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Questions For Assessment 1: Short Answers

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B.S.A.

CRESCENT ENGINEERING COLLEGE

Questions for Assessment 1


Short Answers

1. Define signals. 2. State the condition for a signal to be odd. 3. State the condition for a signal to be even. 4. Define periodic signal. 5. Define discrete-time unit impulse signal. State its properties. 6. What is unit step signal? 7. What is a linear system? 8. What is a time-invariant system? 9. When a system is said to be causal? 10. Define impulse response. Give its significance for an LTI system.
Problems

1. Sketch the waveform for the signal (a) w(t) = sin (t) { u(t+1) u(t-1) } (b) v(t) = 5 u(t-5) - 3 u(t-7) 2 u(t-10) (c) x[n] = ( )-n u[n] (d) y[n] = 3 [] + 2 [ 1] + 4 [ 2] + [ 4] 2. Find the normalized total energy and average power of the signal (a) y(t) = 2t { u(t) u(t-4)} (b) x(t) = e -2t u(t) (c) v(t) = e j(2t + ) (d) x[n] = { 3, 2, 6, 7, 3, 4, 2 } (e) x[n] = ( )-n u[n] (f) w[n] = cos( n)

3. Check whether the following signals are periodic. Determine the fundamental period if periodic.

x[n] (a) = cos(


(b)

n
3

) + sin(

n
4

x[n] = 5e 2 n sin(2 n)
q(t) = [ cos( 2t + ) ] 2

(c)

x[n] (d) = sin( n + 1)


4. Find whether the following systems are linear, time-invariant, memory, causal, and static. (a)

6 7

y [ n ] 3x [ n 1] + 4x [ n ] + x [ n + 2] =

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B.S.A. CRESCENT ENGINEERING COLLEGE

(b) (c) (d) (e)

y[n] = nx[n]

y (t ) =

dx ( t ) dt

5. If the signal x[n] = { 3,2,1,2} is given as the input to the following systems, find the output y[n] (a) (b) (c) y[n] = 2x[n] x[n-1] y[n] = 1/3 { x[n+1] + x[n] + x[n-1] } y[n] = y[n-1] + x[n]
k =

y (t ) = x(t 2) + x(2 t ) 0, () < 0 () = () + ( 2), () 0

6. Prove that

k =

x[ x[k ] [n k ] =n]

7. If w[n] is an odd signal, show that


k = k =

w[k ] = 0

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