前言

之前講了MTM（多錐形窗譜估計）的相關原理，現在來分析一下它的matlab實現。
想要復習的可以參考一下之前的文件：
現代譜估計：多窗口譜
想要復習一下如何實現的可以參考：
MTM：matlab實現1MTM：matlab實現1
MTM：matlab實現2參數解析MTM參數解析
MTM：matlab實現3譜功率計算MTM譜功率計算

目錄

• 前言
• 目錄
• 主函數調用說明

主函數調用說明

function varargout = pmtm(x,varargin) %PMTM Power Spectral Density (PSD) estimate via the Thomson multitaper % method (MTM). % Pxx = PMTM(X) returns the Power Spectral Density (PSD) estimate, Pxx, % of a discrete-time signal X. When X is a vector, it is converted to a % column vector and treated as a single channel. When X is a matrix, the % PSD is computed independently for each column and stored in the % corresponding column of Pxx. Pxx is the distribution of power per unit % frequency. The frequency is expressed in units of radians/sample. % % For real signals, PMTM returns the one-sided PSD by default; for % complex signals, it returns the two-sided PSD. Note that a one-sided % PSD contains the total power of the input signal. % % Pxx = PMTM(X,NW) specifies NW as the "time-bandwidth product" for the % discrete prolate spheroidal sequences (or Slepian sequences) used as % data windows. Typical choices for NW are 2, 5/2, 3, 7/2, or 4. If % empty or omitted, NW defaults to 4. By default, PMTM drops the last % taper because its corresponding eigenvalue is significantly smaller % than 1. Therefore, The number of tapers used to form Pxx is 2*NW-1. % % Pxx = PMTM(X,NW,NFFT) specifies the FFT length used to calculate the % PSD estimates. For real X, Pxx has (NFFT/2+1) rows if NFFT is even, % and (NFFT+1)/2 rows if NFFT is odd. For complex X, Pxx always has % length NFFT. If NFFT is specified as empty, NFFT is set to either % 256 or the next power of 2 greater than the length of X, whichever is % larger. % % [Pxx,W] = PMTM(X,NW,NFFT) returns the vector of normalized angular % frequencies, W, at which the PSD is estimated. W has units of % radians/sample. For real signals, W spans the interval [0,Pi] when % NFFT is even and [0,Pi) when NFFT is odd. For complex signals, W % always spans the interval [0,2*Pi). % % [Pxx,W] = PMTM(X,NW,W) computes the two-sided PSD at the normalized % angular frequencies contained in vector W. W must have at least two % elements. %常規調用，輸入為 x，nw，NFFT，fs % [Pxx,F] = PMTM(X,NW,NFFT,Fs) returns a PSD computed as a function of % physical frequency. Fs is the sampling frequency specified in hertz. % If Fs is empty, it defaults to 1 Hz. % % F is the vector of frequencies (in hertz) at which the PSD is % estimated. For real signals, F spans the interval [0,Fs/2] when NFFT % is even and [0,Fs/2) when NFFT is odd. For complex signals, F always % spans the interval [0,Fs). % % [Pxx,F] = PMTM(X,NW,F,Fs) computes the two-sided PSD at the frequencies % contained in vector F. F is a vector of frequencies in Hz with 2 or % more elements. % % [Pxx,F] = PMTM(...,Fs,method) uses the algorithm specified in method % for combining the individual spectral estimates: % 'adapt' - Thomson's adaptive non-linear combination (default). % 'unity' - linear combination with unity weights. % 'eigen' - linear combination with eigenvalue weights. % % [Pxx,F] = PMTM(X,E,V,NFFT,Fs,method) is the PSD estimate, and frequency % vector from the data tapers in E and their concentrations V. Type HELP % DPSS for a description of the matrix E and the vector V. By default, % PMTM drops the last eigenvector because its corresponding eigenvalue is % significantly smaller than 1. % % [Pxx,F] = PMTM(X,DPSS_PARAMS,NFFT,Fs,method) uses the cell % array DPSS_PARAMS containing the input arguments to DPSS (listed in % order, but excluding the first argument) to compute the data tapers. % For example, PMTM(x,{3.5,'trace'},512,1000) calculates the prolate % spheroidal sequences for NW=3.5, NFFT=512, and Fs=1000, and displays % the method that DPSS uses for this calculation. Type HELP DPSS for % other options. % % [Pxx,F] = PMTM(...,'DropLastTaper',DROPFLAG) specifies whether PMTM % should drop the last taper/eigenvector during the calculation. DROPFLAG % can be one of the following values: [ {true} | false ]. % true - the last taper/eigenvector is dropped % false - the last taper/eigenvector is preserved % % [Pxx,F,Pxxc] = PMTM(...,'ConfidenceLevel',P) returns the P*100% % confidence interval for Pxx, where P is a scalar between 0 and 1. The % default value for P is .95. Confidence intervals are computed using a % chi-squared approach. Pxxc has twice as many columns as Pxx. % Odd-numbered columns contain the lower bounds of the confidence % intervals; even-numbered columns contain the upper bounds. Thus, % Pxxc(M,2*N-1) is the lower bound and Pxxc(M,2*N) is the upper bound % corresponding to the estimate Pxx(M,N). % % [...] = PMTM(X,...,FREQRANGE) returns the PSD over the specified range % of frequencies based upon the value of FREQRANGE: % % 'onesided' - returns the one-sided PSD of a real input signal X. % If NFFT is even, Pxx has length NFFT/2+1 and is computed over the % interval [0,pi]. If NFFT is odd, Pxx has length (NFFT+1)/2 and % is computed over the interval [0,pi). When Fs is specified, the % intervals become [0,Fs/2) and [0,Fs/2] for even and odd NFFT, % respectively. % % 'twosided' - returns the two-sided PSD for either real or complex % input X. Pxx has length NFFT and is computed over the interval % [0,2*pi). When Fs is specified, the interval becomes [0,Fs). % % 'centered' - returns the centered two-sided PSD for either real or % complex X. Pxx has length NFFT and is computed over the interval % (-pi, pi] for even length NFFT and (-pi, pi) for odd length NFFT. % When Fs is specified, the intervals become (-Fs/2, Fs/2] and % (-Fs/2, Fs/2) for even and odd length NFFT, respectively. % % FREQRANGE may be placed in any position in the input argument list % after the second input argument, unless E and V are specified, in % which case FREQRANGE may be placed in any position after the third % input argument. The default value of FREQRANGE is 'onesided' when X % is real and 'twosided' when X is complex. % % PMTM(...) with no output arguments plots the PSD estimate (in decibels % per unit frequency) in the current figure window. % % EXAMPLE: % Fs = 1000; t = 0:1/Fs:.3; % x = cos(2*pi*t*200)+randn(size(t)); % A cosine of 200Hz plus noise % pmtm(x,3.5,[],Fs); % Uses the default NFFT. % % See also DPSS, PWELCH, PERIODOGRAM, PMUSIC, PBURG, PYULEAR, PCOV, % PMCOV, PEIG.% References: % [1] Thomson, D.J."Spectrum estimation and harmonic analysis." % In Proceedings of the IEEE. Vol. 10 (1982). pp. 1055-1096. % [2] Percival, D.B. and Walden, A.T., "Spectral Analysis For Phy ical % Applications", Cambridge University Press, 1993, pp. 368-370. % Copyright 1988-2014 The MathWorks, Inc. 與50位技術專家面對面20年技術見證，附贈技術全景圖

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