An accurate and efficient algorithm for detection of radio bursts with an unknown dispersion measure, for single dish telescopes and interferometers

Astronomical radio bursts disperse while traveling through the interstellar medium. To optimally detect a short-duration signal within a frequency band, we have to precisely compensate for the pulse dispersion, which is a computationally demanding task. We present the Fast Dispersion Measure Transform (FDMT) algorithm for optimal detection of such signals. Our algorithm has a low theoretical complexity of 2N_f N_t+ N_t N_d log_2(N_f) where N_f, N_t and N_d are the numbers of frequency bins, time bins, and dispersion measure bins, respectively. Unlike previously suggested fast algorithms our algorithm conserves the sensitivity of brute force dedispersion. Our tests indicate that this algorithm, running on a standard desktop computer, and implemented in a high-level programming language, is already faster than the state of the art dedispersion codes running on graphical processing units (GPUs). We also present a variant of the algorithm that can be efficiently implemented on GPUs. The latter algorithm's computation and data transport requirements are similar to those of two-dimensional FFT, indicating that incoherent dedispersion can now be considered a non-issue while planning future surveys. We further present a fast algorithm for sensitive dedispersion of pulses shorter than normally allowed by incoherent dedispersion. In typical cases this algorithm is orders of magnitude faster than coherent dedispersion by convolution. We analyze the computational complexity of pulsed signal searches by radio interferometers. We conclude that, using our suggested algorithms, maximally sensitive blind searches for such pulses is feasible using existing facilities. We provide an implementation of these algorithms in Python and MATLAB.