Synthesis of Transfer Functions in a Prescribed Frequency Band

A signal-processing system for synthesizing complicated transfer functions in a prescribed frequency band is described. The system consists of a multiplier followed by a closed loop containing a delay line and phase modulator in series. One of the inputs to the multiplier is the signal to be filtered. The second input to the multiplier is periodic, the period being equal to the loop delay. One cycle of the periodic waveform is identical to the real part of the transfer function over a prescribed frequency band of width equal to the reciprocal of the loop delay. The imaginary component of the transfer function is the negative of the Hilbert transform of the real part, as in all physically realizable filters. Two applications of the system are discussed. It is shown how a continuously variable delay line and chirp filter can be synthesized using these techniques.