czt

Scilab Function
Last update : 25/04/2007

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