Question

In: Electrical Engineering

Consider the first order linear time-invariant (LTI) system given by, ??(?) ?? + 4?(?) = ?(?)...

Consider the first order linear time-invariant (LTI) system given by,

??(?) ?? + 4?(?) = ?(?)

Where the system is initially at rest.

Part a: Determine the Frequency Response H(jω) and impulse response h(t).

Part b: When the input ?(?) = ?23?(?), determine the output of the system ?(?).

Part c: Is the system; memoryless? causal? Stable? please justify your answer

Solutions

Expert Solution

By using fourier transform properties and simple signal and systems analysis, we can determine the required values.

Manojponduru answered 1 year ago
Next > < Previous

Related Solutions

Consider the linear time invariant system described by the transfer function G(s) given below. Find the...
Consider the linear time invariant system described by the transfer function G(s) given below. Find the steady-state response of this system for two cases: G(s) = X(s)/F(s) = (s+2)/(3(s^2)+6s+24) when the input is f(t) = 5sin(2t) and f(t) = 5sin(2t) + 3sin(2sqrt(3)t)
The impulse response of a discrete-time LTI system is given as ℎ[?] = ?[? + 1]...
The impulse response of a discrete-time LTI system is given as ℎ[?] = ?[? + 1] − ?[? − 1] a) State whether or not the system is (i) memoryless, (ii) causal, (iii) stable. Justify your answers mathematically. b) Find the output ?[?] of the system for input ?[?] = (0.5) ??[?].
Determine where the system is 1) linear 2) causal 3) stable and 4) time-invariant. a)y(n)= nx(n)...
Determine where the system is 1) linear 2) causal 3) stable and 4) time-invariant. a)y(n)= nx(n) b) y(n)=x square(n)
Using MATLAB, determine whether the system below are a) linear/non-linear b) time-invariant/timevariant, c) causal/noncausal, d) has...
Using MATLAB, determine whether the system below are a) linear/non-linear b) time-invariant/timevariant, c) causal/noncausal, d) has memory/memoryless: y(t) = x(t) + x(t -1) Provide MATLAB code and graphs to show your work for the linearity and time-invariance testing.
Consider the discrete-time LTI system characterized by the following difference equation with input and initial conditions specified
  Consider the discrete-time LTI system characterized by the following difference equation with input and initial conditions specified: y[n] - 2 y[n-1] – 3 y[n-2] = x[n] , with y[0] = -1 and y[1] = 0, x[n] = (-1/2)n u[n-2]. ? Write a MATLAB program to simulate this difference equation. You may try the commands ‘filter’ or ‘filtic’ or create a loop to compute the values recursively. ? Printout and plot the values of the input signal, x[n] and the...
4. i) An input signal of an LTI system is assumed to be a rectangular pulse...
4. i) An input signal of an LTI system is assumed to be a rectangular pulse sequence x[n] of length 2L samples. Represent x[n] in terms of a unit step sequence and sketch x[n] if it turns on at n=0. ii) Suppose the impulse response of the system is also a rectangular pulse sequence h[n] of length L samples. Represent h[n] in terms of a unit step sequence and sketch h[n] if it turns on at n=0. iii) Determine the...
CHAPTER 13: DISCRETE-TIME SIGNAL (TEXTBOOK SIGNALS AND SYSTEM BY MAHMOOD NAHVI) 12. In an LTI system,...
CHAPTER 13: DISCRETE-TIME SIGNAL (TEXTBOOK SIGNALS AND SYSTEM BY MAHMOOD NAHVI) 12. In an LTI system, x(n) is the input and h(n) is the unit-sample response. Find and sketch the output y(n) for the following cases: i) x(n) = 2[u(n) - u(n - 11)] and h(n) = 0.5nu(n) ii) x(n) = 2[u(n) - u(n - 11)] and h(n) = (-0.5)nu(n) iii) x(n) = u(n) - u(n - 5) and h(n) = 0.5|n|u(n) iv) x(n) = u(n) - u(n - 5)...
Consider each of the following systems for long times, at which their behacioor is time invariant....
Consider each of the following systems for long times, at which their behacioor is time invariant. Identify each system as equilibrium or steady state. 1) A hose supplies water at a constant rate to a bucket with a hole in it. A constant water level is maintained 2)A mixture of reacting gas molecules is constrained to a fixed temperature, e.g., H2, O2 and H2O at 600 K. 3) Ice floats in water, thermally insulated from its surroundings. 4) Molten steel...
Consider each of the following systems for long times, at which their behacioor is time invariant....
Consider each of the following systems for long times, at which their behacioor is time invariant. Identify each system as equilibrium or steady state. 1) A hose supplies water at a constant rate to a bucket with a hole in it. A constant water level is maintained 2)A mixture of reacting gas molecules is constrained to a fixed temperature, e.g., H2, O2 and H2O at 600 K. 3) Ice floats in water, thermally insulated from its surroundings. 4) Molten steel...
Writing Prompt(s) One method for solving a system of first order linear differential equation such as...
Writing Prompt(s) One method for solving a system of first order linear differential equation such as x ′ = a x + b y y ′ = c x + d y is to take the derivative of the first equation and use the second equation to ``decouple'' the system and create a second order equation, which we can solve using our previous techniques. Does this always work? If not, what conditions on the constants a, b, c, and d...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT