cupyx.scipy.signal.chirp#

cupyx.scipy.signal.chirp(t, f0, t1, f1, method='linear', phi=0, vertex_zero=True)[source]#

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 – 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.

Return type:

ndarray

Examples

The following will be used in the examples:

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

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

>>> t = cupy.linspace(0, 10, 5001)
>>> w = chirp(t, f0=6, f1=1, t1=10, method='linear')
>>> plt.plot(cupy.asnumpy(t), cupy.asnumpy(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 cupyx.scipy.signal.spectrogram. We’ll use a 10 second interval sampled at 8000 Hz.

>>> fs = 8000
>>> T = 10
>>> t = cupy.linspace(0, T, T*fs, endpoint=False)

Quadratic chirp from 1500 Hz to 250 Hz over 10 seconds (vertex of the parabolic curve of the frequency is at t=0):

>>> w = chirp(t, f0=1500, f1=250, t1=10, method='quadratic')
>>> ff, tt, Sxx = spectrogram(w, fs=fs, noverlap=256, nperseg=512,
...                           nfft=2048)
>>> plt.pcolormesh(cupy.asnumpy(tt), cupy.asnumpy(ff[:513]),
                   cupy.asnumpy(Sxx[:513]), cmap='gray_r')
>>> plt.title('Quadratic Chirp, f(0)=1500, f(10)=250')
>>> plt.xlabel('t (sec)')
>>> plt.ylabel('Frequency (Hz)')
>>> plt.grid()
>>> plt.show()