Classe « ZoomFFT »

Informations générales

Héritage

builtins.object
    CZT
        ZoomFFT

Définition

class ZoomFFT(CZT):

help(ZoomFFT)

Create a callable zoom FFT transform function.

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`.

See Also
--------
zoom_fft : Convenience function for calculating a zoom FFT.

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]_

References
----------
.. [1] Steve Alan Shilling, "A study of the chirp z-transform and its
       applications", pg 29 (1970)
       https://krex.k-state.edu/dspace/bitstream/handle/2097/7844/LD2668R41972S43.pdf
.. [2] Leo I. Bluestein, "A linear filtering approach to the computation
       of the discrete Fourier transform," Northeast Electronics Research
       and Engineering Meeting Record 10, 218-219 (1968).

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()