`scipy.signal._czt:ZoomFFT`

source: /scipy/signal/_czt.py :275

Signature

   class     ZoomFFT (    n    ,    fn    ,    m    =  None   ,  * ,     fs    =  2   ,    endpoint    =  False     )

Members

__init__

Summary

Create a callable zoom FFT transform function.

Extended Summary

This is a specialization of the chirp z-transform (CZT) for a set of equally-spaced frequencies around the unit circle, used to calculate a section of the FFT more efficiently than calculating the entire FFT and truncating.

Parameters

n : int: The size of the signal.
fn : array_like: A length-2 sequence [f1, f2] giving the frequency range, or a scalar, for which the range [0, fn] is assumed.
m : int, optional: The number of points to evaluate. Default is n.
fs : float, optional: The sampling frequency. If fs=10 represented 10 kHz, for example, then f1 and f2 would also be given in kHz. The default sampling frequency is 2, so f1 and f2 should be in the range [0, 1] to keep the transform below the Nyquist frequency.
endpoint : bool, optional: If True, f2 is the last sample. Otherwise, it is not included. Default is False.

Returns

f : ZoomFFT: Callable object f(x, axis=-1) for computing the zoom FFT on x.

Notes

The defaults are chosen such that f(x, 2) is equivalent to fft.fft(x) and, if m > len(x), that f(x, 2, m) is equivalent to fft.fft(x, m).

Sampling frequency is 1/dt, the time step between samples in the signal x. The unit circle corresponds to frequencies from 0 up to the sampling frequency. The default sampling frequency of 2 means that f1, f2 values up to the Nyquist frequency are in the range [0, 1). For f1, f2 values expressed in radians, a sampling frequency of 2*pi should be used.

Remember that a zoom FFT can only interpolate the points of the existing FFT. It cannot help to resolve two separate nearby frequencies. Frequency resolution can only be increased by increasing acquisition time.

These functions are implemented using Bluestein's algorithm (as is scipy.fft). ^[2]

Array API Standard Support

ZoomFFT has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ⛔                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

To plot the transform results use something like the following:

import numpy as np
from scipy.signal import ZoomFFT
t = np.linspace(0, 1, 1021)
x = np.cos(2*np.pi*15*t) + np.sin(2*np.pi*17*t)
f1, f2 = 5, 27
transform = ZoomFFT(len(x), [f1, f2], len(x), fs=1021)
X = transform(x)
f = np.linspace(f1, f2, len(x))
import matplotlib.pyplot as plt

✓

plt.plot(f, 20*np.log10(np.abs(X)))

✗

plt.show()

✓

`scipy.signal._czt:ZoomFFT`

Signature

Members

Summary

Extended Summary

Parameters

Returns

Notes

Examples

See also

Aliases

Referenced by

This package