void SPcorBWexp (double bwexp, const float rxx, float rxxb, int Nc)
Bandwidth expand a set of correlation values
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 ITU-T G.729 8 kb/s CS-ACELP 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
Y. Tohkura, F. Itakura, and S. Hashimoto, "Spectral smoothing technique in
PARCOR speech analysis-synthesis", IEEE Trans. Acoustics, Speech, Signal
Proc., vol. ASSP-26, pp. 587-596, Dec. 1978.
-> double bwexp
Bandwidth expansion value (normalized one-sided 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
/ Revision 1.5 2003/05/09
Main Index libtsp