plz solve the encircled part

 

Part e -

\([x(t)+x(-t)]*u(t)=x(t)*u(t)+x(-t)*u(t)\)

The x(t)*u(t) signal is the part of x(t) that is in the RHP.
The x(-t)*u(t) signal is the part of x(t) that is in the LHP, reversed into the RHP.
So, the sum of those to signals should be x(t)=0 until t=0. Then a straight line at amplitude 3 from t=0 to 1. And from t=1 to 2 you have a straight line from 1 to -1. The rest of time is x(t)=0.
Part f -

\(x(t)*[\delta(t+\frac{3}{2})-\delta(t-\frac{3}{2})]=x(t)*\delta(t+\frac{3}{2})-x(t)*\delta(t-\frac{3}{2})\)

The delta function is basically a sampler. So what you have is a positive sample of x(t) at t=-3/2 and a negative sample of x(t) at t=3/2.

 

the answer is below


so how I will solve these equations??? I solved the first four parts and don't have any concept of remaining two so please solve completely

 

the answer is below
View attachment 20643

so how I will solve these equations??? I solved the first four parts and don't have any concept of remaining two so please solve completely

They're not really equations that you solve, but descriptions of signals. For example, u(t) describes the unit step signal which is defined as the signal whose amplitude is zero at time ranging from negative infinity to 0 and 1 at time ranging from 0 to positive infinity.

I have attached a pdf that shows drawings of what I am trying to say.

 

I just realized that on part f I drew the samples backward. At t=-3/2, the signal should have amplitude of -1/2, and at t=3/2 the signal should have amplitude of 1/2. Sorry about that.

 

thanks member

 

why the value of unit step u(t) is 1 at t>0 ???

 

Here is a quick wiki link on the matter:

http://en.wikipedia.org/wiki/Heaviside_step_function

 

why the value of unit step u(t) is 1 at t>0 ???

It is so by definition. In order to analyze complex waveforms it helps to consider them as being made up of a sum of simple waveforms. The reason they are so useful in linear systems is that in a linear system you can use the principle of superposition to decompose things into simpler forms, solve them, and recombine the results.

 

so if the qustion is like [x(2t) + x(-2t)] u(t) so still the value of unit step will be 1???

 

Like Papabravo was saying... it is a definition. X(2t) is a signal, X(-2t) is a signal and u(t) is a signal. The resultant signal from adding, time distorting, and multiplying does not change the signal itself.