codes to signal. It should be a vector with one more element than partition. With a second output argument, quantiz gives codebook(i).

With a third output argument, quantiz computes the distortion between input and codebook(i), i.e. the mean of the squared error.

Example

use sigenc
partition = [-1, 0, 1];
codebook = [-2, -0.5, 0.5, 2];
in = randn(1, 5)
  in =
    0.1799 -9.7676e-2   -1.1431   -0.4986    1.0445
(i, out, dist) = quantiz(in, partition, codebook)
  i =
    2    1    0    1    2
  out =
    0.5 -0.5 -2   -0.5  0.5
  dist =
    0.259

See also

lloyds, dpcmenco

ulawcompress

mu-law compressor.

Syntax

use sigenc
output = ulawcompress(input)
output = ulawcompress(input, mu)

Description

ulawcompress(input,mu) compresses signal input with mu-law method using parameter mu. input can be a real array of any size and dimension. The default value of mu is 255.

The compressor and its inverse, the expander, are static, nonlinear filters used to improve the signal-noise ratio of quantized signals. The compressor should be used before quantization (or on a signal represented with a higher precision).

See also

ulawexpand, alawcompress

ulawexpand

mu-law expander.

Syntax

use sigenc
output = ulawexpand(input)
output = ulawexpand(input, mu)

Description

ulawexpand(input,mu) expands signal input with mu-law method using parameter a. input can be a real array of any size and dimension. The default value of mu is 255.

See also

ulawcompress, alawexpand