Module « scipy.signal »

Fonction sweep_poly - module scipy.signal

Signature de la fonction sweep_poly

def sweep_poly(t, poly, phi=0) 

Description

sweep_poly.__doc__

    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.

    >>> 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()