dpcmdeco

Decode using differential pulse code modulation

Syntax

sig = dpcmdeco(indx,codebook,predictor)
[sig,quanterror] = dpcmdeco(indx,codebook,predictor)


Description

sig = dpcmdeco(indx,codebook,predictor) implements differential pulse code demodulation to decode the vector indx. The vector codebook represents the predictive-error quantization codebook. The vector predictor specifies the predictive transfer function. If the transfer function has predictive order M, predictor has length M+1 and an initial entry of 0. To decode correctly, use the same codebook and predictor in dpcmenco and dpcmdeco.

For a description of the formats of partition and codebook, see Quantization.

[sig,quanterror] = dpcmdeco(indx,codebook,predictor) is the same as the syntax above, except that the vector quanterror is the quantization of the predictive error based on the quantization parameters. quanterror is the same size as sig.

Note

You can estimate the input parameters codebook, partition, and predictor using the function dpcmopt.

Examples

DPCM Encoding and Decoding

This example implements a simple case of DPCM that quantizes the difference between the value of the current signal sample and the value of the previous sample. For this case, the predictor is just y(k) = x (k - 1). It then encodes a sawtooth signal, decodes it, plots both the original and the decoded signals, and computes the mean square error between the original and decoded signals.

partition = [-1:.1:.9];
codebook = [-1:.1:1];
predictor = [0 1];      % y(k)=x(k-1)
t = [0:pi/50:2*pi];     % Time samples
x = sawtooth(3*t);      % Original signal

Quantize x using DPCM encoding.

encodedx = dpcmenco(x,codebook,partition,predictor);

Try to recover x from the modulated signal by using DPCM decoding. Plot the original signal and the decoded signal. The solid line is the original signal, while the dashed line is the recovered signal.

decodedx = dpcmdeco(encodedx,codebook,predictor);
plot(t,x,t,decodedx,'-')

Compute the mean square error between the original signal and the decoded signal.

distor = sum((x-decodedx).^2)/length(x)

distor = 
0.0327

Optimize DPCM Parameters

To optimize a DPCM-encoded and -decoded sawtooth signal, use the dpcmopt function with the dpcmenco and dpcmdeco functions. Testing and selecting parameters for large signal sets with a fine quantization scheme can be tedious. One way to produce partition, codebook, and predictor parameters easily is to optimize them according to a set of training data. The training data should be typical of the kinds of signals to be quantized with dpcmenco.

This example uses the predictive order, 1, as the desired order of the new optimized predictor. The dpcmopt function creates these optimized parameters, using the sawtooth signal x as training data. The example goes on to quantize the training data itself. In theory, the optimized parameters are suitable for quantizing other data that is similar to x. The mean square distortion for optimized DPCM is much less than the distortion with nonoptimized DPCM parameters.

Define variables for a sawtooth signal and initial DPCM parameters.

t = [0:pi/50:2*pi];
x = sawtooth(3*t);
partition = [-1:.1:.9];
codebook = [-1:.1:1];
predictor = [0 1];      % y(k)=x(k-1)

Optimize the partition, codebook, and predictor vectors by using the dpcmopt function and the initial codebook and order 1. Then generate DPCM encoded signals by using the initial and the optimized partition and codebook vectors.

[predictorOpt,codebookOpt,partitionOpt] = dpcmopt(x,1,codebook);
encodedx = dpcmenco(x,codebook,partition,predictor);
encodedxOpt = dpcmenco(x,codebookOpt,partitionOpt,predictorOpt);

Try to recover x from the modulated signal by using DPCM decoding. Compute the mean square error between the original signal and the decoded and optimized decoded signals.

decodedx = dpcmdeco(encodedx,codebook,predictor);
decodedxOpt = dpcmdeco(encodedxOpt,codebookOpt,predictorOpt);
distor = sum((x-decodedx).^2)/length(x);
distorOpt = sum((x-decodedxOpt).^2)/length(x);

Compare mean square distortions for quantization with the initial and optimized input arguments.

[distor, distorOpt]

ans = 1×2

    0.0327    0.0009

References

[1] Kondoz, A. M., Digital Speech, Chichester, England, John Wiley & Sons, 1994.

Version History

Introduced before R2006a