Module « scipy.signal »

Fonction chirp - module scipy.signal

Signature de la fonction chirp

def chirp(t, f0, t1, f1, method='linear', phi=0, vertex_zero=True) 

Description

chirp.__doc__

Frequency-swept cosine generator.

    In the following, 'Hz' should be interpreted as 'cycles per unit';
    there is no requirement here that the unit is one second.  The
    important distinction is that the units of rotation are cycles, not
    radians. Likewise, `t` could be a measurement of space instead of time.

    Parameters
    ----------
    t : array_like
        Times at which to evaluate the waveform.
    f0 : float
        Frequency (e.g. Hz) at time t=0.
    t1 : float
        Time at which `f1` is specified.
    f1 : float
        Frequency (e.g. Hz) of the waveform at time `t1`.
    method : {'linear', 'quadratic', 'logarithmic', 'hyperbolic'}, optional
        Kind of frequency sweep.  If not given, `linear` is assumed.  See
        Notes below for more details.
    phi : float, optional
        Phase offset, in degrees. Default is 0.
    vertex_zero : bool, optional
        This parameter is only used when `method` is 'quadratic'.
        It determines whether the vertex of the parabola that is the graph
        of the frequency is at t=0 or t=t1.

    Returns
    -------
    y : 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 below.

    See Also
    --------
    sweep_poly

    Notes
    -----
    There are four options for the `method`.  The following formulas give
    the instantaneous frequency (in Hz) of the signal generated by
    `chirp()`.  For convenience, the shorter names shown below may also be
    used.

    linear, lin, li:

        ``f(t) = f0 + (f1 - f0) * t / t1``

    quadratic, quad, q:

        The graph of the frequency f(t) is a parabola through (0, f0) and
        (t1, f1).  By default, the vertex of the parabola is at (0, f0).
        If `vertex_zero` is False, then the vertex is at (t1, f1).  The
        formula is:

        if vertex_zero is True:

            ``f(t) = f0 + (f1 - f0) * t**2 / t1**2``

        else:

            ``f(t) = f1 - (f1 - f0) * (t1 - t)**2 / t1**2``

        To use a more general quadratic function, or an arbitrary
        polynomial, use the function `scipy.signal.sweep_poly`.

    logarithmic, log, lo:

        ``f(t) = f0 * (f1/f0)**(t/t1)``

        f0 and f1 must be nonzero and have the same sign.

        This signal is also known as a geometric or exponential chirp.

    hyperbolic, hyp:

        ``f(t) = f0*f1*t1 / ((f0 - f1)*t + f1*t1)``

        f0 and f1 must be nonzero.

    Examples
    --------
    The following will be used in the examples:

    >>> from scipy.signal import chirp, spectrogram
    >>> import matplotlib.pyplot as plt

    For the first example, we'll plot the waveform for a linear chirp
    from 6 Hz to 1 Hz over 10 seconds:

    >>> t = np.linspace(0, 10, 1500)
    >>> w = chirp(t, f0=6, f1=1, t1=10, method='linear')
    >>> plt.plot(t, w)
    >>> plt.title("Linear Chirp, f(0)=6, f(10)=1")
    >>> plt.xlabel('t (sec)')
    >>> plt.show()

    For the remaining examples, we'll use higher frequency ranges,
    and demonstrate the result using `scipy.signal.spectrogram`.
    We'll use a 4 second interval sampled at 7200 Hz.

    >>> fs = 7200
    >>> T = 4
    >>> t = np.arange(0, int(T*fs)) / fs

    We'll use this function to plot the spectrogram in each example.

    >>> def plot_spectrogram(title, w, fs):
    ...     ff, tt, Sxx = spectrogram(w, fs=fs, nperseg=256, nfft=576)
    ...     plt.pcolormesh(tt, ff[:145], Sxx[:145], cmap='gray_r', shading='gouraud')
    ...     plt.title(title)
    ...     plt.xlabel('t (sec)')
    ...     plt.ylabel('Frequency (Hz)')
    ...     plt.grid()
    ...

    Quadratic chirp from 1500 Hz to 250 Hz
    (vertex of the parabolic curve of the frequency is at t=0):

    >>> w = chirp(t, f0=1500, f1=250, t1=T, method='quadratic')
    >>> plot_spectrogram(f'Quadratic Chirp, f(0)=1500, f({T})=250', w, fs)
    >>> plt.show()

    Quadratic chirp from 1500 Hz to 250 Hz
    (vertex of the parabolic curve of the frequency is at t=T):

    >>> w = chirp(t, f0=1500, f1=250, t1=T, method='quadratic',
    ...           vertex_zero=False)
    >>> plot_spectrogram(f'Quadratic Chirp, f(0)=1500, f({T})=250\n' +
    ...                  '(vertex_zero=False)', w, fs)
    >>> plt.show()

    Logarithmic chirp from 1500 Hz to 250 Hz:

    >>> w = chirp(t, f0=1500, f1=250, t1=T, method='logarithmic')
    >>> plot_spectrogram(f'Logarithmic Chirp, f(0)=1500, f({T})=250', w, fs)
    >>> plt.show()

    Hyperbolic chirp from 1500 Hz to 250 Hz:

    >>> w = chirp(t, f0=1500, f1=250, t1=T, method='hyperbolic')
    >>> plot_spectrogram(f'Hyperbolic Chirp, f(0)=1500, f({T})=250', w, fs)
    >>> plt.show()