upchirps

An upchirp is a type of chirp signal in which the instantaneous frequency increases with time. In contrast to a downchirp, whose frequency decreases over the duration, an upchirp has a positive chirp rate. Upchirps are a subset of linear frequency modulated (LFM) signals and are commonly used in radar, sonar, and wireless communications to sweep through a band of frequencies within a fixed time.

Mathematically, if the instantaneous frequency is f(t) = f0 + k t for 0 ≤ t ≤ T with k > 0, the complex baseband signal can be written as s(t) = A exp(j 2π [f0 t + (k/2) t^2]). Real-valued implementations may use cos-like versions. The parameter k is the chirp rate, determining how quickly frequency sweeps across the band, and T is the chirp duration.

Generation is achieved with voltage-controlled oscillators or digital synthesis methods, such as direct digital synthesis, often followed by upconversion to the desired RF band. In digital communications, upchirps are used in chirp spread spectrum (CSS) to spread data over a wide bandwidth while enabling robust demodulation in noisy channels.

Detection typically relies on matched filtering: correlating the received chirp with a locally generated replica yields a beat frequency proportional to range (and, in some radar configurations, to relative velocity). CSS uses pairs of upchirps and downchirps to encode information, exploiting their correlation properties.

See also: downchirp, chirp signal, FMCW radar, matched filter, chirp spread spectrum.