![2. Analysis (30pts) Given this difference equation for a system: y[n] = + x[n-2] a. Find h[n] b. Find Hz), and determine the](http://img.homeworklib.com/questions/924c9370-504f-11eb-a72d-d33edb759f64.png?x-oss-process=image/resize,w_560)
Homework Answers
Note: As per HOMEWORKLIB POLICY we have to answer first four parts only.
By using Z transform and impulse response of LTI system we get the solution. By looking at pole zero plot it is observed that the system is band pass system.
![ying = x[n] + = [n++] + <>[-] a) For hin] x[0]=Sin] ] yen] =hing DT LTI but hen] = { Sing + į S(n-1) + ý S[n-2] - 0 b2 Apply](http://img.homeworklib.com/questions/92dfa000-504f-11eb-a000-d17e731eb23c.png?x-oss-process=image/resize,w_560)
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2. Analysis (30pts) Given this difference equation for a system: y[n] = + x[n-2] a. Find...
1. A causal LTI system is implemented by the difference equation y(n) = 2r(n) - 0.5...
1. A causal LTI system is implemented by the difference equation y(n) = 2r(n) - 0.5 y(n-1). (a) Find the frequency response H/(w) of the system. (b) Plot the pole-zero diagram of the system. Based on the pole zero diagram, roughly sketch the frequency response magnitude |H'(w). (c) Indicate on your sketch of H w , its exact values at w=0, 0.5, and . (d) Find the output signal y(n) produced by the input signal (n) = 3 + cos(0.5...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] –...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...
Styles Paragraph 6. Given the difference equation y(n)-x(n-1)-0.75y(n-1)-0.125(n-2) a. Use MATLAB function filterl) and filticl) to...
Styles Paragraph 6. Given the difference equation y(n)-x(n-1)-0.75y(n-1)-0.125(n-2) a. Use MATLAB function filterl) and filticl) to calculate the system response y(n)for n 0, 1, 2, 3, 4 with the input of x(n (0.5) u(n)and initial conditions x(-1)--1, y(-2) -2, and y(-1)-1 b. Use MATLAB function filter!) to calculate the system response y(n) for n-0, 1, 2, 3,4 with the input of x(n) (0.5)"u(n)and zero initial conditions x(-1)-0, (-2)-0, and y(-1)-0 Design a 5-tap FIR low pass filter with a cutoff...
Given the following difference equation that describes the input output relationship, (a) Express Y(z), the z-transform...
Given the following difference equation that describes the input output relationship, (a) Express Y(z), the z-transform of the output, in terms of X(z), the z-transform of the input. (b) Find the system function H(z). (c) Identify the zeros and poles. Sketch the zero-pole plot. (d) For an input rn]- cos (n), find the output yn] (e) Use the zero-pole plot to explain what you obtain in d)
Show all your work for each problem. 1. Given the following DSP system with a sampling...
Show all your work for each problem. 1. Given the following DSP system with a sampling rate 8000 Hz, y(0.5x(n)-0.5x(n -1) where y(n) is the output and x(n) is the input a) Find its transfer function, b) Make a pole-zero plot and determine the stability. c) Obtain He) and then He) d) Compute the filter gain at the frequency of 0 Hz, 1000 Hz, 2000 Hz, 3000Hz, 4000 Hz, respectively e Make a magnitude frequency response plot. f) Determine the...
(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 outp...
(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...
Determine the difference equation relating the input (x[n]) and outpt (y[n])
(a) Determine the difference equation relating the input (x[n]) and outpt (y[n]) for an LTI system whose impulse response is given by: h(n) = (1/4){δ(n) + δ(n - 1) (b) Find and plot the amplitude and phase response of the above LTI system. Indicate what kind of filter this system represents.
(5) For the system described by the following difference equation y(n)= 0.9051y(n 1) 0.598y(n 2) -0.29y(n...
(5) For the system described by the following difference equation y(n)= 0.9051y(n 1) 0.598y(n 2) -0.29y(n 3) 0.1958y(n - 4) +0.207r(n)0.413r(n 2)+0.207a(n - 4) (a) Plot the magnitude and phase responses of the above system. What is the type of this filter? (b) (b) Find and plot the response of the system to the input signal given by /6)sin(w2n +T /4) u(n), where w 0.25m and ws 0.45m a(n) 4cos(win -T = (c) Determine the steady-state output and hence find...
For a causal LTI discrete-time system described by the difference equation:
For a causal LTI discrete-time system described by the difference equation: y[n] + y[n – 1] = x[n] a) Find the transfer function H(z).b) Find poles and zeros and then mark them on the z-plane (pole-zero plot). Is this system BIBO? c) Find its impulse response h[n]. d) Draw the z-domain block diagram (using the unit delay block z-1) of the discrete-time system. e) Find the output y[n] for input x[n] = 10 u[n] if all initial conditions are 0.
EE341
1. (6 pts) Consider a causal LTI system described by the following difference equation:y(n) = —0.8y(n — 1) + x(n)a) Is this system a FIR or IIR filter? Explain.b) Find the frequency response H(Q) of the system. Plot |H(Q)|. Prove that |H(Q)|is symmetric.c) Is this system a low-pass or high-pass filter? Explain.d) Consider the following signal:x(n) = 5 + 10sin(an/6) + 10cos(an/2), -oo<n<tooIs this signal periodic? What is its period? Plot |X(0)|, where X(Q) is the DTFTof x(n).e) Determine the...
1. A causal LTI system is implemented by the difference equation y(n) = 2r(n) - 0.5 y(n-1). (a) Find the frequency response H/(w) of the system. (b) Plot the pole-zero diagram of the system. Based on the pole zero diagram, roughly sketch the frequency response magnitude |H'(w). (c) Indicate on your sketch of H w , its exact values at w=0, 0.5, and . (d) Find the output signal y(n) produced by the input signal (n) = 3 + cos(0.5...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...
Styles Paragraph 6. Given the difference equation y(n)-x(n-1)-0.75y(n-1)-0.125(n-2) a. Use MATLAB function filterl) and filticl) to calculate the system response y(n)for n 0, 1, 2, 3, 4 with the input of x(n (0.5) u(n)and initial conditions x(-1)--1, y(-2) -2, and y(-1)-1 b. Use MATLAB function filter!) to calculate the system response y(n) for n-0, 1, 2, 3,4 with the input of x(n) (0.5)"u(n)and zero initial conditions x(-1)-0, (-2)-0, and y(-1)-0 Design a 5-tap FIR low pass filter with a cutoff...
Given the following difference equation that describes the input output relationship, (a) Express Y(z), the z-transform of the output, in terms of X(z), the z-transform of the input. (b) Find the system function H(z). (c) Identify the zeros and poles. Sketch the zero-pole plot. (d) For an input rn]- cos (n), find the output yn] (e) Use the zero-pole plot to explain what you obtain in d)
Show all your work for each problem. 1. Given the following DSP system with a sampling rate 8000 Hz, y(0.5x(n)-0.5x(n -1) where y(n) is the output and x(n) is the input a) Find its transfer function, b) Make a pole-zero plot and determine the stability. c) Obtain He) and then He) d) Compute the filter gain at the frequency of 0 Hz, 1000 Hz, 2000 Hz, 3000Hz, 4000 Hz, respectively e Make a magnitude frequency response plot. f) Determine the...
(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...
(5) For the system described by the following difference equation y(n)= 0.9051y(n 1) 0.598y(n 2) -0.29y(n 3) 0.1958y(n - 4) +0.207r(n)0.413r(n 2)+0.207a(n - 4) (a) Plot the magnitude and phase responses of the above system. What is the type of this filter? (b) (b) Find and plot the response of the system to the input signal given by /6)sin(w2n +T /4) u(n), where w 0.25m and ws 0.45m a(n) 4cos(win -T = (c) Determine the steady-state output and hence find...
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