# Digital Signal processing-Sampled period

Please can you help me with exam test preparation. I have take the below past year exam paper. I want to know if I am on the correct track and my answers are correct.

x(t) = cos(50.pi.t + 30) which is sampled at 50Hz

to find the sampled signal, F= 0.5 X 50 = 25Hz, Since w= 2.pi.f (angular frequency)

Now I took the sampled Frequency F= 25/50 = 1/2 The Period = 1/F and then The Period = 2

Now for he second question, How many full periods of x(t) are required to obtain the sampled period?

I took the Frequency (F= 0.5 X 50 = 25Hz and the P= 1/f= 1/25 = 0.04

the Period is 0.04 and the Period of the above question is 2/0.04 which is 50.

but the answer is not there so from the below.

Please can you help, me.

regards Kyle.

• Try drawing out the sinusoid and marking the sampled points. – John D Mar 7 '16 at 18:58

## 1 Answer

The question 12 says: how many full periods are requiered to optain the sampled period and not how many full periods are requiered to optain the period of the sampled signal. This last question is what you answered. So the solution for the question 12 is: 0.5. Becouse the T of the signal is 0,04s and 50Hz (sampled period) period is 0,02s, then 0,02/0,04=0.5.

• Hi Alf, thank you for the answer but I am still a little confused on the 0.02s. Is my answer for question correct? where i got the period to be 2? So i am not understanding how the 0.02s comes from. please help me understand this mind my stupidity. thanks – user102734 Mar 8 '16 at 17:01
• Your answer for question 11 is correct, solution is 2 but your answer for question 12 is not correct, solution is 0.5. Regarding your question "So i am not understanding how the 0.02s comes from" here the reason: 50Hz is frequenz (f)of the sampling then to get the sampled period you must proceed with the equation T=1/f then T=1/50=0,02 s. – Alf Mar 12 '16 at 9:43