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Analysis
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University of Baghdad College of Engineering Electrical Engineering Department Third year class Engineering Analysis Final Examination June 2012 Time: three hours ن الرحيم الرحم بسمAnswer All The Following Seven Questions Q.1: Q.1.A. Compute the convolution where and are given by Q.1.B. Compute the convolution sum , where and are given by Q.2: Q.2.A . The impulse response of continuous time LTI system is given by . i. Sketch and check the causality and stability of the system ii. Find the Fourier transform of . iii. Sketch the magnitude and phase of . Q.2.B . Given that prove the time shifting property, that is . Q.3: Q.3.A . Let be an arbitrary signal with even and odd parts denoted by and , respectively. Show that Q.3.B . Compute the transfer function for a continuous-time system and plot the pole zero diagram on S plane, also check the causality and stability of the system, where the impulse response is given by Q.4: Q.4.A . Solve the second order linear differential equation: Q.4.B The output of continuous time LTI system when the input . i. Find and sketch the impulse response of the system ii. Find and sketch the output when the input Q.5: Q.5.A Consider a discrete time system with system function i. Sketch the pole zero plot of on the Z plane ii. Determine the impulse response of the system iii. Check the stability and causality of the system with justification.
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Analysis
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University of Baghdad College of Engineering Electrical Engineering Department Third year class
Engineering Analysis Final Examination June 2012 Time: three hours
بسم هللا الرحمن الرحيم
Answer All The Following Seven Questions Q.1:
Q.1.A. Compute the convolution where and are given by
Q.1.B. Compute the convolution sum , where and are given
by
Q.2:
Q.2.A. The impulse response of continuous time LTI system is given by .
i. Sketch and check the causality and stability of the system
ii. Find the Fourier transform of . iii. Sketch the magnitude and phase of .
Q.2.B. Given that prove the time shifting property, that is
.
Q.3:
Q.3.A. Let be an arbitrary signal with even and odd parts denoted by and ,
respectively. Show that
Q.3.B. Compute the transfer function for a continuous-time system and plot the pole
zero diagram on S plane, also check the causality and stability of the system, where the
impulse response is given by
Q.4: Q.4.A. Solve the second order linear differential equation:
Q.4.B The output of continuous time LTI system when the input .
i. Find and sketch the impulse response of the system ii. Find and sketch the output when the input
Q.5: Q.5.A Consider a discrete time system with system function
i. Sketch the pole zero plot of on the Z plane ii. Determine the impulse response of the system iii. Check the stability and causality of the system with justification.
University of Baghdad College of Engineering Electrical Engineering Department Third year class
Engineering Analysis Final Examination June 2012 Time: three hours
بسم هللا الرحمن الرحيم
Q.5.B Consider a causal discrete time system whose output and input are related by
i. Determine the system function ii. Determine the impulse response of the system .
Q.6
Q.6.A A digital filter has a transfer function
and is used with sampling
frequency of 10 KHz. Estimate the gain and phase at 1.25 KHz.
Q.6. B Convert the continuous time LPF whose transfer function
to equivalent discrete time filter with sampling frequency of 10 Hz using impulse invariant method. Q.7
Q.7.A Realize the digital system whose system function is given by
Q.7.B Reduce the system shown below to canonical form, write the expression of
,
and find the range of K in which the system is stable.
