A direct LiDAR detection system, comprising: a LiDAR signal transmitter (278, 280) for transmitting transmitted LiDAR signals into a region, wherein the transmitted LiD A R signals are frequency- modulated continuous-wave, FMCW, signals or frequency-modulated pulse-burst signals; and wherein a frequency of the transmitted LiD A R signals is controlled to vary according to a ramp between a first frequency and a second frequency; a receiver (254, 256) for receiving reflected signals generated by reflection of the transmitted LiD A R signals and generating receive signals indicative of the reflected signals; and a processor coupled to the receiver for receiving the receive signals and processing the receive signals to generate detections of one or more objects in the region, the processing including: populating a n × N first data matrix with N complex data points acquired for each of n frequency ramps, performing a length- N complex fast Fourier transform, FFT, on each of the n rows of the first data matrix to form N complex FFT elements; forming a first n × N repopulated data matrix with the N complex FFT elements from the n complex FFTs performed on the first data matrix; forming a second n × N repopulated data matrix, wherein each column of the second repopulated matrix is augmented with a numerically incremented, indexed, phase term value or phase shift added to each element, to thereby generate phase-modulated signals from the receive signals; and generating the detections from the phase-modulated signals. a LiDAR signal transmitter (278, 280) for transmitting transmitted LiDAR signals into a region, wherein the transmitted LiD A R signals are frequency- modulated continuous-wave, FMCW, signals or frequency-modulated pulse-burst signals; and wherein a frequency of the transmitted LiD A R signals is controlled to vary according to a ramp between a first frequency and a second frequency; the transmitted LiD A R signals are frequency- modulated continuous-wave, FMCW, signals or frequency-modulated pulse-burst signals; and wherein a frequency of the transmitted LiD A R signals is controlled to vary according to a ramp between a first frequency and a second frequency; a receiver (254, 256) for receiving reflected signals generated by reflection of the transmitted LiD A R signals and generating receive signals indicative of the reflected signals; and a processor coupled to the receiver for receiving the receive signals and processing the receive signals to generate detections of one or more objects in the region, the processing including: populating a n × N first data matrix with N complex data points acquired for each of n frequency ramps, performing a length- N complex fast Fourier transform, FFT, on each of the n rows of the first data matrix to form N complex FFT elements; forming a first n × N repopulated data matrix with the N complex FFT elements from the n complex FFTs performed on the first data matrix; forming a second n × N repopulated data matrix, wherein each column of the second repopulated matrix is augmented with a numerically incremented, indexed, phase term value or phase shift added to each element, to thereby generate phase-modulated signals from the receive signals; and generating the detections from the phase-modulated signals. populating a n × N first data matrix with N complex data points acquired for each of n frequency ramps, performing a length- N complex fast Fourier transform, FFT, on each of the n rows of the first data matrix to form N complex FFT elements; forming a first n × N repopulated data matrix with the N complex FFT elements from the n complex FFTs performed on the first data matrix; forming a second n × N repopulated data matrix, wherein each column of the second repopulated matrix is augmented with a numerically incremented, indexed, phase term value or phase shift added to each element, to thereby generate phase-modulated signals from the receive signals; and generating the detections from the phase-modulated signals.