Signal and Systems Important Questions Nov Dec 2013

Signal and Systems Important Questions Nov Dec 2013 

 

UNIT 1  

1. a. Discuss the classification of DT and CT signals with examples.

     b.Discuss the classification of DT and CT systems with examples.

2. Find whether the following signals are periodic or not

    i. x(t)=2cos(10t+1)-sin(4t-1)

    ii. x(t)-3cos4t=2sint

3. Check whether the following system, y(n)=sgn[x(n)], is

    i. Static or dynamic

    ii. Linear or non linear

    iii. Causal or non-causal

    iv. Time invariant or variant

4. a. For the systems represented by the following functions. Determine whether every system is (1) Stable (2) Causal (3) Linear (4) Shift invariant

        (i) T[x(n)]=ex(n) (ii) T[x(n)]=ax(n)=6

    b. Determine whether the following systems are static or Dynamic, Linear or Non-linear, Shift variant or Invariant, Causal or Non-causal, Stable or unstable.

        (i) y(t)=x(L+10)+x2(t)

        (ii) dy(t)/dt + 10y(t) = x(t)

5. Explain about the classification of continuous time system.

6. a. The input and output of a causal LTI system are related by the differential equation, d2y(t)/dt2+6dy(t)/dt=8y(t)=2x(t)

        i) Find the impulse response of the system.

        ii) What is the response of this system if x(t) = t e-2t u(t)

    b. Explain the classification of signals with examples.

UNIT 2 

1. State and prove properties of fourier transform.

2. a. State the properties of Fourier Series.

    b. Use the Fourier series analysis equation to calculate the coefficients ak for the continuous-time periodic signal

        1.5, 0≤t  ∙ 1;

        x (t) ∙

        --

        1.5, 1 ≤ t ∙ 2 with fundamental frequency Ѡ0=π.

3. a. State and prove Parseval’s power theorem and Rayleigh’s energy theorem.

    b. Find the cosine Fourier series of an half wave rectified sine function.

4. A system is described by the differential equation,

    d2y(t)/dt2+3d(t)/dt=2y(t)/dt if y(0)=2;dy(0)/dt=1 and x(t)=e-t u(t)

    Determine the response of the system to a unit step input applied at t=0.

5. Find the Fourier transform for triangular pulse

    x(t)=_(t/m) ={1-2|t|/m|t|<m

    0 otherwise

6. Determine the Fourier series coefficient of exponential representation of x(t)

    x(t) = 1, |t| < T1

    0, T1 < |t| < T/2

UNIT 3 

1. a. Give the properties of convolution Integral

    b. Determine the state Equation and Matrix representation of systems

2. a. Describe the properties of impulse response

    b. Describe y(t) by convolution integral if x(t)=e at u(t) and h(t)=u(t)

3. a. Find whether the system is causal or not?

         h(t)=e-2t  u(t-1)

    b. Give the summary of elementary blocks used to represent continuous time systems.

4. Find the natural and forced response of an LTI system given by 10dy (t)/dt++2y(t)=x(t)

UNIT 4 

1.State and prove properties of DTFT.

2. a. Find the DTFT of x(n)={1,1,1,1,1,1,0,0}.

    b. Find the convolution of x1(n)={1,2,0,1), x2(n)={2,2,1,1}

3. a. State and prove the sampling theorem.

    b. Derive the Lowpass sampling theorem.

4. Find the z-transform of x{n}=an u(n) and for unit impulse signal

5. a. Give the relationship between z-transform and Fourier transform.

    b. Determine the inverse z transform of following function

        x(z)=1/(1+z-1) (1-z-1)2 ROC : |Z>1|

UNIT 5 

1. a. State and prove the properties of convolution sum.

    b. Determine the convolution of x(n)={1,1,2} h(n)=u(n)-u(n-6) graphically

2.Determine the parallel form realization of the discrete time system

    y(n)  -1/4y(n-1)  -1/8y(n-2) = x(n) +3x(n-1) + 2x(n-2)

3. a. Determine the transposed structure for the system given by difference equation

        y(n) = (1/2)y(n-1)-(1/4)y(n-2)+x(n)+x(n-1)

    b. Realize H(s)=s(1-2)/(s+1)(s+3)(s+4) in cascade form

4. a. Determine the recursive and nonrecursive system

    b. Determine the parallel form realization of the discrete time system is

        y(n) -1/4y(n-1) -1/8y(n-2) = x(n) +3x(n-1) +2x(n-2)