the autocorrelation function for the linear chirp can be written as where in 2 u03c6 is the carrier harmonic that is modulated by both a triangle pulse t u2212 u03c4 and a sinc function of time examination of 2 shows that the autocorrelation function can be completely characterized by the frequency chirp rate u03b1 and the chirp duration t and that the first root of the sinc function occurs at approximately at u03c4 1 u03b1t so the width of the main lobe of the waveform is an inverse function of the time bandwidth product as determined by the baud rate and frequency sweep in most linear chirp applications the time bandwidth product of the chirp is chosen such that its autocorrelation waveform displays a narrow peak with well controlled sidelobes as an example the autocorrelation waveform for u03b1t 2 40 is shown in fig3 the well defined peak combined with the high peak to average ratio make the chirp an ideal waveform for ranging applications however the downhole acoustic channel limits the frequency span of the chirp to tens of hz in the case of the third passband of the down hole channel as shown in fig1 the frequency passband encompasses 550 to 720 hz assuming a symbol rate of t 0 2 0 1 or 0 05 sec for 5 10 or 20 baud with a chirp frequency span of 40 hz results in a time bandwidth product of 1 6 0 4 and 0 1 respectively fig4 shows the evolution of.