Question

ECE-3303-001 Fall - 2019 Homework #4 Due Date: 10/17/2019 (11:59 PM) This assignment MUST be uploaded on Blackboard as a single file (pdf format). [Note: RELEVANT STEPS must be shown to receive full credit for correct answers] 1. Determine the Fourier transform of the following signals: (a) f(b)=et (c) h(t)=e* [u(t+3) –u(1-2)] (b) g(t)=t.e Hl.cos(51) (a) i(t)=cos' (1-1).e"/"+" (-3) 2. Determine the inverse Fourier transform of the following signals: 2 FO) G@) = jo e 0+1)/200-5) H(0) 1() 9 + 0 (1-3) jo-502 3. Determine the Fourier transform of the non-periodic signals shown in the figures below: (b) 8 (1) -2 -1 0 1 2 4. If the Fourier transform of In() is ()–um) or 7In(0) = 4(-a) – u(@), where u() is the unit-step function, determine the Fourier transform of the signal: So=1.In(1-3)

Answer 1

(a) foelt et ut tet utt) - Jetult just at t a et utt) etut at How)t dt ti-jw) + dt - Cl+jw)ta -CTH ) (1-jw) F(W) = Itw2 | Free (6) g(t) = te latl cosst = tealtl cosst utwa we know all < For t=2 / H ft 22 j & ut ]

sj@-5) + 8°(w+5) [44-5 7 [4 + (w t5 e 3 C) n(t) - et fult + 3) - ut-2)] I we know eat alt) <F'T, a tju at aft) & Fit, a-ja we know so h(t) can be written as ht) = (t + 3) & uf+3) - e(t 2) - 2 u E-2) zjw 7 -le i tjw 1 (d) i(t) = cos? (t-1) eist teet ut-3) Let i, (t) = cos(tt) ist ia (A) = est u (t-3) So I (w) = I (W) + Ig(w) e i(t) = cos? (tt) et

i, (t) = [it los a * AE) ( 0 ) -ja(t-1) -j3 (t-1)-33 Lo $fe +1) 3") 4Et sorting 5.5/(W) = 18+5) + (t) = -2t alt-3) Fals - to Kay 2+16 I (W) + Ig (W) So I (W) =

e = ان» و F (9) ) ه 4 weknow بن + 3 یا ال (عا امداد کی اعاقہ ا ااام ( وک اس = ( ( را - = (س) ( له زده ( ه ا ک پ - ( ا و - (94 تر از مو ا د در = ( ( (تا3ر- a-jw at aft) <F. I we know امان- ( ره (0) ادا است و به ز- ل (0) کادا

لبا زمان کالا و .

(d) I(W) = jw - 50 jw(1+5jw) Id = tu - (15) jw so ile) = pure«co) Law

Given non periodic signal 301) - 2 - 1 Fourier tramform of given signal g(t) G(10) = 1 gun event de المال - d -Jut J10 d I-swt 2 Le - (2016cm) Heal) * 2020- 'w [ 2j Siow - 4i sinaw] 9w) [asinw- 4 sinzw] 4 Sin 2w --sinu

|-- | مه 7 Fourier transform of signal 9 (1) او اسانج (180= (ه) ان الفالج (1) 3 = as g(t) is even signal في أمالي (20 == او انهالت (* | == اجمال۔ -jw ليال استان ) - م ا = ( لیا- سطر بعj)

(A) Given en(t) For [ufw) - (W)] (t) = t ent-3) = (t-3) en (t-3 ) + 3 ln (t-3) Let us first find fouriertransform of ten(t) temce Fit -jd (w) – uw)] ES, _nj (w the lucu -uws] = fraco, un basy 5 - (0 -260) – (uw) -(0703] 5 +nj (ucu)-am) (ta)m(-3) FT, mj (ufu)- ows] ss ters) Es nj ſuku) – cc)] 2336 1 + 3 Tucw) - uces) CU