# cupyx.scipy.signal.czt#

cupyx.scipy.signal.czt(x, m=None, w=None, a=1 + 0j, *, axis=-1)[source]#

Compute the frequency response around a spiral in the Z plane.

Parameters
• x (array) – The signal to transform.

• m (int, optional) – The number of output points desired. Default is the length of the input data.

• w (complex, optional) – The ratio between points in each step. This must be precise or the accumulated error will degrade the tail of the output sequence. Defaults to equally spaced points around the entire unit circle.

• a (complex, optional) – The starting point in the complex plane. Default is 1+0j.

• axis (int, optional) – Axis over which to compute the FFT. If not given, the last axis is used.

Returns

out – An array of the same dimensions as x, but with the length of the transformed axis set to m.

Return type

ndarray

`CZT`

Class that creates a callable chirp z-transform function.

`zoom_fft`

Convenience function for partial FFT calculations.

`scipy.signal.czt`

Notes

The defaults are chosen such that `signal.czt(x)` is equivalent to `fft.fft(x)` and, if `m > len(x)`, that `signal.czt(x, m)` is equivalent to `fft.fft(x, m)`.

If the transform needs to be repeated, use CZT to construct a specialized transform function which can be reused without recomputing constants.

An example application is in system identification, repeatedly evaluating small slices of the z-transform of a system, around where a pole is expected to exist, to refine the estimate of the pole’s true location. 1

References

1

Steve Alan Shilling, “A study of the chirp z-transform and its applications”, pg 20 (1970) https://krex.k-state.edu/dspace/bitstream/handle/2097/7844/LD2668R41972S43.pdf