Bandpass Sampling

In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.

A bandpass signal has a spectrum with a lower frequency limit, denoted as ω₁, and an upper frequency limit, denoted as ω₂. The spectrum is nonzero only within this specific frequency range. To sample this signal, the time-domain signal is multiplied by an impulse train, resulting in a sampled signal. The spectrum of this sampled signal is then obtained by convolving the signal's original spectrum with the spectrum of the impulse train over a range of 2π. This convolution process causes the signal’s spectrum to repeat periodically, with a period of 2π/T. Here, T is the sampling interval, and as T increases, the spacing between these repeated spectra decreases.

Aliasing, a phenomenon where overlapping of these repeated spectra occurs, can be avoided by ensuring that the spacing between the repeated spectra is greater than the signal’s bandwidth. This requires careful selection of the maximum value of T to maintain adequate separation between the repeated spectra.

In practice, filters are employed to isolate and pass frequencies within the desired range. These filters have specific constants and frequencies designed to allow only the frequencies within the narrow band to pass through, thus preserving the integrity of the original signal while preventing aliasing. This process ensures that the signal is accurately sampled and reconstructed without distortion.