Editing Ambiguity function (section)

==Ideal ambiguity function==
An ambiguity function of interest is a 2-dimensional [[Dirac delta function]] or "thumbtack" function; that is, a function which is infinite at (0,0) and zero elsewhere.

:<math>\chi(\tau,f) = \delta(\tau) \delta(f) \, </math>

An ambiguity function of this kind would be somewhat of a misnomer; it would have no ambiguities at all, and both the zero-delay and zero-Doppler cuts would be an [[Dirac delta function|impulse]]. This is not usually desirable (if a target has any Doppler shift from an unknown velocity it will disappear from the radar picture), but if Doppler  processing is independently performed, knowledge of the precise Doppler frequency allows ranging without interference from any other targets which are not also moving at exactly the same velocity.

This type of ambiguity function is produced by ideal [[white noise]] (infinite in duration and infinite in bandwidth).<ref>Signal Processing in Noise Waveform Radar By Krzysztof Kulpa (Google Books)</ref>  However, this would require infinite power and is not physically realizable.  There is no pulse <math>s(t)</math> that will produce <math>\delta(\tau) \delta(f)</math> from the definition of the ambiguity function. Approximations exist, however, and noise-like signals such as binary phase-shift keyed waveforms using [[Maximum length sequence|maximal-length sequences]] are the best known performers in this regard.<ref>G. Jourdain and J. P. Henrioux, "Use of large bandwidth-duration binary phase shift keying signals in target delay Doppler measurements," J. Acoust. Soc. Am. 90, 299–309 (1991).</ref>