window

Arguments

n

window length

par

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.

alpha

kaiser window parameter alpha >0).

win

window

cwp

unspecified Chebyshev window parameter

Description

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.

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.

Examples

// 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'))

See Also

• wfir — linear-phase FIR filters
• frmag — magnitude of FIR and IIR filters
• ffilt — coefficients of FIR low-pass

Authors

Carey Bunks

Bibliography

IEEE. Programs for Digital Signal Processing. IEEE Press. New York: John Wiley and Sons, 1979. Program 5.2.