parameters: (n, d=1.0)
return_statement: return results * val
docstring: Return the Discrete Fourier Transform sample frequencies.
  
      The returned float array `f` contains the frequency bin centers in cycles
      per unit of the sample spacing (with zero at the start).  For instance, if
      the sample spacing is in seconds, then the frequency unit is cycles/second.
  
      Given a window length `n` and a sample spacing `d`::
  
        f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
        f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd
  
      Parameters
      ----------
      n : int
          Window length.
      d : scalar, optional
          Sample spacing (inverse of the sampling rate). Defaults to 1.
  
      Returns
      -------
      f : ndarray
          Array of length `n` containing the sample frequencies.
  
      Examples
      --------
      >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
      >>> fourier = np.fft.fft(signal)
      >>> n = signal.size
      >>> timestep = 0.1
      >>> freq = np.fft.fftfreq(n, d=timestep)
      >>> freq
      array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])
docstring_summary: Return the Discrete Fourier Transform sample frequencies.
docstring_tokens: Return the Discrete Fourier Transform sample frequencies .
function: def fftfreq(n, d=1.0):
      """
      Return the Discrete Fourier Transform sample frequencies.
  
      The returned float array `f` contains the frequency bin centers in cycles
      per unit of the sample spacing (with zero at the start).  For instance, if
      the sample spacing is in seconds, then the frequency unit is cycles/second.
  
      Given a window length `n` and a sample spacing `d`::
  
        f = [0, 1, ...,   n/2-1,     -n/2, ..., -1] / (d*n)   if n is even
        f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n)   if n is odd
  
      Parameters
      ----------
      n : int
          Window length.
      d : scalar, optional
          Sample spacing (inverse of the sampling rate). Defaults to 1.
  
      Returns
      -------
      f : ndarray
          Array of length `n` containing the sample frequencies.
  
      Examples
      --------
      >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
      >>> fourier = np.fft.fft(signal)
      >>> n = signal.size
      >>> timestep = 0.1
      >>> freq = np.fft.fftfreq(n, d=timestep)
      >>> freq
      array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])
  
      """
      if not isinstance(n, integer_types):
          raise ValueError("n should be an integer")
      val = 1.0 / (n * d)
      results = empty(n, int)
      N = (n-1)//2 + 1
      p1 = arange(0, N, dtype=int)
      results[:N] = p1
      p2 = arange(-(n//2), 0, dtype=int)
      results[N:] = p2
      return results * val
function_tokens: def fftfreq ( n , d = 1.0 ) : if not isinstance ( n , integer_types ) : raise ValueError ( "n should be an integer" ) val = 1.0 / ( n * d ) results = empty ( n , int ) N = ( n - 1 ) // 2 + 1 p1 = arange ( 0 , N , dtype = int ) results [ : N ] = p1 p2 = arange ( - ( n // 2 ) , 0 , dtype = int ) results [ N : ] = p2 return results * val