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Module « scipy.signal »

Fonction sweep_poly - module scipy.signal

Signature de la fonction sweep_poly

def sweep_poly(t, poly, phi=0) 

Description

help(scipy.signal.sweep_poly)

Frequency-swept cosine generator, with a time-dependent frequency.

This function generates a sinusoidal function whose instantaneous
frequency varies with time.  The frequency at time `t` is given by
the polynomial `poly`.

Parameters
----------
t : ndarray
    Times at which to evaluate the waveform.
poly : 1-D array_like or instance of numpy.poly1d
    The desired frequency expressed as a polynomial.  If `poly` is
    a list or ndarray of length n, then the elements of `poly` are
    the coefficients of the polynomial, and the instantaneous
    frequency is

      ``f(t) = poly[0]*t**(n-1) + poly[1]*t**(n-2) + ... + poly[n-1]``

    If `poly` is an instance of numpy.poly1d, then the
    instantaneous frequency is

      ``f(t) = poly(t)``

phi : float, optional
    Phase offset, in degrees, Default: 0.

Returns
-------
sweep_poly : ndarray
    A numpy array containing the signal evaluated at `t` with the
    requested time-varying frequency.  More precisely, the function
    returns ``cos(phase + (pi/180)*phi)``, where `phase` is the integral
    (from 0 to t) of ``2 * pi * f(t)``; ``f(t)`` is defined above.

See Also
--------
chirp

Notes
-----
.. versionadded:: 0.8.0

If `poly` is a list or ndarray of length `n`, then the elements of
`poly` are the coefficients of the polynomial, and the instantaneous
frequency is:

    ``f(t) = poly[0]*t**(n-1) + poly[1]*t**(n-2) + ... + poly[n-1]``

If `poly` is an instance of `numpy.poly1d`, then the instantaneous
frequency is:

      ``f(t) = poly(t)``

Finally, the output `s` is:

    ``cos(phase + (pi/180)*phi)``

where `phase` is the integral from 0 to `t` of ``2 * pi * f(t)``,
``f(t)`` as defined above.

Examples
--------
Compute the waveform with instantaneous frequency::

    f(t) = 0.025*t**3 - 0.36*t**2 + 1.25*t + 2

over the interval 0 <= t <= 10.

>>> import numpy as np
>>> from scipy.signal import sweep_poly
>>> p = np.poly1d([0.025, -0.36, 1.25, 2.0])
>>> t = np.linspace(0, 10, 5001)
>>> w = sweep_poly(t, p)

Plot it:

>>> import matplotlib.pyplot as plt
>>> plt.subplot(2, 1, 1)
>>> plt.plot(t, w)
>>> plt.title("Sweep Poly\nwith frequency " +
...           "$f(t) = 0.025t^3 - 0.36t^2 + 1.25t + 2$")
>>> plt.subplot(2, 1, 2)
>>> plt.plot(t, p(t), 'r', label='f(t)')
>>> plt.legend()
>>> plt.xlabel('t')
>>> plt.tight_layout()
>>> plt.show()

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