前言
之前讲了MTM（多锥形窗谱估计）的相关原理，现在来分析一下它的matlab实现。
想要复习的可以参考一下之前的文件：
现代谱估计：多窗口谱
想要复习一下如何实现的可以参考：
MTM：matlab实现1MTM：matlab实现1
MTM：matlab实现2参数解析MTM参数解析
目录
正文
子函数的讲解即将收尾，现在是最后一个，多窗口谱计算函数。
输入
x 数据向量
params，pmtm传递的参数，除了输入x
它包含以下值域
nfft，评估功率谱的具体频率点
Fs 采样频率
range 单边还是双边
ConfInt 置信间隔 默认0.95
mtmmethod多窗口谱方法，默认自适应
E，dpss矩阵
V 包含dpss序列中心的向量
NW 时间带宽乘积
输出
s MTM计算出的功率谱
k 构建pxx的加窗数
w dft计算的频率点
%----------------------------------------------------------------------
function [S,k,w] = mtm_spectrum(x,params)
%MTM_SPECTRUM Compute the power spectrum via MTM.
%
% Inputs:
% x - Input data vector.
% params - Structure containing pmtm's input parameter list, except for
% the input data sequence, x; it contains the following fields:
% nfft - Number of frequency points to evaluate the PSD at;
% the default is max(256,2^nextpow2(N)).
% Fs - The sampling frequency; default is 1.
% range - default is 'onesided' or real signals and 'twosided' for
% - complex signals.
% ConfInt - Confidence interval; default is .95.
% MTMethod - Algorithm used in MTM; default is 'adapt'.
% E - Matrix containing the discrete prolate spheroidal
% sequences (dpss).
% V - Vector containing the concentration of the dpss.
% NW - Time-bandwidth product; default is 4.
%
% Outputs:
% S - Power spectrum computed via MTM.
% k - Number of sequences used to form Pxx.
% w - Frequency vector for which DFT is calculated
从输入中提取相关的参数
% Extract some parameters from the input structure for convenience.
nfft = params.nfft;
E = params.E;
V = params.V;
Fs = params.Fs;
如果没有采样频率，则默认为归一化频率2pi
if isempty(Fs)
Fs = 2*pi;
end
列向量计算MTM，每一列是一个单独的采样。
行数即采样点数，列数即独立信号个数
N = size(x,1);
Nchan = size(x,2);
采用的多窗口的窗口个数
k = length(V);
如果nfft不是一个整数而是一个列向量，则代表它是想要计算的点。
if length(nfft) > 1,
isfreqVector = true;
nfft_mod = length(nfft);
else
isfreqVector = false;
nfft_mod = nfft;
end
如果x是single，则信号功率谱也是single
if isa(x,'single') || isa(E,'single')
S = zeros(nfft_mod, Nchan, 'single');
else
S = zeros(nfft_mod, Nchan);
end
对于每一个信号源
for chan=1:Nchan
计算加窗 离散傅里叶
% Compute the windowed DFTs.
如果指定输入频率向量或者不指定且N采样个数小于设定的NFFT点数
if (~isfreqVector && N<=nfft) || isfreqVector
计算每一列的加窗fft变换
% Compute DFT using FFT or Goertzel
使用基本函数，快速计算加窗后的离散傅里叶变换
[Xx,w] = computeDFT(bsxfun(@times,E(:,1:k),x(:,chan)),nfft(:),Fs);
sk是xx的能量值
Sk = abs(Xx).^2;
else % Wrap the data modulo nfft if N > nfft. Note we cannot use datawrap
% and FFT because datawrap does not support matrices
% use CZT to compute DFT on nfft evenly spaced samples around the
% unit circle:
Sk = abs(czt(bsxfun(@times,E(:,1:k),x(:,chan)),nfft(:))).^2;
获得对应的频率点
w = psdfreqvec('npts',nfft,'Fs',Fs);
end
计算多窗口谱估计，在0：NFFt上计算整个特征谱。
% Compute the MTM spectral estimates, compute the whole spectrum 0:nfft.
switch params.MTMethod,
自适应的情况：
case 'adapt'
设置决定自适应的权重的代数
% Set up the iteration to determine the adaptive weights:
初始功率谱，第一列的平方和/数量
sig2=x(:,chan)'*x(:,chan)/N;
% Power
加窗1和加窗2的平均值作为初始值
Schan=(Sk(:,1)+Sk(:,2))/2; % Initial spectrum estimate
S1=zeros(nfft_mod,1);
% The algorithm converges so fast that results are
% usually 'indistinguishable' after about three iterations.
% This version uses the equations from [2] (P&W pp 368-370).
% Set tolerance for acceptance of spectral estimate:
tol=.0005*sig2/nfft_mod;
a=bsxfun(@times,sig2,(1-V));
% Do the iteration:
while sum(abs(Schan-S1)/nfft_mod)>tol
% calculate weights
b=(Schan*ones(1,k))./(Schan*V'+ones(nfft_mod,1)*a');
% calculate new spectral estimate
wk=(b.^2).*(ones(nfft_mod,1)*V');
S1=sum(wk'.*Sk')./ sum(wk,2)';
S1=S1';
Stemp=S1; S1=Schan; Schan=Stemp; % swap S and S1
end
case {'unity','eigen'}
% Compute the averaged estimate: simple arithmetic averaging is used.
% The Sk can also be weighted by the eigenvalues, as in Park et al.
% Eqn. 9.; note that the eqn. apparently has a typo; as the weights
% should be V and not 1/V.
if strcmp(params.MTMethod,'eigen')
wt = V(:); % Park estimate
else
wt = ones(k,1);
end
Schan = Sk*wt/k;
end
S(:,chan) = Schan;
end