Bandpass-sampling

Consider a signal sampled at a rate greater than twice its highest frequency.

A signal with most of its energy concentrated in a narrow frequency band is known as a bandpass signal. The technique used for sampling such signals is called bandpass sampling.

The signal's spectrum has a lower frequency limit,  ω₁, ​that is greater than its bandwidth.

The spectrum is nonzero within the defined lower and upper frequency bands.

Multiplying the time-domain signal by an impulse train produces a sampled signal.

The spectrum of the sampled signal is obtained by convolving the signal's spectrum with the impulse train spectrum over 2​π.

This convolution causes the signal's spectrum to repeat periodically with a period of 2π/T.

As T increases, the spacing between the repetitions decreases. Aliasing occurs when these repeated spectra overlap.

Aliasing can be avoided by ensuring the spacing between the repeated spectra is greater than the signal's bandwidth and with the maximum value of T. 

Filters with specific constants and frequencies pass the frequencies within the desired range.