czt

chirp z-transform algorithm

Calling Sequence

[czx]=czt(x,m,w,phi,a,theta)

Arguments

:x input data sequence : :m czt is evaluated at m points in z-plane : :w magnitude multiplier : :phi phase increment : :a initial magnitude : :theta initial phase : :czx chirp z-transform output :

Description

chirp z-transform algorithm which calcultes the z-transform on a spiral in the z-plane at the points [a*exp(j*theta)][w^kexp(j*k*phi)] for k=0,1,...,m-1.

Examples

a=.7*`exp`_(%i*%pi/6);
[ffr,bds]=`xgetech`_(); //preserve current context
rect=[-1.2,-1.2*`sqrt`_(2),1.2,1.2*`sqrt`_(2)];
t=2*%pi*(0:179)/179;`xsetech`_([0,0,0.5,1]);
`plot2d`_(`sin`_(t)',`cos`_(t)',[2],"012",' ',rect)
`plot2d`_([0 `real`_(a)]',[0 `imag`_(a)]',[3],"000")
`xsegs`_([-1.0,0;1.0,0],[0,-1.0;0,1.0])
w0=.93*`exp`_(-%i*%pi/15);w=`exp`_(-(0:9)*`log`_(w0));z=a*w;
zr=`real`_(z);zi=`imag`_(z);
`plot2d`_(zr',zi',[5],"000")
`xsetech`_([0.5,0,0.5,1]);
`plot2d`_(`sin`_(t)',`cos`_(t)',[2],"012",' ',rect)
`plot2d`_([0 `real`_(a)]',[0 `imag`_(a)]',[-1],"000")
`xsegs`_([-1.0,0;1.0,0],[0,-1.0;0,1.0])
w0=w0/(.93*.93);w=`exp`_(-(0:9)*`log`_(w0));z=a*w;
zr=`real`_(z);zi=`imag`_(z);
`plot2d`_(zr',zi',[5],"000")
`xsetech`_(ffr,bds); //restore context