window — compute symmetric window of various type
win_l=window('re',n)
win_l=window('tr',n)
win_l=window('hn',n)
win_l=window('hm',n)
win_l=window('kr',n,alpha)
[win_l,cwp]=window('ch',n,par)window length
parameter 2-vector par=[dp,df]), where
dp (0<dp<.5) rules the main lobe
width and df rules the side lobe height
(df>0).
Only one of these two value should be specified the other one
should set equal to -1.
kaiser window parameter alpha >0).
window
unspecified Chebyshev window parameter
function which calculates various symmetric window for Disgital signal processing
The Kaiser window is a nearly optimal window function. alpha
is an arbitrary positive real number that determines the shape of the
window, and the integer n is the length of the window.
By construction, this function peaks at unity for k = n/2 ,
i.e. at the center of the window, and decays exponentially towards the
window edges. The larger the value of alpha, the narrower
the window becomes; alpha = 0 corresponds to a rectangular window.
Conversely, for larger alpha the width of the main lobe
increases in the Fourier transform, while the side lobes decrease in
amplitude.
Thus, this parameter controls the tradeoff between main-lobe width and
side-lobe area.
| alpha | window shape |
| 0 | Rectangular shape |
| 5 | Similar to the Hamming window |
| 6 | Similar to the Hanning window |
| 8.6 | Similar to the Blackman window |
The Chebyshev window minimizes the mainlobe width, given a particular sidelobe height. It is characterized by an equiripple behavior, that is, its sidelobes all have the same height.
The Hanning and Hamming windows are quite similar, they only differ in
the choice of one parameter alpha:
w=alpha+(1 - alpha)*cos(2*%pi*x/(n-1))
alpha is equal to 1/2 in Hanning window and to 0.54 in
Hamming window.
// Hamming window
clf()
N=64;
w=window('hm',N);
subplot(121);plot2d(1:N,w,style=color('blue'))
set(gca(),'grid',[1 1]*color('gray'))
subplot(122)
n=256;[W,fr]=frmag(w,n);
plot2d(fr,20*log10(W),style=color('blue'))
set(gca(),'grid',[1 1]*color('gray'))
//Kaiser window
clf()
N=64;
w=window('kr',N,6);
subplot(121);plot2d(1:N,w,style=color('blue'))
set(gca(),'grid',[1 1]*color('gray'))
subplot(122)
n=256;[W,fr]=frmag(w,n);
plot2d(fr,20*log10(W),style=color('blue'))
set(gca(),'grid',[1 1]*color('gray'))
//Chebyshev window
clf()
N=64;
[w,df]=window('ch',N,[0.005,-1]);
subplot(121);plot2d(1:N,w,style=color('blue'))
set(gca(),'grid',[1 1]*color('gray'))
subplot(122)
n=256;[W,fr]=frmag(w,n);
plot2d(fr,20*log10(W),style=color('blue'))
set(gca(),'grid',[1 1]*color('gray'))