def periodogram(x, window=None, window_len=7):
 n = len(x)
 I_w = ((np.abs(fft(x)) ** 2) / n)
 w = (((2 * np.pi) * np.arange(n)) / n)
 (w, I_w) = (w[:(int((n / 2)) + 1)], I_w[:(int((n / 2)) + 1)])
 if window:
  I_w = smooth(I_w, window_len=window_len, window=window)
 return (w, I_w)

def periodogram ( x , window = None , window_len = 7 ) : n = len ( x ) I_w = ( ( np . abs ( fft ( x ) ) ** 2 ) / n ) w = ( ( ( 2 * np . pi ) * np . arange ( n ) ) / n ) ( w , I_w ) = ( w [ : ( int ( ( n / 2 ) ) + 1 ) ] , I_w [ : ( int ( ( n / 2 ) ) + 1 ) ] ) if window : I_w = smooth ( I_w , window_len = window_len , window = window ) return ( w , I_w )
returns the periodogram for the natural frequency of x parameters x : array-like array for which the periodogram is desired .