Consider the feedback system shown below: +e[n] xlnDelay → y[n] (a) Write an expression for y[n]...
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...
Problem # 3 [15 Points] Consider the following single-input, single-output system: (a) Characterize the controllable subspace and the unobservable subspace of the system (b) Determine the transfer function and the impulse response of the sys- tem. (c) Is the system asymptotically stable? Is it BIBO stable? Justify your Problem # 3 [15 Points] Consider the following single-input, single-output system: (a) Characterize the controllable subspace and the unobservable subspace of the system (b) Determine the transfer function and the impulse response...
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...
. (15 points) An unstable system can be stabilized by using negative feedback with a gain K in the feedback loop. For instance, consider an unstable system with transfer function which has a pole in the right-hand s-plane, making the impulse response of the system h) grow as increases. Use negative feedback with a gain K> 0 in the feedback loop, and put H) in the forward loop. Draw a block diagram of the system. Obtain the transfer function Gus)...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
Consider a causal LTI system described by e yin]-ανίn- μ) = xjn] A. What is the condition of o over which the system is BIBO stable? B. For & = /½ and u 2, find this system transfer function. C. For the same conditions in part B, find the frequency response H() D. Determine the magnitude and phase of H(o). E. Use MATLAB to sketch the magnitude spectrum over 0< w s 2n Consider a causal LTI system described by...
7. For a linear system whose input-output relations is represented as: v n]=x[n]+0.5x[n-l]-0.25x[n-2]·(x r input. y[n] output) We also assume this system is originally at rest, ie. yln] -0 ifnco. (a) Write the transfer function of this systenm (b) Determine the first five samples of its impulse response. (c) Is this system a stable system? (d) Write down the input-output relation the causal inverse system of this system (e) Use Matlab to finds zeros and poles of the transfer function...
(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...
(a) A system has the impulse response, h[n], and is excited with the input signal, xIn], as shown below. Using either a mathematical or a graphical convolution technique, determine the output of the system, y[n] (that is, evaluate y[n] h[nl'xIn], where" denotes convolution). 17 marks xIn INPUT FIR filter 0.5 0.25 OUTPUT 0 1 345 6 7 .. 0.5 0123 4567 (b) An IIR filter is shown below: ylnl One sample delay (z) 0.4 i) Derive the difference equation describing...
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...