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National Champion Test EC: Signals & Systems

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Question 1

Gain and NF of a single stage amplifier is 10 dB and 3 dB respectively. When two such amplifiers cascaded then gain and NF of cascaded amplifier will be:

Question 2

Find the discrete-Time Fourier Transform (DTFT) of the following signal?
x(n) = aⁿ where n ≥ 0, -1 < a < 1.

Question 3

Two discrete time systems have impulse response

and

. If these two systems are cascaded then the overall impulse response of the cascaded system is

Question 4

Phase function of a filter is (f) = $Description: E:\Gate\isro-cs\ISRO_EC_2013_files\image311.png$ , k > 0. The group delay of the filter has the shape

Question 5

The function f(t) has the Fourier transform

. The fourier transform of g(t) is

Question 6

Suppose

(t) and

(t) have the Fourier transforms as shown below.

Which one of the following statements is TRUE?

Question 7

The output of a continuous-time, linear time-invariant system is denoted by T{x(t)} where x (t) is the input signal. A signal z(t) is called eigen-signal of the system T, when T {z (t) = γz(t),} , where γ is a complex number, in general, and is called an eigen value of T. suppose the impulse response of the system T is real and even. Which of the following statements is TRUE?

Question 8

Evaluate:

Question 9

What is the energy of a power signal?

Question 10

Determine the stability of the system if its transfer function is given as:

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ESE & GATE EC Signals and Systems

Jun 16ESE & GATE EC