bandpasslimited

Bandpass-limited is a term used in signal processing to describe a signal whose spectral content is confined to a finite band of frequencies away from zero. In practical terms, the Fourier transform X(f) is nonzero only for frequencies within a band [f1, f2], where f1 > 0 and f2 > f1, giving a bandwidth B = f2 − f1. Such signals are distinct from baseband-limited signals, whose spectrum extends to dc, and from signals that are truly zero outside a symmetric interval around zero.

A convenient way to realize a bandpass-limited signal is through modulation: a baseband signal s(t) with spectrum limited to [−W, W] can be multiplied by a carrier e^{j2π f0 t} to produce a spectrum centered at the carrier frequency f0 with the same bandwidth. Filtering with a bandpass filter achieves the same confinement.

Bandpass-limited signals are central to many communications and sensing systems, including AM and FM radio, radar, and medical imaging modalities that operate at a nonzero center frequency. They also underpin certain sampling strategies: bandpass sampling (undersampling) uses sampling rates lower than twice the highest frequency, made possible by the signal's spectral sparsity and the spectral location away from zero.

In summary, bandpass-limited describes signals whose energy is confined to a finite, nonzero-centered frequency band, with practical implications for modulation, filtering, and sampling.