Decimation-in-time (DIT) Radix-2 FFT Presented by Asst.lecturer Noora Hani DIT FFT Butterfly Diagram Observing the basic computations performed at each stage, we can arrive at the following conclusions: (i) In each computation, two complex numbers a and b are considered. (ii) The complex number b is multiplied by a phase factorπΎππ΅ . (iii) The product ππΎππ΅ is added to the complex number a to form a new complex number A. (iv) The product ππΎππ΅ is subtracted from complex number a to form new complex number B. The basic computations can be expressed by signal flow graph shown in the next slide [ DIT FFT] Table showing powers of the factor πΎππ΅ for 4-point and 8-point Example: find the 4-point DFT of the sequence x(n)=[2,1,4,3] using DIT FFT algorithm Sol: Example: given sequence x(n)=[0,1,2,3,4,5,6,7] determine X(k) using DIT FFT SOL: Example: Given a sequence x(n) for 0 ≤ n ≤ 3, where x(0) = 1, x(1) = 2, x(2) = 3, and x(3) = 4, a. Evaluate its DFT X(k) using the decimation-in-frequency FFT method. b. Evaluate its DFT X(k) using the decimation-in-time FFT method. Sol: a. 4 x(0)=1 x(1)=2 6 x(2)=3 -2*π€40 4 10=X(0) π€20 6 -2=X(2) -1 -2 -2+2j=X(1) -1 -2*π€41 x(3)=4 -1 π€20 2j -1 -2-2j=X(3) 4 4 10=x(0) -2 -2+2j=x(1) 6*π€40 -2=x(2) X(0)=1 X(2)=3 π€20 -2 -1 6 X(1)=2 X(3)=4 -1 π€20 -2 -1 -2*π€41 -2-2j=x(3) -1