THEORETICAL DEVELOPMENT OF FAST FOURIER TRANSFORM
Purpose: To find fast fourier transform or fft
Keyword:
n = number of complex data points = 2^igama
igama = integer power to compute N = 2^igama
if isign = -1 and factor = 1; general_fft = FFT operation is performed.
if isign = +1 and factor = 1; general_fft = IFFT operation is performed.
factor
For case 1, the user has to input isign = -1 and factor = 1 and the complex vector fk, then general_fft
code will compute complex vector Cn according to equation 11.59. This result is also matched with
MATLAB built-in function fft (where the user only have to provide input complex vector fk).
For case 2, the user has to input isign = +1, factor = 1 and the complex vector Cn (obtained from
case 1; the user input complex vector has to multiply with a factor 1/n before calling general_fft), then
this general_fft code will compute and get back the original complex vector fk according to
equation 11.60. Our results will also match with MATLAB built-in function "ifft" (Inverse Fast Fourier
Transform) if the user only has to provide the complex vector Cn (obtained from case 1).
Case 1 : fcomp = [1-8i 2-7i 3-6i 4-5i 5-4i 6-3i 7-2i 8-1i];
Case 2 : fcomp = [36.0000-36.0000i -13.6569+5.6569i
-2.3431-5.6569i
freal :: Input data provided by the user (real part)
fimag :: Input data provided by the user (imaginary part)
function name: bitreverse(m,igam)
Revised: July 1, 2009
Authors
Contact: dnguyen@odu.edu
Keywords
function name: unscramble(freal,fimag)
Revised: July 1, 2009
Authors
Contact: dbguyen@odu.edu
Keywords
Input:
Example 1
Example 2