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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 ve...
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...
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, respecti...
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...
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),...
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....
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...
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...
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...
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)...
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)
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)
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