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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def periodic_hann(window_length):
 """Calculate a "periodic" Hann window. The classic Hann window is defined as a raised cosine that starts and ends on zero, and where every value appears twice, except the middle point for an odd-length window. Matlab calls this a "symmetric" window and np.hanning() returns it. However, for Fourier analysis, this actually represents just over one cycle of a period N-1 cosine, and thus is not compactly expressed on a length-N Fourier basis. Instead, it's better to use a raised cosine that ends just before the final zero value - i.e. a complete cycle of a period-N cosine. Matlab calls this a "periodic" window. This routine calculates it. Args: window_length: The number of points in the returned window. Returns: A 1D np.array containing the periodic hann window. """

  return 0.5 - (0.5 * np.cos(2 * np.pi / window_length *
                             np.arange(window_length)))