MATLAB: Hanning Window

hann window function

Why is the Hanning window function best for random signal analysis?

Best Answer

Hi Lisa, I don't whether I would say it's definitely "best". That is a hard thing to say, but the general rationale is that the Hanning, or Hann window is a good compromise between main lobe width, which determines frequency resolution, and side lobe level, which governs spectral leakage.

As you reduce the side lobe levels, you inevitably worsen frequency resolution by increasing the width of the main lobe.

Conversely, as you narrow the main lobe, you inevitably raise the side lobe level.

The Hann window is in a good middle ground on both measures among the commonly-used windows.

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MATLAB: Scaling for periodic signal using hann window

Hi Lisa, it should be the same:

t = 0:0.001:1-0.001;
xn = cos(2*pi*100*t);
w = hanning(length(xn));
x = xn'.*w; 
sc = 1/sum(w);
xdft = fft(xn);
xdft = xdft(1:length(xn)/2+1);
y = sc*xdft;
plot(abs(y));

MATLAB: FFT Spectrum or Welch Spectrum

Hi, Are you attempting to say that you wrote your own Welch overlapped segment averaging routine? The WOSA estimator is an estimate of the power spectral density.

The Welch estimate does result in a broadening of the peaks, which may explain the slight frequency shift you see. If you are attempting to identify a particular frequency then the periodogram has the best frequency resolution of any nonparametric estimator.

For example:

Fs = 1e3;
t = 0:1/Fs:1-1/Fs;
x = cos(2*pi*100*t)+randn(size(t));
psdPer = psd(spectrum.periodogram,x,'Fs',Fs,'NFFT',length(x));
% Welch estimate
hwelch = spectrum.welch;
% 5-Hz DFT bin spacing
hwelch.SegmentLength = 200;
psdWOSA = psd(hwelch,x,'Fs',Fs,'NFFT',hwelch.SegmentLength);
plot(psdPer);
figure;
plot(psdWOSA);

Best Answer

Related Solutions

MATLAB: Scaling for periodic signal using hann window

MATLAB: FFT Spectrum or Welch Spectrum

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