x[n] is the input of an LTI system with the impulse response of h[n]. x[n] =...

x[n] is the input of an LTI system with the impulse response of h[n]. x[n] = [1, 2, 3] and h[n] = [4, 6]. Use 4-point DFT and IDFT and zero padding of x[n] and h[n] to find the output y[n].

Expert Solution

Manojponduru answered 7 months ago

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) ??[?].

A SISO DT LTI system having input x[n] and output is described by the difference equation...

A SISO DT LTI system having input x[n] and output is described by the difference equation y[n] = 0.5x[n] + 0.5x[n-1]. Obtain the unit sample response of the system by solving the difference equation. ( DO NOT USE LaPlace transforms or Z transforms)

if the input signal is x(t)=exp[-at]u(t) and system impulse response is h(t)=u(t+2) what is the outpul...

if the input signal is x(t)=exp[-at]u(t) and system impulse response is h(t)=u(t+2) what is the outpul signal y(t) ?

x[n] is the input of a system and y[n] is the output of the system. The...

x[n] is the input of a system and y[n] is the output of the system. The relationship between the input and output is the following: y[n] = x[n]u[n+1] a) Is the system memoryless? Just yes or no is sufficient. b) Is this system causal? Just yes or no is sufficient. c) Is the system linear? Just yes or no is sufficient. d) Is the system time invariant? Justify. e) Is the system BIBO stable? Justify. f) Is the system invertible?...

consider a system with the impulse response h(t) = e −t [u(t) − u(t − 2)]....

consider a system with the impulse response h(t) = e −t [u(t) − u(t − 2)]. (It's exponential function) Let the input signal x(t) be x(t) = 1 if 0 ≤ t < 1, x(t) = −1 if 1 ≤ t < 2, x(t) = 0 otherwise. (a) Determine the system output y(t). (b) (20) Plot y(t) using a computer and specify the maximum and minimum.

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...

the following are impulse responses/outputs of discrete -time LTI systems. Determine whether each system is causal...

the following are impulse responses/outputs of discrete -time LTI systems. Determine whether each system is causal and/or stable. justify your answers 1. h [n] = 1/5^n u [n] 2. h [n] = 5^n u [3-n] 3. y [n] = 3x [n] - 0.15y [n-1] 4. y [n] = 2e^-x [n] 5. y [n] = n^2 4x [n] B. Show if the systems defined in 1 to 5 above have bounded input and output (BIBO) from the summation of their impulse...

1. a) Compute the impulse response of the following filters. If the impulse response is infinite,...

1. a) Compute the impulse response of the following filters. If the impulse response is infinite, feel free to stop once a pattern becomes apparent. i. y[n] = 2/3 · x[n − 1] − 1/3 x[n − 2] ii. y[n] = x[n − 1] − x[n − 2] − 1/3 y[n − 2] b) What are the feed-back (b[k]) and feed-forward (a[k]) coefficients of the following filters? You may assume that a starts at delay of k = 1 (i.e.,...

Compute the unit-pulse response h[n] for the discrete-time system y[n + 2] - 2y[n + 1]...

Compute the unit-pulse response h[n] for the discrete-time system y[n + 2] - 2y[n + 1] + y[n] = x[n] (for n = 0, 1, 2, 3)

An FIR system produced an output y[n] as given below for an input x[n] = {1,1,1,1},...

An FIR system produced an output y[n] as given below for an input x[n] = {1,1,1,1}, y[n] = {6,11,15,18,14,10,6,3,1}. Find the FIR system. Use bk, d(n-k) equation if applicable. Thanks!

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