5) Determine a frequency ω that will cause the input x(t) cos(or) to p oduce a...
The given input signal for 2.7.2 is: x(t) = 3 cos(2 π t) + 6 sin(5 π t).Plz explain steps.Given a causal LTI system described by the differential equation find \(H(s),\) the \(\mathrm{ROC}\) of \(H(s),\) and the impulse response \(h(t)\) of the system. Classify the system as stable/unstable. List the poles of \(H(s) .\) You should the Matlab residue command for this problem.(a) \(y^{\prime \prime \prime}+3 y^{\prime \prime}+2 y^{\prime}=x^{\prime \prime}+6 x^{\prime}+6 x\)2.7.2 The signal \(x(t)\) in the previous problem is...
QUESTION 4 a. Determine the frequency spectrum of the signal x(t) b. What is the Nyquist rate for this signal? cos(t) + 5sn3t. me-invariant system defined by, dt dt what will the system output y(t) be? QUESTION 5 The system function of a casual LTI system is given as, 2s a. Find the impulse response of the system. b. Find the step response of the system. A causal discrete-time LTI system is described by, y[n] - (3/4) yin-1+(1/8) yin-21 xn]...
Problem 1 A sinusodial signal x(t)- sin2t (t in seconds) is input to a system with frequency response: H(G What signal y(t) is observed at the output? Problem 2 The inverse Fourier transform of a system frequency response is given by h(t)t. The signal x(t) 3 cos(4t 0.5) is input to the system (t in seconds). (a) What is the expression of the signal y(t) at the system output? (b) What is the power attenuation in dB caused by the...
1. Signal f(t) : (5 + rect( )) cos(60πt) is mixed with signal cos(60πt) to produce the signal y(t). Subsequently, COS y(t) is low-pass filtered with a system having frequency response H(w) = 4recG ) to produce q(t). Sketch F(w),Y(w), Q(u), and determine q(t) 2. If signal f(t) is not band-limited, would it be possible to reconstruct f(t) exactly from its samples f(nT) taken with some finite sampling interval T> 0? Explain your reasoning 1. Signal f(t) : (5 +...
Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input torque is supplied by an electric motor Specifically, T(t) T(t) -Kamp Vin(t) where 1) "Vin is the input voltage supplied to the motor N-m 2) "Kamp" is the motor gain (this constant has units of Volt) So, the transfer function for this system is (s)Kamp The moment of inertia is known...
4 a. y(t)-x(t)cos(t/2 b. y(t)-x(t)cos(') x()cos(21) c. X (ju) 5. The signals y(t) in 4a-4e are passed through a filter with unit impulse response h(t) so that the output is z(t)-h(t)*y(t) . Ifthe frequency response of the filter is sketch by hand the Fourier transforms Z(j for 4a-4e Fromjust observing your sketches of Z (jo), which z(1) if any in a-e equal to the original
17. The following system is used to sample and reconstruct the signal x(t)-1-cos(15π) with a sampling interval T-0.1 sec. p(t) xIn] y(t) x(t) -0.5 0.5 1B 1B X.(o) X (o) [2 Marks each] Given that the input signal, x(t) -1+cos(15rt) Sketch |X(a) The sampling interval is set to T= 0, 1 ec. SketchXs(o) where x(t) = p(t)x(t). Determine the expression for y(t). Is y(t) a reconstruction of x()? Does aliasing occur? explain 17. The following system is used to sample...
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)|
4. Given that x(t) has the Fourier transform X(a), p(t) is a periodic signal with frequency of ??. p(t)-??--o nejnaot, where Cn is the Fourier series coefficient of p) (1) Assume y(t)-x(t)p(t), determine Y(?), the Fourier transform of the modulated signal y(t) in terms of X(). (2) Given the spectrum sketch of x(?) shown below, p(t)-cos(2t) cos(t), determine and sketch the Y() X(w) -1
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this...