blt.3

speech signal process tools

.\" Copyright (c) 1987, 1990 Entropic Speech, Inc.; All rights reserved
.\" @(#)blt.3	1.2 30 Apr 1997 ERL
.TH BLT 3\-ESPS 11/10/90
.ds ]W "\fI\s+4\ze\h'0.05'e\s-4\v'-0.4m'\fP\(*p\v'0.4m'\ Entropic Speech, Inc.
.SH NAME
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blt \- Find the bilinear transform of a sequence.

.SH SYNOPSIS
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void 
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blt(data, n, a)
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int n;
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float *data;
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float a;
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.SH DESCRIPTION
The routine \fIblt\fP performs a bilinear transformation of a real
sequence as described in [1].  The transform of the length \fIn\fP 
sequence, \fIdata\fP, is obtained through recursive application of IIR 
filters (see [1]).  The transformed sequence, also length \fIn\fP, is returned in \fIdata\fP.
.PP
A single parameter, \fIa\fP, describes the bilinear transformation. The 
Z-Transform of the original sequence, F, and the transformed 
sequence, G, are related by 
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F( e^(jw) ) = G( e^(jw') ) 
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where
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w = arctan[ ( (1-a^2) sin w')/( 2a + (1+a^2) cos w') ].
.PP
An intendend application of this routine is to obtain a frequency
warping which approximates the mel-scale. An example of this is the
mel-warped cepstrum, which is described in [2].
.SH SEE ALSO
\fIacf\fR(1\-ESPS), \fIafc2cep\fR(3\-ESPS), \fIfft_cepstrum\fR(3\-ESPS)
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.SH COMMENTS
The transformation is performed in-place. Internal static memory is 
allocated as required.  If \fIblt\fP is called with \fIa\fP 
equal to 0, the routine returns without performing any computation; no
error message is generated.
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.SH REFERENCES
[1] A. V. Oppenheim and D. H. Johnson,
\fIDiscrete Representation of Signals.\fP
Proceedings of the I.E.E.E., vol. 60, no. 6, June 1972 p681-691
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[2] K. Lee,
\fIAutomatic Speech Recognition: the Development of the SPHINX System\fP
Kluwer Academic, Norwell, MA. 1989
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.SH AUTHOR
Manual page and program by Bill Byrne.