How do we sample continuous time domain signals?

Question

Whenever a continuous time signal is given, we have to discretise it before converting it to freq. domain.

But while we do sampling, we use the Nyquist theorem to tell the minimum sampling frequency, there we tell minimum frequency required is > 2times max freq.

But actually we don't know frequencies, so how do we know the max. frequency ? Our final intention is only to find the frequency of the signal.

Then how do we discretise a signal when we are just given a continuous signal?

If we know it's frequency before itself, why we make lots of things sampling, dft, ... to find the frequency again?

Answer 1

If we (somehow) know the signal is bandlimited below F Hz, then by the Nyquist–Shannon sampling theorem, discretizing it by sampling point values of the function at 2 F Hz is enough to be able to recover the continuous signal exactly by sinc interpolation.

However, if there is frequency content at frequency f above F, it aliases down to 2 F - f. This is a real problem.

Ideally, one addresses aliasing using analog components to perform lowpass filtering so that aliasing frequencies are attenuated before discretization. For instance an analog microphone could first pass the audio through an analog lowpass circuit before the ADC. Or in digital cameras, most have an "optical lowpass filter" (OLPF), plates with special refractive properties, located in front of the image sensor.

Even without analog processing, something that works is in our favor is that many natural signals are distributed in the frequency domain (have power spectral density) like 1/f, aka "pink noise". So with sufficiently high sample rate, the magnitude of the aliasing content tends to be small.