# 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.

# 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:

Wolfram Research (2012), DiscreteChirpZTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteChirpZTransform.html.

#### Text

Wolfram Research (2012), DiscreteChirpZTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteChirpZTransform.html.

#### CMS

Wolfram Language. 2012. "DiscreteChirpZTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DiscreteChirpZTransform.html.

#### APA

Wolfram Language. (2012). DiscreteChirpZTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiscreteChirpZTransform.html

#### BibTeX

@misc{reference.wolfram_2021_discretechirpztransform, author="Wolfram Research", title="{DiscreteChirpZTransform}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/DiscreteChirpZTransform.html}", note=[Accessed: 17-January-2022 ]}

#### BibLaTeX

@online{reference.wolfram_2021_discretechirpztransform, organization={Wolfram Research}, title={DiscreteChirpZTransform}, year={2012}, url={https://reference.wolfram.com/language/ref/DiscreteChirpZTransform.html}, note=[Accessed: 17-January-2022 ]}