Radix-2 FFT Algorithms

RADIX-2 FFT ALGORITHMS

DECIMATION IN TIME (DITFFT)

There are three properties of twiddle factor WN

N point sequence x(n) be splitted into two N/2 point data sequences f1(n) and f2(n). f1(n) contains even numbered samples of x(n) and f2(n) contains odd numbered samples of x(n). This splitted operation is called decimation. Since it is done on time domain sequence it is called “Decimation in Time”. Thus

f1(m)=x(2m)         where n=0,1,………….N/2-1

f2(m)=x(2m+1)    where n=0,1,………….N/2-1

N point DFT is given as

Since the sequence x(n) is splitted into even numbered and odd numbered samples, thus

Fig 1 shows that 8-point DFT can be computed directly and hence no reduction in computation.