Chapter 1Dec 20101. Let x[n]= u[n] -u[n-5]. Find and skecth even and odd parts of the x[n].2. The analog signal x(t) is given by

x(t) = 2cos(2000πt) + 3sin(6000πt) + 8cos(12000πt)

Calculate: i) Nyquist sampling rateii) If x(t) is sampled at the rate Fs=5KHz, what is the discret signal obtained after sam-

pling?iii) What is the analog signal y(t) we can construct if ideal interpolation is used?

3. Let x(t) = 1.5t 0≤ t ≤ 2= 0 elsewhere

Sketch i) x(t) ii)f(t) = 1 + x(t-1) iii) g(t) = x(1-t)iv) h(t) = x(0.5t + 0.5) w(t) = x(-2t+2)

JUNE 20111. Determine whether the following signals are periodic or not. If yes, find the fundamental period.

i) x(t) = 2 cos(t) + 3 cos( t3)

ii) x[n] = ej[π/4]n

2. Determine whether the following signals are energy or power signals? Calculate their energy orpower

i) x(t) = cos2w0tii) x[n] = [1/2]nu[n]

3. Find and sketch the even and odd parts of the signal:

x(t)=

{t 0 ≤ t ≤ 1

1 1 ≤ t ≤ 2

DEC 2011 1.Determine whether the following signals are energy or power signals? Calculate theirenergy or power

i) x(t) = Acos(2πf0t)ii) x[n] = [1/4]nu[n]

2.Determine whether the following signals are periodic or not. If yes, find the fundamental period.i) x(t) = 5 cos(4πt) + 3 sin(8πt)ii) x[n] =sin [6π

7n+ 1]

3. Plot the signalx(t) = u(t) - r(t-1) + 2r(t-2) - r(t-3) + u(t-4) -2u(t-5)Find the even and odd parts of the signal.4. The analog signal x(t) is given by x(t) = sin(480πt) + 3sin(720πt) is sampled 600 times per second.Calculate: i) Nyquist sampling rate

ii) Folding frequencyiii)What are the frequencies in radians in discrete time signal x[n]iv) What is the analog signal y(t) we can construct if it is passed through an ideal D/A

converter?DEC 20121. Determine whether the signals are energy or power signals:

i). x(t) = 0.9e−3tu(t) ii) x[n]=u[n]2. Sketch x(t) and odd part of x(t):x(t) = 2r(t)-2r(t-1)-2u(t-3)

1

2 CHAPTER 1.

3.Determine whether the following signals are periodic or not. If yes, find the fundamental period.i) x(t) = 3 cos(

√2t) + 4 cos(5πt)

ii) x[n] = cos [4π12n]

4.Sketch: x(t) =

t 0 ≤ t ≤ 1

1 1 ≤ t ≤ 2

3− t 2 ≤ t ≤ 3

Now sketch: i)x(2-t) ii) x(t-3) iii) x(2t) iv) 0.5x(-t)5.The analog signal x(t) is given by x(t) = 5cos(50πt)+2sin(200πt)+2cos(200πt) is sampled 600 timesper second.Calculate: i) Nyquist sampling rate

ii) What is the discrete signal obtained after sampling at 200kHz?JUNE 20131.Determine whether the following signals are periodic or not. If yes, find the fundamental period.

i) x(t) = 2cos(100π t) + 5 sin(50t)ii) x[n] = cos [ π

20n] + cos [ π

10n]

2. x[n] =

1 −1 ≤ t ≤ 2

0.5 3 ≤ t ≤ 4

0 otherwiseSketch even and odd parts of the signal.3.If x[n]=-1, 1

↑,1,1,1

Plot: i)x[n] ii) x[2-n] iii) x[n-3] iv)7x[n-1]DEC 20131.Determine whether the following signals are periodic or not. If yes, find the fundamental period.

i) x(t) = cos(t) + sin(√

2t) ii) x[n]= cos[12n]

iii) x[n] = cos2[π8n] iv)x (t) = sin2t

JUNE 2014 1.Sketch odd and even parts of y(t)=t.u(t-2)2.What is the output of tδ(t) and sin(t).δ(t) ?Prove the same.JUNE 20151. Determine energy and power of the signals:

i) x(t) = e−3|t| ii) x(t)=e−3t

JUNE 2014 CBGS 1. For a continuous signal x(t)= 8cos(200π t)Find: i) Minimum sampling time

ii) If fs=400Hz, what is the discrete time signal?ii) If fs=150Hz, what is the discrete time signal?Comment on the result obtained in the last two questions.

DEC 2014 CBGS1. Find the even and odd components:

i) x(t) =t3 + 3t ii) x[n] = cos n +sin n+cos n.sin n2.For the signal x(t),sketch the signals: i) x(-t) ii)x(t+6) iii)x(3t) iv) x(t/2)JUNE 2015 CBGS1. Determine the fundamental period of signal x(t) =14 + 40 cos(60πt)2. Find the even and odd parts of :

i)x(t)= cos2(πt2

) ii) x(t)=

{t 0 ≤ t ≤ 1

2− t 1 ≤ t ≤ 2