SPcorBWexp
Routine

void SPcorBWexp (double bwexp, const float rxx[], float rxxb[], int Nc)
Purpose

Bandwidth expand a set of correlation values
Description
The procedure forms the bandwidth expanded version of a set of correlation
values. The correlation coefficients are multiplied by a Gaussian function.
This is equivalent to convolving the power spectral density by a Gaussian
function. The bandwidth expansion is measured in terms of the width of
the Gaussian function in the frequency domain. A power spectrum consisting
of spectral lines will have each spectral line converted into a Gaussian
function with this bandwidth.
The Gaussian function is specified in terms of its normalized bandwidth
(measured at the 1 standard deviation point). The 3 dB bandwidth is
related to the 1 sigma bandwidth by the following relationship.
B3dB = sqrt (2 ln 2) Bsigma = 1.1774 Bsigma
The ITUT G.729 8 kb/s CSACELP speech coder uses a 1 sigma bandwidth
expansion of 60 Hz relative to a sampling rate of 8000 Hz. This expansion
is achieved by setting,
bwexp = 60/8000 = 0.015.
Note that the actual bandwidth measured on both sides of a peak is twice
this value.

Reference:
Y. Tohkura, F. Itakura, and S. Hashimoto, "Spectral smoothing technique in
PARCOR speech analysissynthesis", IEEE Trans. Acoustics, Speech, Signal
Proc., vol. ASSP26, pp. 587596, Dec. 1978.
Parameters

> double bwexp

Bandwidth expansion value (normalized onesided bandwidth value relative
to the sampling frequency)

> const float rxx[]

Input correlation coefficients (Nc values)

< float rxxb[]

Output correlation coefficients (Nc values). The output values can
overlay the input values.

> int Nc

Number of correlation coefficients
Author / revision
P. Kabal
/ Revision 1.5 2003/05/09
See Also
SPpcBWexp
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