![Problem 3 (25 points A linear time-invariant filter is described by the difference equation a. (5) Write an expression for the frequency response of the system, H(e/). b. (5) Sketch the magnitude response of the system as a function of frequency over Nyquist interval. (5) Determine the output when the input is xln] 5+2cos(0.5 sequence e. (5) Determine the output when the input is the unit-step sequence uln.](http://img.homeworklib.com/questions/fe0a51e0-c9e7-11ea-b840-d34965815237.png?x-oss-process=image/resize,w_560)
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Problem 3 (25 points A linear time-invariant filter is described by the difference equation a. (5)...
1: A linear time-invariant system is described by the FIR difference equation (a) Write down the...
1: A linear time-invariant system is described by the FIR difference equation (a) Write down the impulse response hin) l, the frequency response H(e), and the system function H(a) of this system. 10 points) (b) Write down the expressions for the magnitude |H(e)) and the angle L) of the frequeney response) Sketch |H(e) and LM(e) with respect to . 10 points (c) Is this filter low-pass, high-pass, or band-pass? Why? [5 points) (d) Given the input z[n] = 6cos (03m...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww +...
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)
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...
6. (15) Consider the following causal linear time-invariant (LTT) discrete-time filter with input in and output...
6. (15) Consider the following causal linear time-invariant (LTT) discrete-time filter with input in and output yn described by y[n] = x[n] – rn - 2 for n 20 . Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? • What are the initial conditions and their values for this causal and linear time-invariant system? Why? • Draw the block diagram of the filter relating input x[n) and output y[n] • Derive a formula for...
P2.19 A linear and time-invariant system is described by the difference equation y(n) 0.5y(n 10.25y(n 2)-x(n)...
P2.19 A linear and time-invariant system is described by the difference equation y(n) 0.5y(n 10.25y(n 2)-x(n) + 2r(n - 1) + r(n -3) 1. Using the filter function, compute and plot the impulse response of the system over 0n100. 2. Determine the stability of the system from this impulse response. 3. If the input to this system is r(n) 5 3 cos(0.2Tm) 4sin(0.6Tn)] u(n), determine the 200 using the filter function response y(n) over 0 n
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n...
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n] and output y[n] described by bx[n-21- ax[n-3 for n 2 0, where a and b are real-valued positive coefficients. A) Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? B) What are the initial conditions and their values? Why? C) Draw the block diagram of the filter relating input x[n] and output y[n] D) Derive a formula for the transfer function in...
solve all 22. The input-output relationship for a linear, time-invariant system is described by differential equation...
solve all
22. The input-output relationship for a linear, time-invariant system is described by differential equation y") +5y'()+6y(1)=2x'()+x(1) This system is excited from rest by a unit-strength impulse, i.e., X(t) = 8(t). Find the corresponding response y(t) using Fourier transform methods. 23. A signal x(1) = 2 + cos (215001)+cos (210001)+cos (2.15001). a) Sketch the Fourier transform X b) Signal x() is input to a filter with impulse response (1) given below. In each case, sketch the associated frequency response...
Consider a linear, time-invariant system with an input given by X(T) = A, sin(Wit) where w,...
Consider a linear, time-invariant system with an input given by X(T) = A, sin(Wit) where w, is a specific frequency. The system has a frequency response given by the amplitude ratio (magnitude ratio) as a function of the frequency, Mw), and the phase difference as a function of frequency, °W). Write an expression for the corresponding output in terms of the input amplitude, A1, the input frequency, W1, the amplitude ratio, and the phase difference.
A causal,d following difference equation linear, time-invariant system is governed by the (a) Determine the transfer...
A causal,d following difference equation linear, time-invariant system is governed by the (a) Determine the transfer function, H(2), of the system and its region of (b) Determine the output yi[n] of the system in response to the input (c) Determine the output y2fn] of the system in response to the input convergence. r2n (2). Note that z2n] does not have a z-transform.
Q.5 (a) Show that a linear, time-invariant, discrete-time system is stable in the bounded- input bounded-output...
Q.5 (a) Show that a linear, time-invariant, discrete-time system is stable in the bounded- input bounded-output sense if, and only if the unit sample response of the system, h[n], is absolutely summable, that is, Alfa]]<00 | [n]| < do ***** (13 marks] (b) Consider a linear, time-invariant discrete-time system with unit sample response, hin), given by hin] = a[n] – đặn – 3 where [n] is the unit sample sequence. (1) Is the system stable in the bounded-input bounded-output sense?...
1: A linear time-invariant system is described by the FIR difference equation (a) Write down the impulse response hin) l, the frequency response H(e), and the system function H(a) of this system. 10 points) (b) Write down the expressions for the magnitude |H(e)) and the angle L) of the frequeney response) Sketch |H(e) and LM(e) with respect to . 10 points (c) Is this filter low-pass, high-pass, or band-pass? Why? [5 points) (d) Given the input z[n] = 6cos (03m...
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)
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...
6. (15) Consider the following causal linear time-invariant (LTT) discrete-time filter with input in and output yn described by y[n] = x[n] – rn - 2 for n 20 . Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? • What are the initial conditions and their values for this causal and linear time-invariant system? Why? • Draw the block diagram of the filter relating input x[n) and output y[n] • Derive a formula for...
P2.19 A linear and time-invariant system is described by the difference equation y(n) 0.5y(n 10.25y(n 2)-x(n) + 2r(n - 1) + r(n -3) 1. Using the filter function, compute and plot the impulse response of the system over 0n100. 2. Determine the stability of the system from this impulse response. 3. If the input to this system is r(n) 5 3 cos(0.2Tm) 4sin(0.6Tn)] u(n), determine the 200 using the filter function response y(n) over 0 n
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n] and output y[n] described by bx[n-21- ax[n-3 for n 2 0, where a and b are real-valued positive coefficients. A) Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? B) What are the initial conditions and their values? Why? C) Draw the block diagram of the filter relating input x[n] and output y[n] D) Derive a formula for the transfer function in...
solve all
22. The input-output relationship for a linear, time-invariant system is described by differential equation y") +5y'()+6y(1)=2x'()+x(1) This system is excited from rest by a unit-strength impulse, i.e., X(t) = 8(t). Find the corresponding response y(t) using Fourier transform methods. 23. A signal x(1) = 2 + cos (215001)+cos (210001)+cos (2.15001). a) Sketch the Fourier transform X b) Signal x() is input to a filter with impulse response (1) given below. In each case, sketch the associated frequency response...
Consider a linear, time-invariant system with an input given by X(T) = A, sin(Wit) where w, is a specific frequency. The system has a frequency response given by the amplitude ratio (magnitude ratio) as a function of the frequency, Mw), and the phase difference as a function of frequency, °W). Write an expression for the corresponding output in terms of the input amplitude, A1, the input frequency, W1, the amplitude ratio, and the phase difference.
A causal,d following difference equation linear, time-invariant system is governed by the (a) Determine the transfer function, H(2), of the system and its region of (b) Determine the output yi[n] of the system in response to the input (c) Determine the output y2fn] of the system in response to the input convergence. r2n (2). Note that z2n] does not have a z-transform.
Q.5 (a) Show that a linear, time-invariant, discrete-time system is stable in the bounded- input bounded-output sense if, and only if the unit sample response of the system, h[n], is absolutely summable, that is, Alfa]]<00 | [n]| < do ***** (13 marks] (b) Consider a linear, time-invariant discrete-time system with unit sample response, hin), given by hin] = a[n] – đặn – 3 where [n] is the unit sample sequence. (1) Is the system stable in the bounded-input bounded-output sense?...
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