code: def 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()
      """
      m = _validate_sizes(1, m)
  
      k = arange(m)
  
      a = 1.0 * a  # at least float
  
      if w is None:
          # Nothing specified, default to FFT
          return a * np.exp(2j * pi * k / m)
      else:
          # w specified
          w = 1.0 * w  # at least float
          return a * w**-k
  
file_path: scipy/scipy/signal/_czt.py
imports: import cmath
  import numbers
  import numpy
  from numpy import pi, arange
  from scipy.fft import fft, ifft, next_fast_len
label_desc: Use image node_id 2 for calling a global function with example usage: czt_points(m, w, a) and returns: unknown, unknown