6. Consider a pulse of amplitude 1 and duration 2. The pulse starts at time t-0....
PROBLEM 12 The message signal m(t) is a rectangular pulse of unit amplitude and duration T (centered about the origin). The radio-frequency (RF) pulse defined by s(t) = {4_cos(wt), -āsts 1 0. Otherwise a) Drive a formula for the spectrum of s(t) and v(t) assuming that WT. >> 211 b) Sketch the magnitude spectrum of s(t) for w.T. = 20 The below figure describing the modulation and the demodulation of the m(t) signal. VO mo Product modulator Product modulator Low-pass...
(1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. "8 6(t 1), y(0) = 3, /(0) = 0. a. Find the Laplace transform of the solution. Y(8)= L{y(t)} = | (3s+e^(-s)-24)/(s^2-8s) b. Obtain the solution y(t) y(t)=1/8(e^(8t-8)-1 )h (t- 1 )+6e^(8t)-3 c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t 1. if...
A rectangular pulse of an amplitude 27 V and a duration 1 µs is applied via a series resistor Rg to the terminals of a lossless transmission line of length l = 400m terminated in a load resistance RL. The phase velocity of waves on the line is up =3 × 108 m/s. (a) Using the bounce diagram, sketch the voltage and current at the mid-point of the transmission line (z = l/2) for 0 < ?< 3 µs. (b)...
7 (10pt) Signal s(t) is created by multiplying a rectangular pulse with a sinusoidal signal: s(t) A cos(2mfet) rect where rect(t) is a rectangular pulse with width 1 and amplitude 1 which occupies -0.5 to 0.5 in time domain. Please find out s(t)'s null-to-null bandwidth. 7 (10pt) Signal s(t) is created by multiplying a rectangular pulse with a sinusoidal signal: s(t) A cos(2mfet) rect where rect(t) is a rectangular pulse with width 1 and amplitude 1 which occupies -0.5 to...
Please help: Consider a pulse that is defined at time ? = 0.00 ? by the equation Problem 1: Consider a pulse that is defined at time t0.00 s by the equation 2.00x 2 fx)y(x,0) (0.05 m)e-2.7720 The pulse moves with a velocity of v 2.00 m/s in the positivex-direction (a) Show that the pulse is centered on x = 0.00 m at time t = 0.00 s. Draw approximately the pulse at t = 0.00 s (b) What is...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x' +2=1 + (t - 2), X(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{a(t)}(8) = b. Obtain the solution z(t). (t) c. Express the solution as a piecewise-defined function and think about what happens to the graph of...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" – 2x' = (t – 4), x(0) = 4, x'(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{x(t)}(s) = b. Obtain the solution z(t). x(t) = c. Express the solution as a piecewise-defined function and think about what...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: z" + 167°1 = 478(t – 5), 7(0) = 0, z'(0) = 0. In the following parts, use h(t - c) for the Heaviside function hc(t) if necessary. a. Find the Laplace transform of the solution. [{r(t)}(s) = bir b. Obtain the solution z(t). z(t) = c. Express the solution as a piecewise-defined function and think about...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x' + x = 9+5(t – 5), x(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{2(t)}(s) = b. Obtain the solution z(t). (t) = c. Express the solution as a piecewise-defined function and think about what happens to the...
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" + 91- x = 318(t – 3), x(0) = 0, x'(0) = 0. In the following parts, use h(t – c) for the Heaviside function he(t) if necessary. a. Find the Laplace transform of the solution. L{x(t)}(s) = b. Obtain the solution z(t). X(t) = c. Express the solution as a piecewise-defined function and think about...