DFT, 1 Sinusoid with Hamming, Kaiser Windows.

Cuthbert Nyack
The Hamming window is defined as :- w(t) = 0.54 + 0.46 * cos(2tp/t)

In this applet a section of a sinusoid from T1 to T2 is sampled and the DTFT and DFT calculated. The variation of the spectra as T1, T2 are changed is illustrated. The spectra when a Hamming window is applied to the signal is also shown.

eg parameters:-
(3.0, NA, 0.01, 20.5, 50, 0, 25, 10.0, 48.5, 0.28), here the non-windowed spectra shows one peak, while the windowed spectra shows 3 lines with the peak only half that of the non-windowed spectra.
(3.0, NA, 0.01, 19.41, 50, 0, 25, 10.0, 48.5, 0.28), here the non-windowed spectra shows many peaks, while the windowed spectra shows 4 lines. The width of the windowed spectrum remains constant when n or n + ½ periods are sampled.
The window decreases the amplitude of the lines in the spectra and increases the width of the spectrum when n periods are sampled. On the other hand it considerably reduces the width of the spectrum when an nonintegral number of periods are sampled or when there are sharp jumps at the edges of the sampling interval.

Changing Fn to 1 shows the spectra on a log scale with 20dB/div.



The Kaiser window is defined as :- w(t) = Io[q(1 - (2t/t)2)½]/ Io(q)

In this applet a section of a sinusoid from T1 to T2 is sampled and the DTFT and DFT calculated. The variation of the spectra as T1, T2 are changed is illustrated. The spectra when a Kaiser window is applied to the signal is also shown. The Kaiser window has a variable parameter q. Increasing q increases the bandwith of the central lobe and increases the attenuation of the side lobes.

eg parameters:-(3.0, NA, 0.01, 8.04, 50, 0.01p, 25, 734.0, 15.0, 0.38)
For q ~ 0, the Kaiser window becomes the Rectangular window, with DTFT = 0.467 at 18.76rad/s.
Increasing q to p reduces the DTFT to 0.077. With q to 3.0p, the DTFT has decreased to ~4E-5.



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COPYRIGHT 2007 Cuthbert Nyack.