by a window function, a process sometimes called apodization. In the case of an antenna array, similar profiling by "weighting functions" is used to reduce the spatial sidelobes of the radiation pattern. Although spectral shaping of a chirp could be applied in the frequency domain, better results are obtained if the shaping is carried out in the time domain. Examples of this process are shown for linear chirps with time-bandwidth products of 250 and 25. They have been shaped by a 3-term Blackman-Harris window given by The spectra, now bell-shaped, are seen to be free of ripples. Non-linear chirps can be devised that have a bell shaped spectrum, such as the Blackman-Harris window just discussed, and consequently will exhibit reduced ripple compared to the linear chirp. By means of the stationary phase method described earlier, an approximate relationship between time and frequency can be obtained and is: Rearranging the equation, a plot of frequency against time can be plotted, as shown. As examples, plots of the spectral magnitudes of non-linear chirps with spectral profiles of Blackman-Harris windows and with time-bandwidth products of 250 and 25 are shown below. As can be seen, there is some ripple reduction, but the disappointing performance can be attributed to the fact that these chirps, although they have reduced energy content in their outer frequency regions, they still have amplitude profiles with fast rise and fall times. See also Pulse compression, a process which uses frequency or phase coded waveforms to improve the signal to noise of received signals. Chirp compression, a compression process for chirps only. References Signal processing