4. (1 mark) Find the numerical value of each integral. a) x)-8(+3)-28(40)]d b) x(t) ?..J(3t-2n) dt....
solve 1 and 2. Evaluate the integral. 3T/4 1) rt/4 D) o B)-16 C) Find the derivative of the integral using the Second Fundamental Theorem of Calculus 2) y- cos nt dt D) cos (3)-1 C) sin (3) B) cos (x3) A) 6x5 cos (x3) Evaluate the integral. 3T/4 1) rt/4 D) o B)-16 C) Find the derivative of the integral using the Second Fundamental Theorem of Calculus 2) y- cos nt dt D) cos (3)-1 C) sin (3) B)...
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from Definition)- For (c) r(t) = te-2, 11(1) (b) x(t)-2t rect(t) 1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from...
let two vectors be a(t) = e^t i + (sin 2t) j + t^3 k and b(t) = (e^-t , cos 3t, - 2 t^3) in euclidean three space R^3. Find d/dt [a(t) * b(t)].
Fourier transforms using Properties and Table 1·2(t) = tri(t), find X(w) w rect(w/uo), find x(t) 2. X(w) 3, x(w) = cos(w) rect(w/π), find 2(t) X(w)=2n rect(w), find 2(t) 4. 5, x(w)=u(w), find x(t) Reference Tables Constraints rect(t) δ(t) sinc(u/(2m)) elunt cos(wot) sin(wot) u(t) e-ofu(t) e-afu(t) e-at sin(wot)u(t) e-at cos(wot)u(t) Re(a) >0 Re(a) >0 and n EN n+1 n!/(a + ju) sinc(t/(2m) IIITo (t) -t2/2 2π rect(w) with 40 2r/T) 2Te x(u) = F {r) (u) aXi(u) +X2() with a E...
♡ Express the value of integral şsin(x}dt asum of a series as a E (-)" (2n +1)! (en+1) no o nso (7n+7) (en+1)! h so (14n+8)(2n +1)! swi -1) (2n+1)! (14n+1) Non of the above e a b
Find the instantaneous frequency of the next signal at t = 4. (a) x(t) = 10 cos[20xt+10 sin(t/4)) (b) x(t) = 262719) () X(t)=10[cos(2nt) cos(atº/4) + sin(24t) sin( nt/ 4)] Suppose that the information signal is as shown in the following figure. When each modulating this signal using 100KHz as the carrier frequency, find the frequency shift and phase shift when FM is modulated with 5,=10. What is the maximum frequency shift and maximum phase shift? 0.5+ -0.5 ost Suppose...
Find the Nyquist rates for these signals: (a) X(t) = sinc (20) (b)x(t) = 4 sinca (100t) (C) x(t) = 8 sin(50TTT) (d) x(t) = 4 sin(30TTt) + 3 cos(70nt) (e) X(t) = rect(300t) (f) X(t) = -10 sin(40nt) cos(300Tt) (g) X(t) = sinc(t/2)*710(t) (h) x(t) = sinc(t/2) 70.1() (i) X(t) = 8tri((t - 4)/12) (1) X(t) = 13e-201 cos(70TTt)u(t) (k) x(t) = u(t)-u(t-5)
Signal system 8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the Fourier series coefficients for this signal. (4 points). b. If this signal passes through a LTI system with the impulse response h(t)=e* u(t), particularly, would the output signal also be a periodic signal ? If so, what would be the Fourier coefficients of the output signal ? (4 points). c. Give the mathematical expression for the output signal y(t). (2 points).
Q.3) 120 Marks] [8 Marks] Determine the DTFT of the following DT signals i) x[n] = (0.5)" [u[n]-n(n-3)) a) ii) ? [n] = n (0.5)" u[n-2] b) [8 Marks] Consider the following CTFT pair: jw x(t) ?? (-v^2 + 5 i) e -/00t x(t) 6) using the CTFT properties determine the Fourier transform (CTFT) of: i x(3t-6) e) [4 Marks] Prove the Parseval's relationship for a CT signal x e
HW 1_Chi 1) Find the energies of the following signals below. 2) Find the power and the rms value of the signal belo a) x(-4) b)x(-t) c) x(2-4) 3) for the signal x(t) shown below, sketch the signals b) (-4)[u(t-2)-(-4)] 4) sketch the following signals a) uſt-5) - ult-7) 5) Simplify the following expressions: (a) (2+2) (1) (+3)sw) (c) le='cos (31 – 60°)80) () (sin ka ) s() 6) Evaluate the following integrals: (a) , 8(7)x(1 – t)dt (b) *()8(1-1)dt...