A useful property of the generalized chirp signal ambiguity function

The generalized chirp signal ambiguity function |X(τ, ω, µ)|²describes the output of a filter matched to a chirp signal when the input is mismatched in frequency sweep rate as well as carrier frequency and arrival time. This letter provides an interpretation of |X(0, ω, µ)|²in terms of the amplitude spectrum of a chirp signal. A relationship between |X(0, ω, µ)|²and |X(τ, 0, µ)|²is then developed which simplifies the computation of the latter function.