given a N-point window h(n), how do I create an oversampled Fourier
transform H out of h(n)? I need to have very high resolution of the H so
that I can find out the magnitude of arbitrary frequency with little
frequency error.
This is what I did: to oversample h(n) with factor 2, I first sampled the
window h with N * 2 points, and then simply FFT the 'new h' with N*2-point.
But the H with N*2 points looks very different from H with N points. What
am I doing wrong?
Here is detailed description with some sample output of the original and
oversampled fft
This is my windowing function:
*function blackman(N)*
a0 = 0.42659;
a1 = 0.49656;
a2 = 0.076849;
w = zeros(N);
for n = 1:N
w[n] = a0 - a1 * cos(2*pi*n/(N-1)) + a2 * cos(4*pi*n/(N-1));
end
return w;
end
I assume an oversampled fft of the window function by a factor of 2 would
be *fft(blackman(N*2))*
However, the fft values of the original and the oversampled value aren't
increasing/decreasing in a similar way (I expect the oversampled version to
takes twice as much samples to increase and decrease, in case the
over-sample factor is 2).
Here are some the fft sample values from 1 - 10. the original is
FFT(blackman(512)), the oversampled is FFT(blackman(512 * 2))
k = 1
original: 217.9943833003818 + 0.0im
oversampled: 873.2366098911153 + 0.0im
k = 2
original: -127.11893711697411 - 2.340240508514901im
oversampled: -508.4935935475258 - 2.3400747304536136im
k = 3
original: 19.845020222085132 + 0.7309352010595286im
oversampled: 78.87486492124337 + 0.7259756614936985im
k = 4
original: 0.00044320678301414774 + 2.423663020980352e-5im
oversampled: 0.0005516543659794568 + 7.61242746175689e-6im
k = 5
original: 0.007485288714345478 + 0.0005517961643643162im
oversampled: 0.00748836292444639 + 0.00013785416101184825im
k = 6
original: 0.0060558634779024605 + 0.000558513387226844im
oversampled: 0.00605535370050697 + 0.00013934970191932598im
k = 7
original: 0.004581346143077173 + 0.0005075321354533686im
oversampled: 0.004584081103264545 + 0.0001265980340830028im
k = 8
original: 0.0035101418651299794 + 0.0004541979779443242im
oversampled: 0.003516027383715841 + 0.0001132935089731223im
k = 9
original: 0.0027517589243924367 + 0.00040747551324277084im
oversampled: 0.0027600729094881945 + 0.00010164856218561597im
k = 10
original: 0.002205670972923391 + 0.0003679932983093956im
oversampled: 0.0022158009449307643 + 9.181309340287595e-5im
What's wrong with my approach?
Thanks in advance!
--
dupswapdrop -- the music-dsp mailing list and website:
subscription info, FAQ, source code archive, list archive, book reviews, dsp
links
http://music.columbia.edu/cmc/music-dsp
http://music.columbia.edu/mailman/listinfo/music-dsp
