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# scipy.signal.chirp

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

  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.waveforms.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.