Highly accurate zero crossings for frequency determination

Apparatus for measuring an angle of arrival .theta. of an incoming signal using first and second antennas separated by a distance d coupled to receiver means;

• said receiver means comprising input means coupling input signals form the first and second antennas to an analog-to-digital converter means operated at a sampling frequency which is at least four times the frequency of the input signals to provide first and second sets of digitized samples at points where y represents the digitized value of the amplitude, the time between samples in each of said sets being designated as .DELTA.t;
• means for selecting three of said samples from each of said first and second sets having digitized amplitude values as follows:
• y.sub.0 =A sin (.omega.t.sub.1 +.alpha.)
• y.sub.1 =A sin [.omega.(t.sub.1 +.DELTA.t)+.alpha.)]
• y.sub.2 =A sin [.omega.(t.sub.1 +2.DELTA.t)+.alpha.)]
• where A is the analog amplitude, .omega.=2.pi.f is the angular frequency, and .alpha. is a phase shift;
• means for finding zero crossings at times t.sub.1 and t.sub.2 for the first and second sets respectively, the zero crossing time t.sub.1 being calculated as follows:
• ##EQU14## and the time t.sub.2 being calculated in a similar manner using three points from the second set:
• means for calculating the time difference that it takes the signal to be received by both of said antennas as the difference between the zero crossing values t.sub.1 and t.sub.2, and means for calculating a lag distance k from the following equation:
• k=time difference.times.c
• where c=speed of light(3.times.10.sup.8 m/s) and means for calculating the angle of arrival as ##EQU15##