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This document contains 13 problems related to signals and systems. Problem 1 involves representing signals on frequency and phase scales. Problem 2 deals with radio broadcasting frequencies in the MW band. Problem 3 is about sampling two sinusoidal waves at a given rate. The remaining problems ask to identify systems as linear/nonlinear, time-variant/invariant, causal/non-causal and determine output signals and powers for various systems and signals.

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45 views3 pages

Sheet

This document contains 13 problems related to signals and systems. Problem 1 involves representing signals on frequency and phase scales. Problem 2 deals with radio broadcasting frequencies in the MW band. Problem 3 is about sampling two sinusoidal waves at a given rate. The remaining problems ask to identify systems as linear/nonlinear, time-variant/invariant, causal/non-causal and determine output signals and powers for various systems and signals.

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b5fc94cdd3
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Exercise-1

1. Represent the following signals on frequency and phase scales;


(a) V(t) = 5 cos[2 ( ]
(b) V(t) = 2 sin[2 *100t - ( /3)]
(c) V(t) = 3 cos[2 *104 t - ( /6)] - 4 sin[6 *103 t + ( /2)]
(d) V(t) = 6 sin[4 *104 t - ( /6)] + 5 cos[8 *103 t + ( /2)]

2. For radio broadcasting in the Medium Wave (MW) band, the band
ranges from 546 kHz to 1593 kHz. Assuming that the band width
of each channel is 18 kHz (Double Side Band and Carrier) and the
guard band between successive channels is 3 kHz. Determine
(a) The frequency of the first carrier.
(b) The frequency of the last carrier.
(c) The maximum number of channels.
(d) Draw the carrier frequency distribution in the MW band.
(e) Determine the frequency of the carrier of the 5 th. channel.
(Ans. 555 kHz, 1584 kHz, 50, 639 kHz)

3. Two sinusoidal waves x1(t) and x2(t) are sampled at the rate of four
samples per cycle. If
x1(t) = 3 sin (2 *104 t)
x2(t) = 5 sin {(2 *104 t) + ( /3)}
Determine (a) The sampling frequency.
(b) The maximum width of the sampling pulse.
(Ans. 40 kHz and 12.5 s)

4. Determine which of the following systems is linear and which is


non linear?
(a) y(t) = 7 x(t) + 6
(b) y(t) = 1
=0 t<0
(c) y(t) = 4 x(t)
(d) y(t) = dx(t)/dt
(e) y(t) = x(t )dt

5. Determine which of the following systems is time variant or time


invariant?
(a) y(t) = (2t + 1) x(t)
(b) y(t) = x2(t) + x(t)
(c) y(t) = x(t) -3t*x(t)
(d) y(t) = 3 x3(t)

6. Determine which of the following systems is causal or non-causal?


(a) y(t) = 2 x(t-2) + 5 x(t)
(b) y(t) = t x(t + 1) + x(t 1)
(c) y(t) = d/dt [t2x(t)]

7. Determine the power of a square wave of a voltage swinging


between zero and 5 V and duty cycle 50 %.

8. Determine the power of a full wave (sinusoidal wave) rectifier of


maximum voltage 10 V.

9. Using superposition theorem prove that y(t) = x 2(t) is a non linear


system.
10. Determine the power of the following periodic discrete signals

(b) x[n] = n2+ 1 -3 3


(c) x[n] = (1/2)n -

11. Identify the following systems to be linear or non linear, time


invariant or time variant, and causal or non causal system.

(a) y(t) = x(t-1) + 2 x(t)


(b) y(t) = x2(t) + x(t+1)
(c) y(t) = 2t x(t-2) + x(t)
(d) y(t) = (1/3) [ x(t-2) + x(t-1) + x(t)]
(e) y(t) = (1/3) [ x(t-2) + x(t+1) + x(t)]

12. A signal x(t) is applied to a 5th. oder filter whose characteristics is


1
IH( )I =
2n
1 ( / C)

If x(t) = 4 cos(2 *104 t) and C = 10 *103, determine the


amplitude of the output signal.

13. A signal x(t) is applied to a filter whose characteristics is given by


1
IH( )I =
2
1 ( C/ )
If x(t) = 4 cos(10 *103 t) and C = 2 *104, determine the
amplitude of the output signal.

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