# Relation between bandwidth and amplitude of auto correlation of chirp signal

I am trying to understand the properties of chirp signals and their characteristics. I plotted the autocorrelation of a chirp signal in MATLAB. How can I compute the relation between the amplitude of the autocorrelated signal and the chirp parameters (time duration/bandwidth)?

Thanks!

## 1 Answer

For wideband FM (which a typical chirp represents) the power spectral density will be approximately a rectangular pulse in frequency. The autocorrelation is the inverse Fourier Transform of the power spectral density. The inverse Fourier Transform of a rectangular pulse in frequency with total bandwidth $$B$$ is a Sinc function in time with the null to null duration of the main lobe as $$2B$$ as the OP has shown. The height is the integrated area under that rectangular function, so there is no information on the actual frequency or range of frequencies but simply the total power (except we can deduce that the range of frequencies is much larger than the rate of the chirp, hence wideband FM).