Question: Given y{n}=2*x[n], what does the impulse response tell us about its stability? aside: Stability is...
Question: Given y{n}=2*x[n], what does the impulse response tell us about its stability?
aside: Stability is when you have a bounded input, you get a bounded output. And its bounded if its absolutely summable. So is the delta function (impulse response is an impulse times a constant) absolutely summable? What is the absolute value of an impulse response...just 1?
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Question: Given y{n}=2*x[n], what does the impulse response tell
us about its stability?
aside: Stability is...
Consider the LTI system described by the following impulse response: (a) h(n) = 2(0.5)n u(n). Determine:...
Consider the LTI system described by the following impulse response: (a) h(n) = 2(0.5)n u(n). Determine: (i) The system function representation; (ii) the difference-equation representation (Note: this is just terminology that refers to expressing the input and output time-domain signals in the form of an equation. E.g., what we did when we went over the equations for block diagrams); (iii) The pole-zero plot, sketched by hand; and (iv) the output y(n) if the input is x(n) = (0.25)n u(n) [10...
(i) An FIR system has the impulse response hln] = 3?[n 2 . When the signal...
(i) An FIR system has the impulse response hln] = 3?[n 2 . When the signal a [n] is passed (ii) Consider a signal In] whose DTFT is given by X(es*). What is the DTFT of ii) Suppose hi [n] is the impulse response of an ideal lowpass filter. Which of the options through the system, what is the output, written as a function of rn]? y[n] = x[n-3), written as a function of X(eM)? below is the impulse response...
9-5. Given: an ideal digital BPF has impulse response h(n) = z sinc(n) - sinc(n). What...
9-5. Given: an ideal digital BPF has impulse response h(n) = z sinc(n) - sinc(n). What is its output signal when the input signal is the sequence cos(2n)?
1. An LTI system has impulse response defined by h (n )={2 ,2 ,−1,−1 ,−1,−1}first 2...
1. An LTI system has impulse response defined by h (n )={2 ,2 ,−1,−1 ,−1,−1}first 2 zero . Determine the outputs when the input x(n) is (a) u(n ) ; (b) u(n−4 ) 2. Let the rectangle pulse x ( n )=u ( n ) −u (n −10 ) be an input to an LTI system with impulse response h (n )=(0.9 )n u (n ) . Determine the output y ( n ) . (Hint: You need to consider muliple...
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...
5 pts D Question 1 A system has the following impulse response: .2 Sample number, n From the choices below, select the frequency response of this system. H (eju)-e(1.5 ) (2 sin( 1.5ώ) +...
5 pts D Question 1 A system has the following impulse response: .2 Sample number, n From the choices below, select the frequency response of this system. H (eju)-e(1.5 ) (2 sin( 1.5ώ) + 4 sin(0.δώ)) H (ee) = e-j(1.5e-5) (cos( 1.5 ) +2 cos(0.54)) @ H (ee)-e-n1.si) (sin( 1.54) t. 2 sin(0.δώ)) (sin(l.50) +4sin(0.0) H (ee)-e-j(1.5i) (2 cos( 1.5ώ) + 4 cos(0.5a)) H (efo)-e-n1.5u) (cos( 1.50) + 2 cos(0.50)) https://rmitinstructure.comcoursesy 5 pts DQuestion 2 A system has the following...
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)...
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...
(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...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n)...
(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...
aliasing? A continuous-time system is given by the input/output differential equation 4. H(s) v(t) dy(t) dt dx(t) + 2 (+ x(t 2) dt (a) Determine its transfer function H(s)? (b) Determine its impulse...
aliasing? A continuous-time system is given by the input/output differential equation 4. H(s) v(t) dy(t) dt dx(t) + 2 (+ x(t 2) dt (a) Determine its transfer function H(s)? (b) Determine its impulse response. (c) Determine its step response. (d) Is the stable? (a) Give two reasons why digital filters are favored over analog filters 5. (b) What is the main difference between IIR and FIR digital filters? (c) Give an example of a second order IIR filter and FIR...
(i) An FIR system has the impulse response hln] = 3?[n 2 . When the signal a [n] is passed (ii) Consider a signal In] whose DTFT is given by X(es*). What is the DTFT of ii) Suppose hi [n] is the impulse response of an ideal lowpass filter. Which of the options through the system, what is the output, written as a function of rn]? y[n] = x[n-3), written as a function of X(eM)? below is the impulse response...
9-5. Given: an ideal digital BPF has impulse response h(n) = z sinc(n) - sinc(n). What is its output signal when the input signal is the sequence cos(2n)?
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...
5 pts D Question 1 A system has the following impulse response: .2 Sample number, n From the choices below, select the frequency response of this system. H (eju)-e(1.5 ) (2 sin( 1.5ώ) + 4 sin(0.δώ)) H (ee) = e-j(1.5e-5) (cos( 1.5 ) +2 cos(0.54)) @ H (ee)-e-n1.si) (sin( 1.54) t. 2 sin(0.δώ)) (sin(l.50) +4sin(0.0) H (ee)-e-j(1.5i) (2 cos( 1.5ώ) + 4 cos(0.5a)) H (efo)-e-n1.5u) (cos( 1.50) + 2 cos(0.50)) https://rmitinstructure.comcoursesy 5 pts DQuestion 2 A system has the following...
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...
(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...
(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...
aliasing? A continuous-time system is given by the input/output differential equation 4. H(s) v(t) dy(t) dt dx(t) + 2 (+ x(t 2) dt (a) Determine its transfer function H(s)? (b) Determine its impulse response. (c) Determine its step response. (d) Is the stable? (a) Give two reasons why digital filters are favored over analog filters 5. (b) What is the main difference between IIR and FIR digital filters? (c) Give an example of a second order IIR filter and FIR...
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