# v_meansqtf

## PURPOSE

V_AVEPSPEC calculates the mean square transfer function for a filter D=(B,A)

## SYNOPSIS

function d=v_meansqtf(b,a)

## DESCRIPTION

    V_AVEPSPEC calculates the mean square transfer function for a filter D=(B,A)

     Inputs: B,A         Numerator and denominator filter coefficients.

     Output: D           The mean square transfer function of the filter B/A. This equals
                         the average otuput power when the filter is fed with unit variance
                         white noise.

                         D may be obtained approximately by:
                             N=1024; D=sum(filter(B,A,[1 zeros(1,N)]).^2)

## CROSS-REFERENCE INFORMATION

This function calls:

- v_lpcar2rr V_LPCAR2RR Convert autoregressive coefficients to autocorrelation coefficients RR=(AR,P)

This function is called by:

## SOURCE CODE

    0001 function d=v_meansqtf(b,a)
    0002 %V_AVEPSPEC calculates the mean square transfer function for a filter D=(B,A)
    0003 %
    0004 % Inputs: B,A         Numerator and denominator filter coefficients.
    0005 %
    0006 % Output: D           The mean square transfer function of the filter B/A. This equals
    0007 %                     the average otuput power when the filter is fed with unit variance
    0008 %                     white noise.
    0009 %
    0010 %                     D may be obtained approximately by:
    0011 %                         N=1024; D=sum(filter(B,A,[1 zeros(1,N)]).^2)
    0012
    0013 % Since the power spectrum is the fourier transform of the autocorrelation, we can calculate
    0014 % the average value of pb/pa by taking the 0'th order term of the convolution of the autocorrelation
    0015 % functions associated with b and 1/a. Since b is an FIR filter, this convolution is
    0016 % a finite sum even though the autocorrelation function of 1/a is infinite in extent.
    0017
    0018 %      Copyright (C) Mike Brookes 1997
    0019 %      Version: $Id: v_meansqtf.m 10865 2018-09-21 17:22:45Z dmb $
    0020 %
    0021 %   VOICEBOX is a MATLAB toolbox for speech processing.
    0022 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
    0023 %
    0024 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    0025 %   This program is free software; you can redistribute it and/or modify
    0026 %   it under the terms of the GNU Lesser General Public License as published by
    0027 %   the Free Software Foundation; either version 3 of the License, or
    0028 %   (at your option) any later version.
    0029 %
    0030 %   This program is distributed in the hope that it will be useful,
    0031 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
    0032 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    0033 %   GNU Lesser General Public License for more details.
    0034 %
    0035 %   You can obtain a copy of the GNU Lesser General Public License from
    0036 %   https://www.gnu.org/licenses/ .
    0037 %
    0038 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    0039
    0040 if length(a)==1
    0041    d=(b(:)')*b(:);
    0042 else
    0043    m=lpcar2ra(b(:)');
    0044    m(1)=m(1)*0.5;
    0045    d=2*v_lpcar2rr(a(:)',length(m)-1)*m';
    0046 end