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.

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.

Frequency-swept cosine generator.

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

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()

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

def plot_spectrogram(title, w, fs):
    ff, tt, Sxx = spectrogram(w, fs=fs, nperseg=256, nfft=576)
    fig, ax = plt.subplots()
    ax.pcolormesh(tt, ff[:145], Sxx[:145], cmap='gray_r',
                  shading='gouraud')
    ax.set_title(title)
    ax.set_xlabel('t (sec)')
    ax.set_ylabel('Frequency (Hz)')
    ax.grid(True)

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()

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()

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()

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()