DiscreteChirpZTransform

DiscreteChirpZTransform[list]

gives the chirp Z transform of list.

DiscreteChirpZTransform[list,n]

returns a length n chirp Z transform.

DiscreteChirpZTransform[list,n,w]

uses a spiral path on the complex plane defined by w.

DiscreteChirpZTransform[list,n,w,a]

uses a as the complex starting point.

DiscreteChirpZTransform[list,{n1,n2,},{w1,w2,},{a1,a2,}]

gives the multidimensional chirp Z transform.

Details • The chirp Z transform is an algorithm for evaluating the list Z transform of a finite duration sequence along a spiral path in the plane of the form . With DiscreteChirpZTransform[list,n,w,a], the Z transform is evaluated at points for integers from 0 to .
• DiscreteChirpZTransform[list] is equivalent to DiscreteChirpZTransform[list,Length[list]].
• DiscreteChirpZTransform[list,n] is equivalent to DiscreteChirpZTransform[list,n,Exp[2π /n],1].
• DiscreteChirpZTransform[list] is equivalent to Fourier[list,FourierParameters->{1,-1}]. »

Examples

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Basic Examples(1)

Chirp Z transform of a list:

Scope(3)

Return a length 16 chirp Z transform:

Evaluate the transform on a spiral path:

Specify a starting point:

Applications(2)

Improve the resolution of the discrete Fourier transform:

Compare the two discrete Fourier spectra:

Zoom into a portion of the spectrum, in the range from ω1 to ω2 in steps of Δω:

Properties & Relations(4)

DiscreteChirpZTransform[list] is equivalent to Fourier[list,FourierParameters->{1,-1}]:

DiscreteChirpZTransform[list,n] is equivalent to evaluating the Z transform of list on a circular path defined by for k from 0 to n-1:

DiscreteChirpZTransform[list,n,w,a] is equivalent to evaluating the Z transform of list on a spiral path defined by for k from 0 to n-1:

Visualize the spiral path :

DiscreteChirpZTransform is faster compared to the explicit sampling of the Z transform:

Neat Examples(1)

Define Z transform of a finite duration constant sequence:

Compute the chirp Z transform of the sequence and the complex plane contour:

Plot the magnitude and path of the chirp Z transform on the complex plane: