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.
Return to main page
Return to page index
COPYRIGHT © 2007 Cuthbert Nyack.