MATLAB: Scaling for periodic signal using hann window

hann windowscaling

How can i scale for periodic signal using hann window. i know for flattop i.e 1/sum(window)but i do not know how to scale with hann window with a periodic signal. kindly help

Best Answer

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));

Related Solutions

MATLAB: Fft dosen’t conserve energy

From the fft documentation:

Y = fft(X,n) returns the n-point DFT. If no value is specified, Y is the same size as X.

If X is a vector and the length of X is less than n, then X is padded with trailing zeros to length n.
If X is a vector and the length of X is greater than n, then X is truncated to length n.

The original ‘x’ has a length of 101. That is not compromised in the computation of ‘Y1’ becasue zero-padding simply increases the frequency resolution. The length of ‘x’ in ‘Y2’ is 64, so 37 elements of the original signal have been removed before the Fourier transform was calculated.

To illustrate:

Y1 = fft(x,nfft1)*dt; 
Y2 = fft(x,nfft2)*dt; % Fourier transforms
Y3 = fft(x(1:64))*dt; % Truncate First
Y1Y2 = mean(abs(Y1)) - mean(abs(Y2))
Y2Y3 = mean(abs(Y2)) - mean(abs(Y3))

produces:

Y1Y2 =
  -0.003722334257938
Y2Y3 =
     0

There is no difference between ‘Y2’ and ‘Y3’. (The small difference between ‘Y1’ and ‘Y2’ is the effect of zero-padding in creating a longer ‘Y1’ vector without changing any of the other elements.)

MATLAB: Hanning Window

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.

Best Answer

Related Solutions

MATLAB: Fft dosen’t conserve energy

MATLAB: Hanning Window

Related Question