Questions For Assessment 1: Short Answers
Questions For Assessment 1: Short Answers
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.
n
3
) + sin(
n
4
x[n] = 5e 2 n sin(2 n)
q(t) = [ cos( 2t + ) ] 2
(c)
6 7
y [ n ] 3x [ n 1] + 4x [ n ] + x [ n + 2] =
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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 =
6. Prove that
k =
x[ x[k ] [n k ] =n]
w[k ] = 0
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