Homework - 11

Dear ALL !

If you find time, do study additional material without worrying too much in case you do not understand something.

You will be doing a GREAT FAVOUR to the class by sharing all your doubts with me.
This will help me in preparing for the next class better.

Collect the following graphic representations before next week :

1. Time-domain and frequency domain representation of a rectangular waveform with a time-period of T.
    (Hint : Fourier Series).

Observe : What happens in the frequency domain as T tends to infinity in the time-domain ?

2. Time-domain and frequency domain representation of a pulse (width/duration = Tp). A pulse can be thought of as a rectangular waveform with a time-period of T = Infinity. (Hint : Fourier Transform.)

3. Time-domain and frequency domain representation of a periodic train of  unit impulses with a frequency of fs( = 1/T). (Hint : See chapter on Sampling). Assume fs is the Nyquist rate.

Now, take a signal which is band-limited (No frequencies above the highest frequency say +W/2.) Note : If W/2 is the highest frequency, Nyquist rate fs will be W.

4. What will be the plot in the frequency domain when the above band-limited signal is sampled at its Nyquist rate fs ? Sketch it.

5.What will be the plot in the frequency domain when the above band-limited signal is sampled at LESS THAN the  Nyquist rate fs ? Sketch it.

6. What will be the plot in the frequency domain when the above band-limited signal is sampled at GREATER THAN Nyquist rate fs ? Sketch it.

You will find all the answers in the  text books.
You are encouraged to discuss this with your colleagues to get  a clear picture of signals and their spectra (frequency domain representation).

I will give you some more hints tonight.

I will post the solutions on Sunday.

Good Day.