FM spectrum can be considered to have three major components, namely an Amplitude Term, a Square Law Phase term, and a Residual Phase Term The ratio is approximately unity over a large part of frequency range of interest so approximates to a constant phase angle /4 there. If a frequency scaling term n is introduced, where , then the expressions for the Fresnel arguments become and The spectra are now functions of the product T.F, independent of any particular values of center frequency and bandwidth. This product, T.F, is often referred to as the time-bandwidth product of the chirp. Tables of the Fresnel integrals have been published, together with mathematical routines with which to compute the integrals manually or by means of a computer program. In addition, a number of mathematical software programs, such as Mathcad, MATLAB and Mathematica have built-in routines to evaluate the integrals, either as standard functions or in extension packages. Some plots of the power spectrum |S()|2 as a function of frequency are shown, for time-bandwidth products of 25, 100, 250 and 1000. When the product is small, the Fresnel ripples are very much in evidence, but the spectrum does tend to a more rectangular profile for larger values. In the case of the plots of residual phase, 2(), the profiles tend to be very similar over a wide range of time-bandwidth products. Two examples, for TxB = 100 and 250 are shown below. They have a phase angle close to a value of /4 within the chirp range and they only start to change significantly for frequencies beyond this range. Consequently, for frequencies within the sweep range of the chirp, it is the square-law phase term 1() and its group delay function ( = -d1/d() ) that are of most interest. There is a plot of the group delay shown below. Both this function and the phase 1() are independent of the value of the time-bandwidth product. As expected, the group delay is a linear function with a duration T secs, over a frequency sweep of rads. The residual phase term adds only minor perturbations to this characteristic within the frequency range . At frequencies outside this range, 2() deviates rapidly from /4, and so the total phase will deviate seriously from a square law there. Fortunately, the energy content of the chirp spectrum is very small at these frequencies (as is demonstrated in a