ELECTRICAL DEPARTMENT NOTICE BOARD

                                                                                                    

Question Bank

Subject Code:2141005

Subject Name: Signals and Systems

Prepared by: Prof. A.K.Giri

Q.1  For each of the following systems

i)                    y(t) = x(t-2) + x(2-t)

ii)                  y(n) = nx(n)

determine which of properties “memoryless”, “time invariant”, “linear”, “casual” holds and justify your answer.

Q2  Using the convolution integral to find the response y(t) of the LTI system with
impulse	response	h(t) = e −β t u(t)		to the input  x(t) =e −α t u(t) for α = β and
α ≠ β .
Q.3    Determine the Fourier transform of each of the following signals:
i)		−αt		α > 0
	x (t) = e		cos ω 0 t u(t),
ii)		1 −n
	x[n] =		u[ − n −1]
		2
Q4  Determine the Fourier series representations for the signal x(t) shown in figure
below.

				OR
Q5  Let x(t) be a periodic signal whose Fourier series coefficients are
	2,							k = 0
ak
	=	j(	1	)		k		, otherwise
			2

Use Fourier series properties to answer the following questions:

(a)    Is x(t) real ?

(b)   Is x(t) even ?

(c)    Is ^dx(t) even ? dt

         Q6 Consider a causal and stable LTI system S whose input x[n] and output y[n] are 07 related through the second-order difference equation

y[n] − ¹₆ y[n− 1] − ¹₆ y[n− 2] = x[n].

1

i)                    Determine the frequency response H[e ^jw ] for the system S.

ii)                  Determine the impulse response h[n] for the system S.

Q7  State and prove the following properties of the Fourier transform.

i)                    Time Shifting

ii)                  Time Scaling.

Q8

Determine the z-transform for the following sequences. Sketch the pole-zero

plot and indicate the ROC. Indicate whether or not the Fourier transform of the

sequence exists.

i)

δ[n+5]

ii)

1 n

u[3 −n]

4

Q9  Determine the Laplace transform and the associated region of convergence and

pole zero plot for each of the following functions of time:

i)

x(t) = e −2 t u(t) +e −3t u(t)

ii)

x(t) = δ (t) +u(t)

Q10

Using the long division method, determine the sequence that goes with the

1−

1

−1

2

z

following z-transforms: x[z] =

and x[n] is right sided.

1

−1

1+

2

z

Q11  Explain with example the properties and importance of LTI Systems.

Q12

Consider a causal LTI system whose input x[n] and output y[n] are related by

the difference equation

1 y[n− 1] + x[n].

y[ n ] =

Determine y[n] if x[n] = δ [n−1]

4

Q13

Using the Partial fraction method, determine the sequence that goes with the

following z-transforms: X (z) =

3

and x[n] is absolutely summable.

z −

1

−

1 z−1

4

8

Q14

List the properties of the region of convergence (ROC) for the z-Transform.

Q15

Consider the signal

1

n

π

cos

n

, n ≤ 0

3

x[n] =

4

n > 0

0

Determine the poles and ROC for X[z].

Q16  Compute and plot the convolution y[n] = x[n]*h[n] where
1,		3 ≤ n ≤8	and
x[n]=	0,	otherwise
1,		4 ≤ n ≤15
h[n]=	0,	otherwise

Q17 Determine whether or not each of the following signals is periodic. If the signal 07 is periodic, determine its fundamental period.

i)                      x(t) = [cos(2 t−^π₃ )]²

ii)                      x[n] = cos(n^{2 π}₈ )

 and GTU QUESTION PAPER WINTER 15