How to see Signal frequency and Sampling frequency on the frequency spectrum

Question

If I have a 100 Hz periodic analog signal and let us say it is band limited to 1kHz and I sample it at 3 kHz. If I want to see its frequency spectrum then how to differentiate between the signal frequency 100 Hz from the sampling frequency 3 kHz in the spectrum?

Edit:

What I understand is that frequency spectrum shows the frequency components at even or odd or mix multiples of a fundamental frequency. But what I don't understand is that whether the frequency is the periodic signal frequency or the sampling frequency?

If it is the harmonics of the fundamental signal frequency then how to find out the sampling frequency from looking at the spectrum?

Answer 1

If you sample a 100Hz signal at 3kHz, then here's what you will see:

1. Time domain: Think of this as a digital oscilloscope view. You will have a series of numbers that represent the voltage. These numbers are spaced at 1/3000 second along the time axis. Basically, a bunch of dots on an xy coordinate system. X is time, and all of your dots are 1/3000 of a second long. Y is voltage, and your dots are at the height indicated by the voltage.

2. Frequency domain: You take your digitized data, and apply a fourier transformation to it. You now have a bunch of dots which represent the intensity of each frequency in the signal. The frequencies range from 0 to 1500Hz. Refer to the Nyquist/Shannon theorem for the reasoning. In your (idealized case) you will see a single peak representing 100Hz.

The sampling rate is not part of the spectrum. You'll never see it.

The sampling rate is also not part of the digitized data - you would never see it in an oscilloscope view of your data.

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Really, you need to look up sampling theory. The wikipedia link is a starting point. If you understand what is going on, then you would never wonder how to seperate signal and sampling rate - you would know that they are already seperate.