# Electronics and Communication Engineering - Signals and Systems

### Exercise :: Signals and Systems - Section 1

21.

If then for this to be true x(t) is

 A. exp (j2p f/t) B. exp (-j2p f/t) C. exp (j2p ft) D. exp (-j2p f/t)

Explanation:

If     .

22.

For the discrete time system of the given figure A. yk - 0.5 yk - 1 - 0.25 yk - 2 = uk B. yk + 0.5 yk - 1 - 0.25 yk - 2 = uk C. yk - 0.5 yk - 1 + 0.25 yk - 2 = uk D. yk + 0.5 yk - 1 + 0.25 yk - 2 = uk

Explanation:

uk + 0.5 yk - 1 - 0.25 yk - 2 = yk.

23.

The analog signal m(t) is given below m(t) = 4 cos 100 pt + 8 sin 200 pt + cos 300 pt, the Nyquist sampling rate will be

 A. 1/100 B. 1/200 C. 1/300 D. 1/600

Explanation:

m (t) = 4 cos 100 pt + 8 sin 200 pt + cos 300 pt

Nyquist sampling freq fs ≤ 2fm where fm is highest frequency component in given signal and highest fm in 3rd part

2pfmt = 300 pt

fm = 150 Hz

fs = 2 x 150 p 300 Hz .

24.

The ROC of sequence in the Z.T. of sequence x[n] = an ∪ [n] is

 A. z > a B. z < a C. |z| > a D. |z| < a

Explanation:

The simplest method to find the ROC. Put denominator to greater than zero.

25.

In Laplace transform, multiplication by e-at in time domain becomes

 A. translation by a in s domain B. translation by (-a) in s domain C. multiplication by e-as in s domain D. none of the above