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

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.

Notes

There are four options for the method . The following formulas give the instantaneous frequency (in Hz) of the signal generated by :None:None:`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 :None:None:`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.

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 :None:None:`f1` is specified.

f1 : float

Frequency (e.g. Hz) of the waveform at time :None:None:`t1`.

method : {'linear', 'quadratic', 'logarithmic', 'hyperbolic'}, optional

Kind of frequency sweep. If not given, :None:None:`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 :None:None:`phase` is the integral (from 0 to t) of 2*pi*f(t) . f(t) is defined below.

Frequency-swept cosine generator.

See Also

sweep_poly

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()

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.signal._waveforms.chirp scipy.signal._waveforms._chirp_phase scipy.signal._waveforms.sweep_poly scipy.signal._signaltools.hilbert scipy.signal._peak_finding.peak_widths

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