Question

(47 points) In the parts below your answer must be entered using sqrt() (Use of sin() and cos() is disabled) (A) Compute the discrete Fourier transform of f = -(2t + 1) on (-2, 0) with length 4 F{f} = (( 9 9 (B) Compute the discrete Fourier transform of g = -(2t + 2) on [1, 4) with length 3 3

Answer 1

Discorete 7 fourier transform j271 Kt E ft) e N-) F(K) = t=0 (A) Eriven N=4 $(-2): -((-2) +1) -(-4+1)=3 SA= (24+1) on [-2,0) F (-2) G flt) tattoo $(-1-5)= - (-3+1) = 2 Stl = -(-2+1) = ] +j4tt 4 $(-0.5) jut (-1+1) = 0 f(t) е t=-2 -j1:55 + $(-1.5) + $(-1) 327 5(-2) e -joist + $(-0.5) e 3 e925 + gejala + 1. -jt 12 t e = 3x1 + 2x1 + (1) F(-2) = 4 #6-7)= 1943 e 57 Mix 4 S-2) set the +91-3/2) VST + f(-1) + $(-2) 2 -j37x jat/s 11 3 eje ..) 37114 + 2 e the -j96/8 + 2e Il 3 + CSScanned with CamScanner at2

زا0.101 -00 : 16 : 31 - زد 5 4 10.1 1.834 -3 : (3 -)1 0592 .0+دوها ها o 1 (3) F (-1) T زاد (4) و =-2 |ات - -j36/ = 'f- e (3) = ان (1-3 1 (1) + (نا0 : 30 - 0.4041-)2+(1-)3 + || 12 | 10 - 2 اها ۱۰ - با - 42 1 ا -1 - 42 41 5 -- 0 (14 *(- ) = E flt) 2-ا۔ - n/ -357/ والے -2) و (3) 3 e و (-) 3 + C برا + 3(-) + 2( 5,3826- 09126) + 101- 0.1071) + -3 + 009653 - 108417) +0000 - 0 1570) - FC-%): - |.5 76 - .5s + 8 ,دارو - - 5۰۹۱۷2 - 0.058 +4,50952) = ای) * - 09216 - 2 .5s 6 ) م= CSScanned with CamScanner

BY g= -(2472) 9(1): - 4 , N=3 9(2) = -6 9 (3) = -8 3 TCK) Z E sit) -jattk N to1 F(1) 3 -j2 Titli) E s(tj e t=1 3 3 -j.217 f(t) t=1 f(1) e/?/3 + f(2) e 345/34 813) 16 5/3 = -4 (-0.5-0.866) + (6)(-0.570-863)-8 (1) 2 + 3-46443 +3-51963 - 8 F (1) 11 -3-1-4323 3 F(2) - 녀 { $(t) ejtening juhla & f (1) e + $(2) 6/3 11 + f(3) 14 -4(-0.5+0.8663)+(-6) (-0.5-0-866j)+( -8) Q-3,46413 + 3+5.1961; -8 CSScanned with CamScanner
it
F(2) - 3 + 1.432 ۴(3): 3 - 2014 Estje t=| e(دا3 + 1201م (3 = f(a)ejen * 3( 3) 361) 1] ها - 6 - % -1% F (3) (18- ,1013 +3 - رژ1.132 -3- ) CSScanned with CamScanner