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In this paper, we present signal processing techniques to detect meteor returns from Arecibo Observatory 430-MHz UHF radar data. We exploit the characteristics of the transmit waveform in the frequency domain as well as in the time domain. Two detection methods are investigated. First, when a meteor is present in the radar return over several interpulse periods, there will be a periodic structure in frequency spectrum. By detecting this structure, we detect the presence of a meteor. Second, we construct a matched filter bank to detect the energy of different Doppler frequency components. When the energy exceeds a certain threshold, we declare meteor detection. We also find the altitude of a meteor by finding the peak of the matched filter output. Analytical and experimental results show that we can efficiently and reliably detect meteors using these methods.