3. Impulse response 10.18. Suppose that the system of Figure P10.3 is described by each of...
Consider a DT system with input x[n] and output y[n] described
by the difference equation 4y[n+1]+y[n-1]=8x[n+1]+8x[n]
73 Consider a DT system with input xin and output yin] described by the difference equation (a) What is the order of this system? (b) Determine the characteristic mode(s) of the system (c) Determine a closed-form expression for the system's impulse response hln].
73 Consider a DT system with input xin and output yin] described by the difference equation (a) What is the order...
03/14/2019 Name An L.TI system has an impulse response hn) and input xInl displayed in Figure 2 below. Apply the method of graphical convoluti and sketch the convolution output y[n] of the system givern 4. on to find y[n] x[n]*h[n]. ん[n] xIn] -4 3 2 2 3 n Figure 2
Suppose that for the LTI system depicted in the following figure (a), the impulse response and the transfer function are given by h(t) = e-tu(t) H(S) = s+1 1 H 100 The input signal x(t) is the square wave of Figure (b), where t is in seconds. Since the fundamental period is To = 2π, the fundamental frequency is ao-2π/L = 1 rad/s and kaa-k. 3t (a) Use the Table provided to find the exponential Fourier series of the signal...
For the LTI system described by the following impulse response: \(h(n)=n\left(\frac{1}{3}\right)^{n} u(n)+\left(-\frac{1}{4}\right)^{n} u(n)\)Determine the following:1) The system function representation,2) The Difference equation representation3) The pole-zero plot4) the output \(y(n)\) if the input \(x(n)\) is: \(x(n)=\left(\frac{1}{4}\right)^{n} u(n)\)
Please show full Calculations for part C)
1. Consider the following causal LTI systems with difference equations (a) yIn]+3 y[n-1]+2y[n-2] - x[n] + 2xln-1] (b) y[n] +0.8 y[n-21 x[n-1]. (c) y[n] -0.5 yln-2 2x[n] -xln-21]. In each of cases a,b and c i) Find and sketch the impulse response, hin) by recursive solution. ii) Is the system FIR or IIR ? ii) Find and sketch the corresponding step response, s[n] iv) Draw the direct form & direct-form Il structures for...
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the given block diagram to the transposed direct form II one. 2 (b) Determine the difference-equation representation of the system 4 (c) Find the transfer function for this causal filter and state the pole-zero pattern (d) Determine the impulse response of the system 2 (e) For what values of k is the system stable? (f) Determine yln if k 1 and...
Consider a linear time-invariant system with impulse response hin (-1, n o 2, n 1 h[n]--1, n=2 0, otherwise (a) Determine the system frequency response H(e"). Then compute the magnitude and (b) Does the system have a linear phase? Briefly explain your answer. (2 marks) (c) Compute the system output yin] for all values of n if the input r[n] has the form of: phase of H(e (6 marks) 1,n=1 2, n 2 n3, n 3 4, n-4 0, otherwise...
4. Consider a causal FIR filter of length M 6 with impulse response h[n] = {2.2, 2,2, 2,2) (a) Provide a closed-form expression for the 8-point DFT of hin], de- (b) Consider the sequence xIn of length L 8 below, equal to a sum noted by H8 , as a function of k. Simplify as much as possible. of several finite-length sinewaves: n] is formed by computing X,lk as an 8-point DFT of n), Hslk) as an 8-point DFT of...
Determine the impulse response h[n] of the LTI system described by the difference equationy[n] - 0.35y[n-1] = x[n]
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution determine yin, 1f XIn = 1 un.(6 marks
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution...