downchirps

Downchirps are a type of chirp signal in which the instantaneous frequency decreases with time. They are the opposite of upchirps, where the frequency increases. Downchirps are commonly used in radar, sonar, and communications systems that rely on linear frequency modulation due to their well-defined time-frequency structure and ease of matched-filtering.

In a linear downchirp, the instantaneous frequency is f_inst(t) = f0 + k t with k < 0, where f0 is the starting frequency and k is the (negative) chirp rate. The analytic signal can be written s(t) = A cos(2π( f0 t + (k/2) t^2 )). The phase is quadratic in time, producing a downward sweep in frequency. Decreasing frequency over the duration produces a constant amplitude sweep that is easily compressed by a matched filter designed to the same chirp.

Generation can be done with frequency-modulated oscillators, digital signal processing, or by applying a negative slope to a standard chirp generator. In digital systems, complex envelope representations allow efficient synthesis and arbitrary sampling rates. In receiver processing, dechirping or stretch processing multiplies the received signal by a reference downchirp, converting a sweeping waveform into a stationary tone proportional to range, which simplifies range estimation.

Common applications include coherent radar and sonar systems that use linear frequency modulation, as well as chirp spread spectrum communication schemes in which information is carried by relative shifts of downchirp sequences. Compared with upchirps, downchirps offer similar processing benefits but may be chosen to match specific Doppler or hardware constraints.

See also: chirp signal, linear frequency modulation, chirp spread spectrum, FMCW radar.