Patent ID: 7640282

Claim:
A method of matched filtering in accordance with a reference signal sequence comprising a plurality of signal samples at regular sampling time intervals λ, said method comprising the use of apparatus to effect the following operations: receiving an input time domain signal r(t) to be filtered; sampling the input time domain signal r(t), at sampling time intervals τ that are not synchronized to the sampling intervals λ of the reference signal sequence, to produce an input signal sequence; computing the Fourier transform of the input signal to be filtered evaluated at discrete frequencies f determined by the intervals τ at which the input signal is sampled; computing the Fourier transform of the reference sequence, evaluated at the same discrete frequencies f; forming the product of the two Fourier transforms; and computing the inverse Fourier transform of said product to produce an output time domain signal y(t) representing, a filtered version of the input time domain signal; wherein the reference sequence is defined as a function of time by a process of iteratively combining shifted versions of shorter sequences, and wherein computing the Fourier transform of the reference sequence comprises an iterative process of combining the Fourier transforms of a shorter starting sequence using only the operations of inverting, addition, and multiplication, or equivalents thereof, performed by machine implemented digital signal processing.