# scipy.signal.czt_points

scipy.signal.czt_points(m, w=None, a=1 + 0j)

  Return the points at which the chirp z-transform is computed.

  Parameters:
    m int

      The number of points desired.

    w complex, optional

      The ratio between points in each step. Defaults to equally spaced points around the entire unit circle.

    a complex, optional

      The starting point in the complex plane. Default is 1+0j.

  Returns:
    out ndarray

      The points in the Z plane at which `CZT` samples the z-transform, when called with arguments m, w, and a, as complex numbers.

  See also

  `CZT`

    Class that creates a callable chirp z-transform function.

  `czt`

    Convenience function for quickly calculating CZT.

  Examples

  Plot the points of a 16-point FFT:

      >>> import numpy as np
      >>> from scipy.signal import czt_points
      >>> points = czt_points(16)
      >>> import matplotlib.pyplot as plt
      >>> plt.plot(points.real, points.imag, 'o')
      >>> plt.gca().add_patch(plt.Circle((0,0), radius=1, fill=False, alpha=.3))
      >>> plt.axis('equal')
      >>> plt.show()

  and a 91-point logarithmic spiral that crosses the unit circle:

      >>> m, w, a = 91, 0.995*np.exp(-1j*np.pi*.05), 0.8*np.exp(1j*np.pi/6)
      >>> points = czt_points(m, w, a)
      >>> plt.plot(points.real, points.imag, 'o')
      >>> plt.gca().add_patch(plt.Circle((0,0), radius=1, fill=False, alpha=.3))
      >>> plt.axis('equal')
      >>> plt.show()