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Problem 9.5 (Superposition input) A linear time-invariant system has frequency response The input...
4. Consider the magnitude and phase of the frequency response Hi(2) of a linear and time-invariant...
4. Consider the magnitude and phase of the frequency response Hi(2) of a linear and time-invariant (LTI) discrete-time System 1, given for-r < Ω-T, as: H, (12)| 10 phase H1(Ω)--0 for all Ω (a) Suppose an 5cos(n s input to System 1. Find the output ya[n] (b) Suppose ancos(is input to System 1. Find the output ybn] (c) Suppose I take the discrete-time signal from part (a): xa[n] 5cos(n), but I remove half of the values: to arrive at a...
Explain how fourier transform is done? 1. (8 points) Suppose a particular discrete-time linear and time-invariant...
Explain how fourier transform is done?
1. (8 points) Suppose a particular discrete-time linear and time-invariant (LTI) system has frequency response H(e) and that when its input is z[n] = 2 cos (n). the corresponding output is y[n] = 6 cos (n+ ) Find the real part and imaginary part of H(e)") at w = .
3. Suppose that the frequency response of an LTI system is given by (a) What is...
3. Suppose that the frequency response of an LTI system is given by (a) What is the impulse response hinl) of the system? (b) Suppose that the input signal has the form zin-Ae'? n. For what values of ?0 in the range -r S will we have yn0 for all n? (c) Find the output y[n] of the system for the input x[n] = 3 + ?[n-2] cos(0.5?n 0.25m
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?...
Question 2 A linear time-invariant (LTI) system has its response described by the following second-order differential...
Question 2 A linear time-invariant (LTI) system has its response described by the following second-order differential equation: d'y) 3-10))-3*0)-6x0) dy_hi dx(t) where x() is the input function and y(t) is the output function. (a) Determine the transfer function H(a) of the system. (b) Determine the impulse response h(t) of the system.
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.
Te signal sn2mie' s-is . power signal. It is input to a linear time invariant j4n...
Te signal sn2mie' s-is . power signal. It is input to a linear time invariant j4n n +1 x(t) = is a power signal. It is input to a linear time invariant system whose impulse response is ht) 40sinc(t/20). The corresponding output is ) (a) Find the power of ) (b) Express a(t) by its trigonometric Fourier Series (c) Find ut). (d) Find the power of x)
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...
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...
Problem 5.3 (20 Points) A discrete-time, linear time-invariant system H is formed by ar- ranging three...
Problem 5.3 (20 Points) A discrete-time, linear time-invariant system H is formed by ar- ranging three individual LTI systems as shown below. LTI LII System 1 System 2 n] > >yn] ATI System 3 Figure 2: The cascaded LTI system H. The frequency response of the individual system H, is as follows: H2 : H el) = -1 + 2e- ja The impulse response of the other individual systems are as follows: Huhn = 0[n] - [n - 1] +...
4. Consider the magnitude and phase of the frequency response Hi(2) of a linear and time-invariant (LTI) discrete-time System 1, given for-r < Ω-T, as: H, (12)| 10 phase H1(Ω)--0 for all Ω (a) Suppose an 5cos(n s input to System 1. Find the output ya[n] (b) Suppose ancos(is input to System 1. Find the output ybn] (c) Suppose I take the discrete-time signal from part (a): xa[n] 5cos(n), but I remove half of the values: to arrive at a...
Explain how fourier transform is done?
1. (8 points) Suppose a particular discrete-time linear and time-invariant (LTI) system has frequency response H(e) and that when its input is z[n] = 2 cos (n). the corresponding output is y[n] = 6 cos (n+ ) Find the real part and imaginary part of H(e)") at w = .
3. Suppose that the frequency response of an LTI system is given by (a) What is the impulse response hinl) of the system? (b) Suppose that the input signal has the form zin-Ae'? n. For what values of ?0 in the range -r S will we have yn0 for all n? (c) Find the output y[n] of the system for the input x[n] = 3 + ?[n-2] cos(0.5?n 0.25m
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?...
Question 2 A linear time-invariant (LTI) system has its response described by the following second-order differential equation: d'y) 3-10))-3*0)-6x0) dy_hi dx(t) where x() is the input function and y(t) is the output function. (a) Determine the transfer function H(a) of the system. (b) Determine the impulse response h(t) of the system.
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.
Te signal sn2mie' s-is . power signal. It is input to a linear time invariant j4n n +1 x(t) = is a power signal. It is input to a linear time invariant system whose impulse response is ht) 40sinc(t/20). The corresponding output is ) (a) Find the power of ) (b) Express a(t) by its trigonometric Fourier Series (c) Find ut). (d) Find the power of x)
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...
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...
Problem 5.3 (20 Points) A discrete-time, linear time-invariant system H is formed by ar- ranging three individual LTI systems as shown below. LTI LII System 1 System 2 n] > >yn] ATI System 3 Figure 2: The cascaded LTI system H. The frequency response of the individual system H, is as follows: H2 : H el) = -1 + 2e- ja The impulse response of the other individual systems are as follows: Huhn = 0[n] - [n - 1] +...
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