Hanning Window

[Emil09]

I know how to find the amplitude spectrum of a sine wave

t=(0:99)/100;
S=sin(2*pi*25*t);
Y=fft(S);
plot(abs(Y))

and I know how to generate a Hanning window

n=100;
whann=hanning(n);
[Px,f]=freqz(whann/sum(whann),1,512,2);
plot(f,20*log10(abs(Px)))

but how do I use a Hanning window to plot the amplitude spectrum of a sine wave?
I've tried all kinds of variations on what I would imagine should work but it just doesn't happen.

 

[dougy83]

The hanning window is applied to the time-domain data first, and then the data is passed to fft(). Because the sample you are using may have discontinuities (large assumed jumps) at the beginning and end of the sample, this puts unwanted harmonics into your fft - the hanning et al. windows reduce the size of the discontinuity.

So, your first example, but applying the hanning window:

t=(0:99)/100;
S=sin(2*pi*25*t);
Y=fft(S .* hanning(length(S))');
plot(abs(Y))

 

[Emil09]

The hanning window is applied to the time-domain data first, and then the data is passed to fft(). Because the sample you are using may have discontinuities (large assumed jumps) at the beginning and end of the sample, this puts unwanted harmonics into your fft - the hanning et al. windows reduce the size of the discontinuity.

So, your first example, but applying the hanning window:

t=(0:99)/100;
S=sin(2*pi*25*t);
Y=fft(S .* hanning(length(S))');
plot(abs(Y))

Thanks. I was surprised to see that it looks almost identical to the plot without the Hanning window.