4. Sketch a graph ot the following signals. Use the grid provided. (t) = r(t) Hint:...
4. X(c)-1 for lol < 5 and is zero elsewhere. Use the theorems to find and sketch the amplitude versus ω and the phase angle versus ω of the transforms of the following signals. (a) t0, (b, (e) x(2), and (e) x() expG10) dx(t) dt' TABLEme Selected Properties of the Fourier Transform X (o) 2. 3. x(-t) X (-o) 5. x(-o) x (at) la l 8. lx ()12 dr x(t)h(C) x (t) 9. 10. 2π X (ω-@g) d"X (0) 12....
1. Sketch each of the components of the following signals on the graphs provided. Sketch and highlight the resultant signals on the same graphs as well. (a) xy(t)=u(t+1)-u(1-1) (5 points) Ixl(t) . : + ---. t +--+ -3 + -2 + -1 0 1 2 (b) x2(t)=r(t +2) - 2r(t+1)+r(t) (5 points) + + + + + + + + + + + + + + + + 4 + + + + + + + + 3+ + +...
For the remainder of this problem, the signals (t) and y(t) denote the input and output, respectively, of a stable LTI system whose (double-sided) frequency response is known to be w-4m 27T 4m H(w) = rect ( 2π with rect(t) denoting the unit-pulse function i.e., rect(t) 1 for lt| < 1/2 and is zero otherwise. Hint: Use sketches as a guide for answering each question most efficiently. (c) (15 points) Determine y(t) for all t given the applied input is...
4. X(c)-1 for lol < 5 and is zero elsewhere. Use the theorems to find and sketch the amplitude versus ω and the phase angle versus ω of the transforms of the following signals. (a) t0, (b, (e) x(2), and (e) x() expG10) dx(t) dt' TABLEme Selected Properties of the Fourier Transform X (o) 2. 3. x(-t) X (-o) 5. x(-o) x (at) la l 8. lx ()12 dr x(t)h(C) x (t) 9. 10. 2π X (ω-@g) d"X (0) 12....
Problem 3.10: Compute the Fourier transform of each of the following signals. si(t) = [e-ot cos(wot)]u(t), a > 0; zz(t) = e34 sin(24); 13(t) = e T -00 X5(t) = [te-2+ sin(4t)]u(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...
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)
DIFFERENTIATION: For the signals x(t) in Problems (1-2), (a) Compute the fomula for and (b) sketch the signal's derivative x'(t) = x(t). If necessary, use the Differentiation Product Rule: (f.g)' = fg + fig', or "RUD", e. g u (t) = 8(t). In your plots, label both axes, and indicate key values of time and amplitude. (1) X(t) = 4 rect ). (Hint: express rect(t/10) in terms of the difference of Two unit step functions.) ( 10 points) (2) X(t)...
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...
Given the functions below, use MATLAB to plot x2(t), x4(t/2), x6(2t) x2(t) u(sin(t)) x4(t)rt)r(t - 2) 2u(t - 4) x6 (t) 3 sgn(t) rect(t/4) 28 (t 1) 36(t - 3)