Q1 Define the signal Q6 Find the z-transformation of the Q8 Find the Fourier transformation of

a) Periodic signal given signal: the given signal below:

b) Even and odd signal x(n) = a n u(n) x(t ) = e
−a t

Q2 Find the period of the signal Q9 Define the signal

a) 4cos3t + 5sin11t a) Even and odd signal
b) 6sin4t + 8cos13t b) Discrete signal

Q23 Find the Fourier transformation of

the given signal below:
x(t ) = e − at

Q3 Define: Q10 Write the properties of Properties

A) Power signal of periodic signal?
B) Energy signal

Q Find the Laplace transformation of

the signal:
x(t ) = e −5t u(t + 2)

Q4 Write the Dirichlet’s conditions in

Fourier Transformation

Q11 Find the period of the signal

a) cos3πt + 9sin2πt/4
b) cosπt/3 + 4sin7πt/4
 Q7 Explain whether the system y(t) = x(2t - 3) is linear,
Q12 Find power of the given signal time-invariant, causal, and stable
Q Find the period of the signal
x(t) = 4cosπt + 6sin(π/2) t + 2cos3πt Ans :- y(t)=x(2t−3) i. 6sin4t + 8cos13t
Linearity A system is linear if it satisfies superposition and
homogeneity, i.e.: ii. cos3πt + 9sin2πt/4
If
x1(t)→y1(t),x2(t)→y2(t)
a1x1(t)+a2x2(t)→a1y1(t)+a2y2(t)
Apply to the system:Let y(t)=x(2t−3) Then for input
a1x1(t)+a2x2(t)
y(t)=a1x1(2t−3)+a2x2(2t−3)
This equals a1y1(t)+a2y2(t) So the system is linear
Time Invariance :- A system is time invariant if a time shift
in input causes an equivalent time shift in output .
let input x(t) = y(t)=x(2t-3)
now shift the input by t0 :
let x’(t) =x(t-t0) then system output becomes
y’(t) =x’(2t-3) =x(2t-3-t0)
Now shift the original output y(t)=x(2t−3) by t0
Q13 Find the R. O.C of y(t−t0)=x(2(t−t0)−3)=x(2t−2t0−3)
These are not equal unless t0=0
2 5
− So the system is Not Time-Invariant
S −3 s +8 Causality
A system is causal if the output at time ttt depends only on
the present and past values of the input (i.e., no future).
Here,
y(t)=x(2t−3)
At time t, the system requires input at 2t−3
If 2t−3>t, the system uses future input → non-causal
For example, at t=3: x(2∗3−3)=x(3)x
But at t=1: x(2−3)=x(−1) Q Find power of the given signal
At t=2t =2: x(1) (future for current time)
Since the system sometimes needs future input, it is not x(t) = 6cosπt + 3sin(π/2)t + 4cos3πt
causal
4. Stability
Q14 Find the Fourier coefficients of A system is BIBO stable if bounded input gives bounded
output.
given signal Assume input is bounded:
x(t) = 6sin2πt/3 + 4cos3πt/4 ∣x(t)∣≤ M ∀t
Then output:
y(t)=x(2t−3)⇒∣y(t)∣=∣x(2t−3)∣≤M
Because a bounded input remains bounded even when its
argument is scaled and shifted, the output stays bounded.
So the system is:Stable

Q15 Find the z-transformation of the

given signal: Q What is Power signal? give some
x(n) = a u(−n) n example of power signal

Find the Laplace transformation of the

Q5 Find the Laplace transformation of
signal:
the signal:
+5t x(t ) = e +5t u(t ) + e −2t u(t )
x(t ) = e u(t − 2)