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]
Consider a DT system with input x[n] and output y[n] described by the difference equation 4y[n+1]...
Consider a DT system with input.xin] and output (n] 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 h[n].
Question 2. Consider the DT system described by the difference equation y[n] - 0.2y[n-1]xIn-1] Determine directly yl-1]-1. in the time domain its zero-input response for the initial value of Question 2. Consider the DT system described by the difference equation y[n] - 0.2y[n-1]xIn-1] Determine directly yl-1]-1. in the time domain its zero-input response for the initial value of
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...
Question 3. Consider the DT system described by the difference equation y[n+1]+ 0.3 y[n] 0.4x[n] Using the Z-transform, determine the system's zero-input response for the initial value of y[0] 1/3. The solution directly in the time domain is not accepted
5. A DT system having input x[n] and output yIn] is described by the difference equation J?nJ 0.8 IJln 2] x[n]-0.75x(n-l]. Assuming that x[n]-n(0.75)" u[n], use transfomn methods to determine the output y[n]. The property of DTFTs glnl Lm?G(e'?) then > / G(er) should help in obtaining the DTFT of the input. (20 pts.) ds2
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation y[n – 1] + 3 y[n] + $y[n + 1] = x[n]. Determine the three possible choices for the impulse response that makes this system 1) causal, 2) two-sided and 3) anti-causal. Then for each case, determine if the system is stable or not. Causality Impulse Response Stability Causal Unstable v two-sided Unstable anti-Causal Unstable y In your answers, enter z(n) for a discrete-time...
Determine and plot the output response of a DT system described by the difference equation if the input is given as x[n]= δ[n-1].
Consider an LTI system with input sequence x[n] and output sequence y[n] that satisfy the difference equation 3y[n] – 7y[n – 1] + 2y[n – 2] = 3x[n] – 3x[n – 1] (2.1) The fact that sequences x[ ] and y[ ] are in input-output relation and satisfy (2.1) does not yet determine which LTI system. a) We assume each possible input sequence to this system has its Z-transform and that the impulse response of this system also has its Z-transform. Express the...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)