A radar apparatus for obtaining a higher range resolution than conventional radar apparatus without increasing the bandwidth comprises a transmitter antenna that transmits a frequency modulated transmit signal having a transmit bandwidth and a receiver antenna that receives a receive signal reflected from said scene in response to the transmission of said transmit signal. A mixer mixes said receive signal with said transmit signal to obtain a mixed receive signal, a sampling unit samples said mixed receive signal to obtain receive signal samples from a period of said receive signal, and a processor processes said receive signal samples by defining a measurement matrix and determines the positions of one or more targets of the scene by applying compressive sensing using said measurement matrix and said receive signal samples.