profiles. This low spectral spread is particularly significant when baseband signals are to be digitized since it permits a sampling frequency to be chosen which is only slightly higher than twice the maximum frequency excursion of the chirp. Reducing Spectral Ripple The Fresnel ripples on a chirp spectrum are very obtrusive, especially when time-bandwidth products are low (under 50, say) and their presence leads to high time sidelobe levels when chirps are subject to pulse compression as in radar and sonar systems. They arise because of the sudden discontinuities in the chirp waveform at the commencement and termination of the pulse. Although there are a number of procedures that can be applied to reduce the ripple levels, they are not all equally effective. Furthermore, some of the methods require amplitude shaping, or amplitude modulation, of the chirp pulse and this makes those methods unsuitable when, for example, the chirp pulses are to be transmitted by a power amplifier operating in a near-limiting condition. For such systems only the methods using frequency (or phase) pre-distortion are appropriate. Introducing Rise and Fall Times of Finite Duration If the transitions at the start and end of the chirp are made less sudden (or more 'rounded'), then a reduction in ripple amplitude is achieved. The durations of the two transition regions need only be a small fraction of the pulse duration, and suggested values are between 2/F and 3/F but, as expected, when the time-bandwidth product of the pulse is small, longer transition periods are needed. The actual profiles of these rise and fall regions of a pulse do not seem to be critical and may be provided, for example, by band limiting filters in analogue implementations and a linear slope in digital ones. Two examples show the spectra of linear chirps with finite rise-times. The first is for a chirp with time-bandwidth of 250, where the rise and fall times are 4% of the total pulse duration and the second is for a chirp with time-bandwidth of 25, where the rise and fall times are 10% of the total. These two spectra show a marked reduction in ripple amplitude compared to the spectra of unmodified linear chirps shown earlier. Applying Phase or Frequency Distortion to the Chirp Pulse A analogous technique can be applied to the frequency characteristic of the chirp waveform by adding linear FM distortion segments (quadratic phase modulation distortion) to