Question

show work please

15. What is the minimum sampling rate needed in order to successfully capture and reproduce an analog signal with frequencies up to 500 MHz?

Answer 1

In this question we apply the concept of Sampling Theorem.

The sampling theorem states that a signal can be exactly reproduced if it is sampled at the rate F_s which is greater than twice the maximum frequency F.

where is the sampling rate and is the maximum frequency of analog signal.

In other words, the sampling rate for an analog signal must be at least two times as high as the highest frequency in the analog signal in order to avoid aliasing. It is also known as the Nyquist rate. (It is the minimum rate at which a finite bandwidth signal needs to be sampled to retain all of the information.)

So the minimum sampling rate is,

Note: The analog signal should be in the range of

where is the frequency of the analog signal

and is the sampling rate

So using the formula

we are given in the question = 500 Mhz

Therefore,

The minimum sampling rate :