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This can be achieved by placing the transmitter at the center of the circular receiver array. With the same integration method, this system is capable of accurately estimating the bearing angle of the reflected waveform. Because the transmitted signal is readily available, the time delay between a received waveform r(t) and transmitted signal T(t) can be estimated by using the double-integration method in a similar manner. Subsequently, the range distance of the target can be calculated from the time delay.
For example, in the horizontal direction, the vector can be written as u = D [1, 0, 0]. Consider the simple case of the circular receiver array with radius D/2 and N uniformly spaced receivers. The N receivers are located at the positions of un = D j 2πn exp N 2 where n = 0, 1, 2, … , N − 1. Utilizing the circular symmetry, the receivers of the N-element array can be grouped into N/2 pairs corresponding to the directional vectors, 2πn 2πn un = D cos ,0 , sin N N where n = 0, 1, 2, … , N/2.
Fx 33 System Analysis 1/2 1 H −1( f x, f y ; z) = exp − j 2π 2 − ( f x2 + f y2 ) z λ 0 1 ≥ ( f x2 + f y2 ) λ2 otherwise This also means the reconstruction filter is lowpass with the same cutoff frequency. Then, since the transfer function is phase-only with unity amplitude over the lowpass region, inverting the transfer function is the same as conjugating it, H −1( f x , f y ; z) = H * ( f x , f y ; z) This suggests that the inverse filter designed for image reconstruction is in fact the matched filter and the image formation process is simply matched filtering.