D

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D5830
10 a) Obtain the differential equation representation of the circuit shown in Figure 2.
625 11
‏له‎ ~~
= 9.25 *
Figure 2.

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Using Laplace transform, solve the differential equation obtained for Qn. 10(a) and

get voltage across the capacitor. (Assume all initial conditions are zeros).

Find x(t) + h(t) where, x(t) = u(t) — u(t — 2), h(t) = e~2*u(t)and + represents the

convolution operator.

How will you determine the stability of a system from its transfer function?

Comment on the stability of the following systems:

i)G,(s) = 1) G,(s) =

52+65+18

5-2
52418

PART C
Answer any two full questions, each carries 10 Sane
a(t

Obtain complex exponential Fourier series of
the signal x(t) shown in Figure 3.

Figure 3.

Find the Fourier transform 0 €-०।५

State and prove sampling theorem.

The impulse response of a system is given by h(n) = [2 3 1]. Find the response of

the system when it is excited by the input x(n) = u(n — 1) — u(n — 5)

Explain energy spectral density and power spectral density.

PART 0

Answer any two full questions, each carries 10 marks

State and prove following properties of Z transform:

i)Multiplication by n ii) Accumulation iii) Convolution
Find inverse z transform of
2 1
X(z) = ‏ل لي سے‎ 2 ಆಇ
(८) - ‏ور‎ उदय 2! ‏وک‎

State the properties (atleast eight) of discrete Fourier transform(no proof is required).

Obtain Discrete Fouriertransform of the following signals:

i)x[n] = 0.5" u[n] ii) + [1] = 0.5!"!

Determine the stability of the following discrete transfer function:

2

i)H, (2) = 2210 72401 ii)H(z) =
Give any five properties of nonlinear systems.
‏اد‎ ೫ ೫ ೫

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