Help me count how many full periods of x(t) is need for one period of sampled signal

A 100Hz sinusoid x(t) is sampled at 240Hz. How many full periods of x(t) are required to obtain one period of the sampled signal??
Plz sort this problem for me... I am confused!!:!:

sampling process

Posted by Anonymous (it was posted wrongly in report system):

see here the input signal x(t) having period=0.01sec is sampled with a sampling period 0.00416 sec .ur question is saying that n*0.01=0.00416 what is the value of n u r asking ......the value of n here getting is 0.416 since n is an integer in ur question so obviously n =0

Click to expand...

sampling sinusoidal signals

hey Klug,
f= frequency of the sampled signal is=100/240=0.41667Hz
therefore time period is,T=1/0.41667=2.4 sec (2.4 samples/cycle)
that means 0.01xn=2.4 => n=240.
that means 240 cycles of x(t) makes 1 complete period of the sampled signal.

Whats ur take on this... plz reply.

what is mean by sampling process of signals

Hello!
If I understood clearly you have:
Fss = 100 Hz,
Tss = 10ms
Fd=240Hz,
Fd = 4.166ms
Tss = 2.4*Tss
N = Fd/Fss = 2.4
You have 2.4 samples per cycle of the SS.
You have 2.4 periods of the sampling signal at one period of the sampled signal.
Or you could not have “ p full periods” in “one period of the sampled signal” .
If for example you have N=4 you will have 4 full periods of Fd in one period of Fss.


May be that will help you at least when you sample sinusoidal and co sinusoidal signals:
“A New Approach to Sampling Sinusoidal and Cosinusoidal Signals”, P T Petrov,
https://www.ieindia.org/pdf/88/88ET104.pdf

Also may be it will be useful to know:

“Sampling of the Simplest Signals”, P T Petrov
https://www.ieindia.org/pdf/89/89CP109.pdf

Any feedback is welcomed
BR
Petre Petrov

Added after 2 hours 50 minutes:

In fact to have “ k full (integer) periods of the SS x(t)” Tss
in one period of the sampling signal Td you should have:
SSF N =1 or ½, or 1/3 , etc
or
N = 1/k
or
Tss = k*Td, k=1,2,3,4, …
OK?