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Test: LTI System Frequency Characteristics


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10 Questions MCQ Test Digital Signal Processing | Test: LTI System Frequency Characteristics

Test: LTI System Frequency Characteristics for Electrical Engineering (EE) 2022 is part of Digital Signal Processing preparation. The Test: LTI System Frequency Characteristics questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: LTI System Frequency Characteristics MCQs are made for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: LTI System Frequency Characteristics below.
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Test: LTI System Frequency Characteristics - Question 1

 If x(n)=Aejωn is the input of an LTI system and h(n) is the response of the system, then what is the output y(n) of the system? 

Detailed Solution for Test: LTI System Frequency Characteristics - Question 1

Explanation: If x(n)= Aejωn is the input and h(n) is the response o the system, then we know that

Test: LTI System Frequency Characteristics - Question 2

 If the system gives an output y(n)=H(ω)x(n) with x(n)= Aejωnas input signal, then x(n) is said to be Eigen function of the system.

Detailed Solution for Test: LTI System Frequency Characteristics - Question 2

Explanation: An Eigen function of a system is an input signal that produces an output that differs from the input by a constant multiplicative factor known as Eigen value of the system.

Test: LTI System Frequency Characteristics - Question 3

What is the output sequence of the system with impulse response h(n)=(1/2)nu(n) when the input of the system is the complex exponential sequence x(n)=Aejnπ/2?

Detailed Solution for Test: LTI System Frequency Characteristics - Question 3

Explanation: First we evaluate the Fourier transform of the impulse response of the system h(n)

Test: LTI System Frequency Characteristics - Question 4

 If the Eigen function of an LTI system is x(n)= Aejnπ and the impulse response of the system is h(n)=(1/2)nu(n), then what is the Eigen value of the system? 

Detailed Solution for Test: LTI System Frequency Characteristics - Question 4

 

Explanation: First we evaluate the Fourier transform of the impulse response of the system h(n)

If the input signal is a complex exponential signal, then the input is known as Eigen function and H(ω) is called the Eigen value of the system. So, the Eigen value of the system mentioned above is 2/3.

Test: LTI System Frequency Characteristics - Question 5

If h(n) is the real valued impulse response sequence of an LTI system, then what is the imaginary part of Fourier transform of the impulse response?

Detailed Solution for Test: LTI System Frequency Characteristics - Question 5

Explanation: From the definition of H(ω), we have

Test: LTI System Frequency Characteristics - Question 6

 If h(n) is the real valued impulse response sequence of an LTI system, then what is the phase of H(ω) in terms of HR(ω) and HI(ω)?

Detailed Solution for Test: LTI System Frequency Characteristics - Question 6

Explanation: If h(n) is the real valued impulse response sequence of an LTI system, then H(ω) can be represented as HR(ω)+j HI(ω).
=>

Test: LTI System Frequency Characteristics - Question 7

What is the magnitude of H(ω) for the three point moving average system whose output is given by y(n)=1/3[x(n+1)+x(n)+x(n-1)]?

Detailed Solution for Test: LTI System Frequency Characteristics - Question 7

Explanation: For a three point moving average system, we can define the output of the system as

Test: LTI System Frequency Characteristics - Question 8

What is the magnitude of the frequency response of the system described by the difference equation y(n)=ay(n-1)+bx(n), 0<a<1?

Detailed Solution for Test: LTI System Frequency Characteristics - Question 8

Explanation: Given y(n)=ay(n-1)+bx(n)

Test: LTI System Frequency Characteristics - Question 9

If an LTI system is described by the difference equation y(n)=ay(n-1)+bx(n), 0 < a < 1, then what is the parameter ‘b’ so that the maximum value of | H(ω)| is unity?

Detailed Solution for Test: LTI System Frequency Characteristics - Question 9

Explanation: We know that,

Since the parameter ‘a’ is positive, the denominator of | H(ω)| becomes minimum at ω=0. So, | H(ω)| attains its maximum value at ω=0. At this frequency we have,
(|b|)/(1-a) =1 =>b=±(1-a).

Test: LTI System Frequency Characteristics - Question 10

 If an LTI system is described by the difference equation y(n)=ay(n-1)+bx(n), 0

Detailed Solution for Test: LTI System Frequency Characteristics - Question 10

Explanation: From the given difference equation, we obtain

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