TUTORIAL 1

Signals and Systems

Solution

 

 

 

Q.1 Find out whether the signal s(t)= A cos (wt+r) is an energy or power signal

Ans:-The given signal is a power signal as it is a cosine function which varies periodically with respect to time.If we will calculate the power of the above signal then that is also  a finite value. This function has a period of w and a phase shift r.

2.Input and output relations of continuous time system is given by:-

y(t)=x(t-2)+x(2-t) . Check whether the system is memoryless or with memory.

b)casual or non-casual.

Ans:- The given signal has  a memory as it as for finding the value of y(t) the system has to remember the value of x at t-2 interval.

The given signal is non-casual as for finding the future value of the signal it has to remember the previous values of the signal.

3.Determine the unit step response of a discrete time LTI system when unit sample response is h(n)= Aⁿu(n).

Ans:- x(n)= u(n). The signal varies from  zero to inifinity. It is a discrete signal .

             Y(n)=Σx(k)h(n-k) with a variation from zero to infinity.

Y(n) = ΣA^n-k

4.Discuss discrete time and continuous time impulse function.

 Ans:- The discrete time impulse function is given by:-

                       δ (n)= 1, n=0

                               =0,n not equal to 0

The continuous  time impulse function is given by:-

                       δ (t)= 1, t=0

                               =0,t not equal to 0

 

           

 

5.Write short notes on the following :-

Exponential functions of signals: Any signal which has an exponential variation with respect to time is called exponential signal. E.g. e^at, e^-at are the examples of exponential signals. These signals usually tend to zero value as they approach towards infinity and thus they are energy signals. They have finite energy level.

Sinusoidal signals:- Any signal which has a sinusoidal variation with respect to time is called sinosuidal signal. These signals vary periodically  towards infinity and thus they are power  signals. They have infinite energy level and finite power level.

6.What is signum function?

Ans:- The function which has a value 1 for t>0

                                                             0, t=0

                                                             -1,t<0

7.What are singularity function?

Ans:- Any function having single value is called singularity function.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TUTORIAL 2

Signals and Systems

Solution

 

 

 

 

 

1. A discrete system described by the following difference equation

              y(n)=1/6y(n-1)+1/6y(n-2)+x(n).The system is causal as well as stable.Find whether the system is time variant or not.

Ans:- The system is time-invariant system as the value of x will change only when the n at the output will change. n as such will not have any effect on the value of y(n).

 

2.Find out whether the following systems are casual or not:-

a)y(t)=x(-t)                           b)y(t)=x(t²)

Ans:- a)Non-casual. As the output of the system will depend on the future input values.

b)Non-causal as the output of the system will depend on the future input values.

3.Derive the Parseval’s relation for continuous time Periodic Signals.

Ans:- P-150, Sanjay Sharma

4.Diffrentiate between even and odd signals.

Ans:- Even  signals are given by:- ½[x(t)+x(-t)]

Odd signals are given by:- ½[x(t)-x(-t)]

5.Determine the trigonometric fourier  series representation of the periodic rectangular waveform varying from –T/4 to T/4.

Ans:- Use the fourier series expansion formula

                     a ₀+ a_ncosnwt+ b_nsin nwt

where a_n= ∫x(t) cos nwt dt

         b_n= ∫x(t) sin nwt dt