Added fft/ifft wrapper (cont'd)

proxtoolbox/Utilities/FFT.py

@@ -29,3 +29,120 @@ def FFT(f):
 
     return np.fft.fftshift(F);
 
+
+def fft(a):
+  """
+  fft(a)
+  Compute the one-dimensional discrete Fourier transform of a the way Matlab
+  does. When a is a vector, the Fourier transform of the vector is
+  returned. When a is a matrix, each column vector of a is
+  transformed individually, and a new matrix containing the transformed
+  column vectors of a is returned.
+    
+  Parameters
+  ----------
+  a : array_like
+      1-D or 2-D input array (can be complex)
+  Returns
+  -------
+  result : ndarray
+      1-D or 2-D array of similar shape and type
+      containing the discrete fourier transform of a
+
+  See Also
+  --------
+  ifft 
+  
+  Notes
+  -----
+  Using the Numpy function fft on a matrix does not 
+  produce results similar to what Matlab does.
+  This helper function uses the Numpy functions to produce
+  a resut that agrees with what Matlab does. 
+  """  
+  return transformVectors(a, np.fft.fft)
+
+def ifft(a):
+  """
+  ifft(a)
+  Compute the one-dimensional inverse discrete Fourier transform the
+  way Matlab does. When a is a vector, the inverse Fourier transform
+  of the vector is returned. When a is a matrix, each column vector
+  of a is transformed individually, and a new matrix containing the
+  transformed column vectors of a is returned.
+    
+  Parameters
+  ----------
+  a : array_like
+      1-D or 2-D input array (can be complex)
+      
+  Returns
+  -------
+  out : ndarray
+      1-D or 2-D array of similar shape and type
+      containing the inverse discrete fourier transform of a
+
+  See Also
+  --------
+  fft 
+  
+  Notes
+  -----
+  Using the Numpy function ifft on a matrix does not 
+  produce results similar to what Matlab does.
+  This helper function uses the Numpy functions to produce
+  a resut that agrees with what Matlab does.
+  """  
+  return transformVectors(a, np.fft.ifft)
+
+def transformVectors(a, transform):
+  """
+  transformVectors(a, transform)
+  Transform a according to the given transform function. 
+  When a is a vector, it applies the transform function to a
+  and returns the result. When a is a matrix, each column vector
+  of a is transformed individually using the given transform function,
+  and a new matrix containing the transformed column vectors
+  of a is returned. 
+    
+  Parameters
+  ----------
+  a : array_like
+      1-D or 2-D input array
+  transform : callable function
+      This function takes a 1-D array as argument and returns
+      a 1-D array of same size. This function is applied to a if 
+      it is a vector or to the column vectors of a if a is a matrix.
+  Returns
+  -------
+  out : ndarray
+      1-D or 2-D array of similar shape and type
+      containing the transformed data
+  See Also
+  --------
+  fft, ifft 
+  
+  Notes
+  -----
+  This function is used by fft(a) and ifft(a).
+  """  
+
+  if a.ndim == 1:
+    # a is a vector
+    out = transform(a)
+  else:
+    # assume a is a matrix (2d array)
+    shape = a.shape
+    colCount = shape[1]
+    #result = np.empty_like(a)
+    out = np.zeros_like(a)
+    # for each column vector in a
+    for i in range(0, colCount):
+      col = a[:,i]
+      fft_col = transform(col)
+      out[:,i] = fft_col
+  
+  return out
+  
+
+