crit_band_filt_wt.3

speech signal process tools

.\" Copyright (c) 1998 Entropic, Inc. All rights reserved.
.\" @(#)crit_band_filt_wt.3	1.1 9/4/98 ESI/ERL
.ds ]W (c) 1998 Entropic, Inc.
.TH CRIT_BAND_FILT_WT 3\-ESPSsp 9/4/98
.SH NAME
crit_band_filt_wt \- Compute the critical band filter weight for a bark value
.SH SYNOPSIS
.ft B
double
.br
crit_band_filt_wt (barkValue)
.br
double   barkValue;
.SH DESCRIPTION
.PP
This function evaluates the critical-band filter-weight function at a point
and returns the filter weight corresponding to that bark value 
([1, 2] with a small alteration).
The input \fIbarkValue\fP specifies the distance from
the filter peak. Note that the critical
band filter function is not symmetric around the peak, so 
both positive and negative values need evaluation.
.LP
The critical band filtering function
.I F
is determined by the following equation:
.IP
.if n \{\
10 log\x'1'\d\d10\u\u F(b)  =  7 \- 7.5 (b \- 0.210)
.br
			\- 17.5 [0.196 + (b \- 0.210)\x'-1'\u\u2\d\d] \x'-1'\u\u1/2\d\d
\}
.if t \{\
.EQ
.\" 10~log sub 10~F(b)~=~7~-~7.5^(b~-~0.210)
.\" ~-~17.5^ {[0.196~+~(b~-~0.210) sup 2 ]} sup 1/2
.nr 99 \n(.s
.nr 98 \n(.f
.ps 10
.ft 2
.ds 11 "\f11\fP\f10\fP
.ds 12 "\ 
.as 11 "\*(12
.ds 12 "\f1log\fP
.ds 13 "\f11\fP\f10\fP
.as 12 \v'0.3m'\s-3\*(13\s+3\v'-0.3m'
.as 11 "\*(12
.ds 12 "\ 
.as 11 "\*(12
.ds 12 "F\|\f1(\fPb\|\f1)\fP
.as 11 "\*(12
.ds 12 "\ 
.as 11 "\*(12
.ds 12 "\(eq
.as 11 "\*(12
.ds 12 "\ 
.as 11 "\*(12
.ds 12 "\f17\fP
.as 11 "\*(12
.ds 12 "\ 
.as 11 "\*(12
.ds 12 "\(mi
.as 11 "\*(12
.ds 12 "\ 
.as 11 "\*(12
.ds 12 "\f17\fP\f1.\fP\f15\fP
.as 11 "\*(12
.ds 12 "\|
.as 11 "\*(12
.ds 12 "\f1(\fPb
.as 11 "\*(12
.ds 12 "\ 
.as 11 "\|\*(12
.ds 12 "\(mi
.as 11 "\*(12
.ds 12 "\ 
.as 11 "\*(12
.ds 12 "\f10\fP\f1.\fP\f12\fP\f11\fP\f10\fP\f1)\fP
.as 11 "\*(12
.ds 12 "\ 
.as 11 "\*(12
.ds 12 "\(mi
.as 11 "\*(12
.ds 12 "\ 
.as 11 "\*(12
.ds 12 "\f11\fP\f17\fP\f1.\fP\f15\fP
.as 11 "\*(12
.ds 12 "\|
.as 11 "\*(12
.ds 12 "\f1[\fP\f10\fP\f1.\fP\f11\fP\f19\fP\f16\fP
.ds 13 "\ 
.as 12 "\*(13
.ds 13 "\(pl
.as 12 "\*(13
.ds 13 "\ 
.as 12 "\*(13
.ds 13 "\f1(\fPb
.as 12 "\*(13
.ds 13 "\ 
.as 12 "\|\*(13
.ds 13 "\(mi
.as 12 "\*(13
.ds 13 "\ 
.as 12 "\*(13
.ds 13 "\f10\fP\f1.\fP\f12\fP\f11\fP\f10\fP\f1)\fP
.ds 14 "\f12\fP
.as 13 \v'-0.65m'\s-3\*(14\s+3\v'0.65m'
.as 12 "\*(13
.ds 13 "\f1]\fP
.as 12 "\*(13
.ds 13 "\f11\fP\(sl\f12\fP
.as 12 \v'-0.7m'\s-3\*(13\s+3\v'0.7m'
.as 11 "\*(12
.ds 11 \x'0'\f2\s10\*(11\s\n(99\f\n(98
.nr 11 \w'\*(11'
.nr MK 0
.if 132>\n(.v .ne 132u
.rn 11 10
\*(10
.ps \n(99
.ft \n(98
.EN
\}
.LP
where \fIb\fP is the bark value.
.PP
The function was designed so that
the following three properties hold to good approximation [2]:
(1) The 3 dB bandwith is 1 bark.
(2) The asymptotic slopes are +10 dB/bark below the center frequency
and \-25 dB/bark above.
(3) The peak value is 0 dB and occurs when
.IR b " = 0 bark."
Both instances of the constant 0.210 above
were shown as 0.215 in the original references.
That value and the constant 0.196 were the result
of a numerical search with limited precision [2].
The value 0.210 used here results from an exact calculation,
given the other coefficients.
The \-3 dB points for
.I F
are
.IR b " = \-0.59 bark"
and
.IR b " = 0.41 bark";
the \-60 dB points for
.I F
are 
.IR b " = \-6.465 bark"
and
.IR b " = 2.865 bark."
.SH BUGS
None known.
.SH SEE ALSO
.nf
\fIhz_to_bark\fP(3\-ESPS), \fIbark_to_hz\fP(3\-ESPS), \fIbarkspec\fP(1\-ESPS)
.fi
.SH REFERENCES
.HP
[1] S. Wang, A. Sekey, and A. Gersho,
``An objective measure for predicting subjective quality of speech coders,''
.I "IEEE Journal on Selected Areas in Communications,"
.BR SAC-10
(5), 819\-829 (June 1992)
.HP
[2] A. Sekey and B. A. Hanson,
``Improved 1-Bark bandwidth auditory filter,''
.I "Journal of the Acoustical Society of America"
.B 75
(6), 1902\-1904 (June 1984)
.SH AUTHOR
Code extracted from \fIbarkspec\fP(1\-ESPS) by David Burton; manual page by David Burton.