def idft(f, scale=True):
"""
Function to evaluate the inverse of the dft for an array.
Args:
f (1d-array): array to calculate the dft of
scale (optional[boolean]): scales the result by dividing it by the
number of array elements
Returns:
Array of the inverse fourier transformation
"""
def swap(f):
"""
Function to swap the imaginary and real components of an imaginary array
"""
return f.real * (0 + 1j) + f.imag
M = f.shape[0]
scaleFactor = 1
if (scale):
scaleFactor = (1 / M)
transform = swap(numerical.dft(swap(f))) / scaleFactor
return transform
def idft(f, scale=True):
"""
Function to evaluate the inverse of the dft for an array.
Args:
f (1d-array): array to calculate the dft of
scale (optional[boolean]): scales the result by dividing it by the
number of array elements
Returns:
Array of the inverse fourier transformation
"""
def swap(f):
"""
Function to swap the imaginary and real components of an imaginary array
"""
return f.real*(0+1j) + f.imag
M = f.shape[0]
scaleFactor = 1
if (scale):
scaleFactor = (1/M)
transform = swap(numerical.dft(swap(f)))/scaleFactor
return transform
def idft(F, scale=False):
def swap(F):
return F.real * (0 + 1j) + F.imag
M = F.shape[0]
scaleFactor = 1
if (scale):
scaleFactor = (1 / M)
ift = swap(numerical.dft(swap(F))) / scaleFactor
return ift
def dft2(f, scale=True):
c = f.swapaxes(0, 1)
Columns = []
for col in range(c.shape[0]):
Columns.append(numerical.dft(c[col], False))
x = np.array(Columns)
r = x.swapaxes(0, 1)
Rows = []
for row in range(r.shape[0]):
Rows.append(numerical.dft(r[row], False))
fU = np.array(Rows)
M = f.shape[0] * f.shape[1]
scaleFactor = 1
if (scale):
scaleFactor = (1 / M)
return fU * scaleFactor
def dft2(f, scale=True):
"""
Function to evaluate the dft for a 2D array.
Args:
f (2d-array): array to calculate the 2 dimensional dft of
scale (optional[boolean]): scales the result by dividing it by the
number of array elements
Returns:
2 dimensional array of fourier transformation
"""
# for every column, evaluate the dft
columns = f.swapaxes(0, 1)
Columns = []
for col in range(columns.shape[0]):
Columns.append(numerical.dft(columns[col], False))
newSpace = np.array(Columns)
# for every row in the new space, evaluate the dft
# swap the axes again to set it back to normal
rows = newSpace.swapaxes(0, 1)
Rows = []
for row in range(rows.shape[0]):
Rows.append(numerical.dft(rows[row], False))
finalSpace = np.array(Rows)
M = f.shape[0] * f.shape[1]
scaleFactor = 1
if (scale):
scaleFactor = (1 / M)
return finalSpace * scaleFactor
def dft2(f, scale=True):
"""
Function to evaluate the dft for a 2D array.
Args:
f (2d-array): array to calculate the 2 dimensional dft of
scale (optional[boolean]): scales the result by dividing it by the
number of array elements
Returns:
2 dimensional array of fourier transformation
"""
# for every column, evaluate the dft
columns = f.swapaxes(0, 1)
Columns = []
for col in range(columns.shape[0]):
Columns.append(numerical.dft(columns[col], False))
newSpace = np.array(Columns)
# for every row in the new space, evaluate the dft
# swap the axes again to set it back to normal
rows = newSpace.swapaxes(0, 1)
Rows = []
for row in range(rows.shape[0]):
Rows.append(numerical.dft(rows[row], False))
finalSpace = np.array(Rows)
M = f.shape[0] * f.shape[1]
scaleFactor = 1
if scale:
scaleFactor = 1 / M
return finalSpace * scaleFactor
scaleFactor = (1/M)
ft = scaleFactor * np.sum((f*e), axis = 1)
return ft
if __name__ == '__main__':
import numerical
import numpy
import time
N = 2**12
f = numpy.ones(N, dtype=numpy.complex128)
repeats = 10
print('Repetitions = {0}'.format(repeats))
startTime = time.clock()
for repeat in range(repeats):
F = numerical.dft(f)
string = 'Average time per transform = {0:.8f} [s] ({1}-point DFT)'
print(string.format((time.clock() - startTime)/repeats, len(f)))
startTime = time.clock()
for repeat in range(repeats):
F = numpy.fft.fft(f)
string = 'Average time per transform = {0:.8f} [s] ({1}-point FFT)'
print(string.format((time.clock() - startTime)/repeats, len(f)))
scaleFactor = (1/M)
transform = scaleFactor * np.sum((f*phase), axis=1)
return transform
"""
PYTHON TEST HARNESS
"""
if __name__ == '__main__':
import numerical
import numpy
import time
N = 2**12
f = numpy.ones(N, dtype=numpy.complex128)
repeats = 10
print('Repetitions = {0}'.format(repeats))
startTime = time.clock()
for repeat in range(repeats):
F = numerical.dft(f)
string = 'Average time per transform = {0:.8f} [s] ({1}-point DFT)'
print(string.format((time.clock() - startTime)/repeats, len(f)))
startTime = time.clock()
for repeat in range(repeats):
F = numpy.fft.fft(f)
string = 'Average time per transform = {0:.8f} [s] ({1}-point FFT)'
print(string.format((time.clock() - startTime)/repeats, len(f)))