MATLAB: Paramerer setting for pmtm() multitaper method

multitaper; psd; spectral analysis

Hi all, I'm trying to do spectral analysis by pmtm method:
clear
clc; close all
% artificial data
Fs = 300;                    % Sampling frequency
T = 1/Fs;                     % Sample time
L = 3000;                     % Length of signal
t = (0:L-1)*T;                % Time vector
% Sum of a 50 Hz sinusoid and a 120 Hz sinusoid
x = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t); 
y = x + 3*randn(size(t));     % Sinusoids plus noise
y=y(:);
% Spectral analysis
T = 0.5; % sec
W = 3; % -Hz
% Matlab multitaper method
nw = T*W;  % nw is the time-bandwidth product 
[Pxx, f] = pmtm(y, nw, [], Fs); 
plot(f, Pxx) % PSD
title('Spectral analysis by Matlab')
The graph looks fine, but actually, I have no ideas to set T and W. I just randomly put some numbers there. Could anyone please explain as simple as possible that how to select T and W, also how many tapers should be implemented to a specified signal (with unknown frequency of cause in a practical case).
Many thanks for any help Kyle

Best Answer

Hi Kyle, the mainlobe is approximately [-w/n, w/n]*Fs in Hz where Fs is your sampling frequency. For a given time-bandwidth product, nw, there are approximately 2*nw-1 Slepian tapers that have eigenvalues near unity, meaning that they have approximately all their energy in the bandwidth [-w/n,w/n]*Fs. The eigenvalue gives the proportion of energy in that band. To follow up on what Honglei wrote, as you increase your nw, you can use more tapers (because more of them will have eigenvalues near 1). Using more tapers increases the degrees of freedom and reduces the variance of your spectal estimate (it looks smoother), but widens the main lobe so you will less precisely localize the frequency of a peak and if there are multiple peaks within the mainlobe, those peaks can be smeared together (meaning multiple peaks may look like broad one).
Wayne
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