Problem (10 pts) Let a function g(a) be given by the following: cos(ma), 0, 0 <...
Problem 1 (10 pts). A time-domain signal x(t) is given in the figure below: - - - - - - - 9 X(t) 0 2 t, msec (a) Compute the simplest real-valued math function for the spectrum X($). (b) Plot X(f) over a Hz frequency range large enough to show all the important properties.
Problem 6. (10 pts) Write down the following in the form of x(t) = A cos(2t + o), where A> 0 x(t) = sin(2t + 7) + cos2t
What is the value of i(t) for t>=0? Given L = 10 H, R = 5 ohms and Vs = 40V. URO - w vs 40e^(-0.5t) 20e^(-0.5t) 40e^(-0.02t) 8e^(-0.5t)
Let a system have impulse response h(t) and input x(t) given by (1257) (37704) +20 cos t0.01 20 cos C = 628 e-628t u(t), h(t) r(t) 0, else Using the same frequency scale (you can use different magnitude scales), plot the following over the range 1500 Hz (a) Hf) (b) X(f)(e) |Y(f)|
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t) = 〉 1 0 < t < 1 0 t>1 Find the output y(t) of this system if the input is given by a) x(t) = 1 + cos(2nt) b) x(t)-cos(Tt) c) x(t) sin (t )l d) x(t) = 1 0 < t < 10 0 t 10 e) x(t) = δ(t-2)-5(t-4) f) a(t)-etu(t) Problem 2: For the same LTI system in Problem 1,...
Problem 4.(30 pts) Given the analog signal x(t) cos(2 cos(3t)+2 sin(4mt) A.(10 pts) Find the Nyquist frequency (sampling frequency) which guarantees That x() can be recovered from it's sampled version xIn] with no aliasing. B.(10 pts) If the sampling period of Ts 0.4 see is used identify all discrete frequencies Of the signal x(t), also indicate if this sampling period is adequate to recover x(t) from xn] C.(10 pts) Suppose signal x(t) is modulated by signal e(t) = cos(2000mt) what...
Let a linear system with input x(t) and output y(t) be described
by the differential equation .
(a) Compute the simplest math function form of the impulse
response h(t) for this system. HINT: Remember that with zero
initial conditions, the following Laplace transform pairs hold:
Let the time-domain function p(t) be given by p(t) = g(3 − 0.5
t). (a) Compute the simplest piecewise math form for p(t).
(b) Plot p(t) over the range 0 ≤ t ≤ 10 ....
2. Let g(t)=e-2,[sin(6π) + 2 cos(3m)]. FindJa-2)g(t)dt. 3. Let g(1)=-2111(1)-11(1-2)|. Plot g(t) Using g(t) from problem 3, plot g| and g 4. i-2 5. Let g(t)=Πcos(2km. Is this an even or odd function. (Justify your answer) に!
Exercises: u used to the instructor b the end of next lab. 20 102 Plot the f(t)-sinc(20r) cos(300t)sinc (10t) cos(100t) Use the fast Fourier transform to find the magnitude and phase spectrum of the signal and plot over an appropriate range. Use appropriate values for the time interval and the sampling interval. Note that in Matlab sinc(x)-, so we need to divide the argument by n to make it match the given function. Le, sinc(20t/pi) Hint: Use the parameters from...
1. (2 pts each) The graph of some unknown function f is given below. 10 6/ 8-64-2 624 10 12 Use the graph to estimate the following quantities: (0 f (9) (g) f(4) b) lim (a) lim (e) (d) lim ( 6) (e) lim f(x) (c) lim f(x) if g(x)f(x) 6) a value of r where f is continuous but not differentiable (k) a value of r where f"(x) 0 and f"(x)>0 (1) the location of a relative maximum value...