TUTORIAL CLASS
UNIT I
1. Sketch the following signal x(t) = 3r(t) where r(t) is a ramp signal
2. Sketch
[ 2 2]
( 3
)
δ t+ −δ ( t − )
3
3. If x(n) = {1,2,3,4,5}. What is x (n-3)?
4. If x(n) = [4,3,2,1,1,2,3,4], find x(2n)
5. Find the fundamental period T of the continuous time signal
(
x (t )=10 sin 15 πt+
π
3 )
6. Determine the energy and power signal for the following signal x (t )=3 u ( t )
7. Find if the following signal is causal or non-causal x(n) = an u(n)
8. Find the even and odd parts of given signal x(n) = [1,3,5,7,9]
2
9. Determine whether the following system is linear or not y ( n )=bx ( n )
10. Check if the system y ( n )=nx ( n ) is time invariant or not.
11. Given y ( t ) =x ( t−2 ) +x ( 2−t ) , check if this system is causal or not.
d
y (t)= x (t )
12. Check if the system dt is static or dynamic.
UNIT II
1. Obtain the trigonometric Fourier series for the half wave rectified sine wave.
2
2. Find the Fourier series representation of x (t )=sin t .
−|t|
3. Find the Fourier transform of x (t )=e for−2≤t≤2
4. Find the Fourier transform of the rectangular pulse of duration T and amplitude A.
5. Find the Laplace Transform of x(t) = u(t-2)
−at
6. Find the Laplace transform of x (t )=e sin ωtu(t )
1
X ( s) = 2
7. Find the inverse Laplace Transform of s +3 s+ 2 where
ROC is -2 < Re(s) < -1.
s
X ( s) = 2
8. Find the inverse Laplace Transform of s +5 s+ 6
9. Find the inverse Fourier Transform for X ( jω )=∂ ( ω ) .
UNIT III
1. Given H(s) = s(s+2)/ (s+1) (s+3) (s+4), realize the system using cascade form.
2. Realize the system H(s) = s+1/s2+3s+5 in direct form I.
3. Obtain the convolution of the signals x(t)= e-atu(t) and h(t) = e-btu(t)
4. Find the convolution of x(t) =1 for 0 ≤ t ≤ 2
0 otherwise
h(t) = 1 for 0 ≤ t ≤ 2
0 otherwise
5. Find the convolution x(t) = u(t) and h(t) = u(t)
6. The system is described by the input output relation
d 2 y (t ) dy (t ) dx (t )
2
+ −3 y (t )= +2 x (t )
dt dt dt
Find the system transfer function and impulse response using Laplace transform.
7. A system is described by the following differential equation
d 2 y (t ) dy (t )
+7 +12 y (t )=x (t )
dt 2 dt . Determine the response of the system to a unit step
applied at t = 0. The initial conditions are y(0) = -2, dy(0)/dt = 0
8. For a system with transfer function H(s) = s+5/s2+5s+6 find the zero-state response if
the input x(t) = e-3t u(t).
UNIT IV
1. Determine the z transform and ROC of x(n) = an u(n) – bn(-n-1)
2. Find the z transform and ROC of x(n) = [ 1,2,3,4]
3. Find the z transform of x(n) = (sinωon)u(n)
4. Determine all possible signals x(n) associated with z transform X(z) = 5z-1/(1-2z-1)(1-
3z-1)
5. Find the inverse z transform X(z) = 1/1+z-1+z-2 , ROC |z|>1
6. Find the inverse z transform X(z) = 8z-9/z2-5z+6 , ROC |z| >3
7. Find the DTFT of x(n) = [1,-1,2,2]
8. Find the Fourier transform of x(n) = (1/2)n-1 u(n-1)
9. Find the DTFT of x(n) = δ(n+2)-δ(n-2)
UNIT V
1. Obtain the cascade realization of the system given by
y(n) -1/4y(n-1)-1/8y(n-2) = x(n) +3x(n-1) +2x(n-2)
2. Realize the given system in direct form II
y(n) =5/6y(n-1) +1/6y(n-2) = x(n) +2x(n-1)
3. Find the output of the system y(n) = 7y(n-1)-12y(n-2) +2x(n)-x(n-2) for the input x(n) =
u(n)
4. Find the impulse response of the system y(n) =3/4y(n-1) + 1/8y(n-2) = x(n)
5. Find the response of y(n) +y(n-1)-2y(n-2) = u(n-1) +2u(n-2) due to y(-1) =0.5, y(-2) =
0.25
6. Find the convolution of x(n) = bn u(n) and h(n) = an u(n)
7. Find the convolution of x(n) = [1, -2,3,1] and h(n) = [2, -3, -2]
8. Find the convolution of x(n) = u(n) –u(n-7) and h(n) = u(n-1)-u(n-4)
