iaidft

iaidft
Inverse Discrete Fourier Transform.

Synopsis

f = iaidft( F )

Implemented in Python.

Input

F	Image. Gray-scale (uint8 or uint16) or binary image (logical).

Output

f	Image. Gray-scale (uint8 or uint16) or binary image (logical).

Examples

>>> import Numeric

>>> f = iaread('cameraman.pgm')

>>> F = iadft(f)

>>> H = iagaussian(F.shape, Numeric.array(F.shape)/2., [[50,0],[0,50]])

>>> H = ianormalize(H,[0,1])

>>> FH = F * iaifftshift(H)

>>> print iaisdftsym(FH)

>>> g=iaidft(FH)

>>> iashow(f)

(256, 256) Min= 0 Max= 251 Mean=137.066 Std=87.20

>>> iashow(iadftview(F))

(256, 256) Min= 50 Max= 255 Mean=128.205 Std=16.56

>>> iashow(ianormalize(H,[0,255]))

(256, 256) Min= 0.0 Max= 255.0 Mean=1.222 Std=12.42

>>> iashow(iadftview(FH))

(256, 256) Min= 0 Max= 255 Mean=4.047 Std=21.40

>>> iashow(abs(g))

(256, 256) Min= 5.32992978393 Max= 227.023038904 Mean=137.066 Std=71.50


f	iadftview(F)


ianormalize(H,[0,255])	iadftview(FH)


abs(g)

Equation

Source Code

def iaidft(F):
    from Numeric import asarray, Complex64, NewAxis, matrixmultiply, conjugate, sqrt
    F = asarray(F).astype(Complex64)
    if len(F.shape) == 1: F = F[:,NewAxis]
    (m, n) = F.shape
    if (n == 1):
        A = iadftmatrix(m)
        f = (matrixmultiply(conjugate(A), F))/sqrt(m)
    else:
        A = iadftmatrix(m)
        B = iadftmatrix(n)
        f = (matrixmultiply(matrixmultiply(conjugate(A), F), conjugate(B)))/sqrt(m*n)
    return f

iadft	Discrete Fourier Transform.
iaisdftsym	Check for conjugate symmetry

iaidft Inverse Discrete Fourier Transform.

Synopsis

Input

Output

Examples

Equation

Source Code

See also

iaidft
Inverse Discrete Fourier Transform.