Question

(a) Suppose you sample a signal at 2,048 Hz for 300 seconds. From the information you have learnt in the course, you estimate that calculating the DFT will be faster using the FFT than the direct DFT by a factor of approximately X What is X? Give your answer to the nearest integer Xs数字 (b) Consider six samples contained in the vector f=12, -2, 8, 2, -2,-5)? Suppose you are going to calculate the DFT using the FFT. You are given fev = 12,8, -2,7 and fod = (-2, 2, -5j7. Find the vectors fev and fod Enter as a vector, with entries separated by commas. For example, the vector [1+1,3,2-47 would be entered as (2+1, 3,2-4*I). Give exact values. fev = 1 fod = 07

Answer 1

solution than (a FFT is faster 7 DET by. Now here, N = (2048) (300) logan X = (2048) (300) = 31952 times log2 (2018)(300)) > T: Giv en six-samples f=[2; (b) :2,3,2,-2,-5) few [2,8, -2] R food (-2, 2, -5]ł. Now for few [2, 5; -2) & fod [-2,2,-5), the 3-point EFI algorithm is Xlo) Teo=2] an X19) -1/2 TEI ala) E = 2/2)th(4) -2 Hlo) - 8 = 6 ei 212 E2 E2= a(z)-n14 X14). Ez 8-(-2 Ez = = 10 (-2) Eo' - Eot E, = 2+6 Ed=8 to-lei = 2 =-2-468) -- 2 vey (Ev): -25(10) X = 1 +82-1+(-svaj)=4-4-5V5)g 22-1-(-5 Bj) = -/+5 13; -1-513';,-1+5835] El E2 E = -5/3) Xlo)=80 = EiE fer=[8, = X(4)

Now for odd 001 0. 0' 0 Y) X(s). 최고 02 mD(+2) 7312) 75) T-s) 연 N. 9) Do = -2) 02 드 - 5. ើ 0) - 2(3) +ms) = 2 - S = -3 기 S-3 1113) - (3) - 2-(-) 2 2 - 9 O + D = - a + (-3) - S -- = D. 길이 - - 2 - (-3) 2 - (-3) = -0.5 , 2 -0.5) 502 크 일 01 3 - - 2 02 5 = X D =00 رزرو-) (3) = 0 +02 - + D2 - - D. St 구 35) - 2 (s) (3) - 0)' - D T = (+5) fou s, 2컬), 결별이