Tapped Delayed-Line Detector for a Modified Chirp Signal
Richard O. Rowlands · The Journal of the Acoustical Society of America · 1962
The technique of pulse compression by the use of a linear frequency-modulated signal in conjunction with a delay network as detector is well known. If the duration of the signal is T and the instantaneous frequency varies from f0 to f1, the slope of the delay network must be −T/(f1−f0). Since the Doppler effect keeps the product T(f1−f0) constant, the quotient varies as the square of the Doppler shift, and so this signal is only usable if the Doppler shift is small. This paper describes a modified chirp signal and its matched filter detector that are not subject to this limitation. It is shown that the signal x(t) defined by the equation x(t)=A cos [(2πf0/K) log 1/(1−Kt)]0⩽t⩽T=0tT possesses the property that the ratio between any 2 adjacent intervals enclosing m cycles of the signal is a constant. It is further shown that a delay line with taps spaced in a geometrical progression is a matched filter for detecting this signal. The matched filters for Doppler-shifted signals may then be formed by extending the progression at each end and connecting together the same number of adjacent taps.