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Consider a causal LTI system described by e yin]-ανίn- μ) = xjn] A. What is the...
2.6.1 Consider a causal continuous-time LTI system described by the differential equation u"(t) +...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
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.
A causal discrete-time LTI system is described by the equation
A causal discrete-time LTI system is described by the equationwhere z is the input signal, and y the output signal y(n) = 1/3x(n) + 1/3x(n -1) + 1/3x(n - 2) (a) Sketch the impulse response of the system. (b) What is the dc gain of the system? (Find Hf(0).) (c) Sketch the output of the system when the input x(n) is the constant unity signal, x(n) = 1. (d) Sketch the output of the system when the input x(n) is the unit step signal, x(n)...
(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...
Consider a causal LTI system with frequency response H(jw) = 1 2 + jw For a...
Consider a causal LTI system with frequency response H(jw) = 1 2 + jw For a particular input x(t) this system is observed to produce the output y(t) = e-ºut) - e-stutt) i) Determine x(t). ii) Is this system stable? Explain your reasoning. iii) Plot the magnitude and phase responses of H (jw).
]\ Please can some help me with this one, snip the code and the sketch from...
]\
Please can some help me with this one, snip the code and the
sketch from MATLAB and post it here thanks
Consider a causal LTI system described by y[n]-a y[n H = x[n] For o / and u 2 Use MATLAB to sketch the magnitude spectrum over 0 < w < 2n
Consider a causal LTI system described by y[n]-a y[n H = x[n]
For o / and u 2
Use MATLAB to sketch the magnitude spectrum over 0
Problem 3. The input and the output of a stable and causal LTI system are related...
Problem 3. The input and the output of a stable and causal LTI system are related by the differential equation dy ) + 64x2 + 8y(t) = 2x(t) dt2 dt i) Find the frequency response of the system H(jw) [2 marks] ii) Using your result in (i) find the impulse response of the system h(t). [3 marks] iii) Find the transfer function of the system H(s), i.e. the Laplace transform of the impulse response [2 marks] iv) Sketch the pole-zero...
Consider the cascade of LTI discrete-time systems shown in Figure P2.37. LTI System 1 hi[n], H...
Consider the cascade of LTI discrete-time systems shown in Figure P2.37. LTI System 1 hi[n], H (el) LTI System 2 h2[n], H2(eje) Figure P2.37 The first system is described by the frequency response Hi(j =c-joo < 0.25% 11 0.25% < and the second system is described by <A hain) = 2 Sin(0.57) (a) Determine an equation that defines the frequency response, H(e)®), of the overall system over the range -- SUSA. (b) Sketch the magnitude. He"), and the phase, ZH(e)),...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
BC:9.4 A LTI discrete time system has an impulse response h[n] = (−0.6)nu[n] + (0.95)nu[n −...
BC:9.4 A LTI discrete time system has an impulse response h[n] =
(−0.6)nu[n] + (0.95)nu[n − 1] Find the transfer function, Hˆ (e jωˆ
), in the normalized frequency domain. Use Matlab to plot the
magnitude and phase (in degrees) of Hˆ (e jωˆ ) in the range of −π
≤ ωˆ ≤ π. Attach your Matlab source code with the plots.
BC:9.4 A LTI discrete time system has an impulse response h[n] = (-0.6)"u[n] + (0.95)"u[n-1] Find the transfer...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
(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...
Consider a causal LTI system with frequency response H(jw) = 1 2 + jw For a particular input x(t) this system is observed to produce the output y(t) = e-ºut) - e-stutt) i) Determine x(t). ii) Is this system stable? Explain your reasoning. iii) Plot the magnitude and phase responses of H (jw).
]\
Please can some help me with this one, snip the code and the
sketch from MATLAB and post it here thanks
Consider a causal LTI system described by y[n]-a y[n H = x[n] For o / and u 2 Use MATLAB to sketch the magnitude spectrum over 0 < w < 2n
Consider a causal LTI system described by y[n]-a y[n H = x[n]
For o / and u 2
Use MATLAB to sketch the magnitude spectrum over 0
Problem 3. The input and the output of a stable and causal LTI system are related by the differential equation dy ) + 64x2 + 8y(t) = 2x(t) dt2 dt i) Find the frequency response of the system H(jw) [2 marks] ii) Using your result in (i) find the impulse response of the system h(t). [3 marks] iii) Find the transfer function of the system H(s), i.e. the Laplace transform of the impulse response [2 marks] iv) Sketch the pole-zero...
Consider the cascade of LTI discrete-time systems shown in Figure P2.37. LTI System 1 hi[n], H (el) LTI System 2 h2[n], H2(eje) Figure P2.37 The first system is described by the frequency response Hi(j =c-joo < 0.25% 11 0.25% < and the second system is described by <A hain) = 2 Sin(0.57) (a) Determine an equation that defines the frequency response, H(e)®), of the overall system over the range -- SUSA. (b) Sketch the magnitude. He"), and the phase, ZH(e)),...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
BC:9.4 A LTI discrete time system has an impulse response h[n] =
(−0.6)nu[n] + (0.95)nu[n − 1] Find the transfer function, Hˆ (e jωˆ
), in the normalized frequency domain. Use Matlab to plot the
magnitude and phase (in degrees) of Hˆ (e jωˆ ) in the range of −π
≤ ωˆ ≤ π. Attach your Matlab source code with the plots.
BC:9.4 A LTI discrete time system has an impulse response h[n] = (-0.6)"u[n] + (0.95)"u[n-1] Find the transfer...
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