czt

czt — chirp z-transform algorithm

Calling sequence

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

Parameters

`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

Author

C. Bunks