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Reconstructing the Hartley intensity spectrum from its sinusoidal crossings

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Abstract

It is shown that a 2M-point representation IH(f) of the Hartley intensity spectrum IHa(f) can be reconstructed from the intersections of IHa(f) with the reference sinusoid R(f) of period 2δ. As required by the Nyquist sampling criterion, one sinusoidal crossing is detected within every frequency interval δ when the bandwidth of IH (f) is 2. Specifically, the 2M crossings are used to determine the 2M expansion coefficients [h(mΔ)] of IH (f) with respect to the Hartley basis functions: cas(2πfmΔ), where Δ = 1/2 and m = −M, −M + 1, . . . ,M. An accurate and efficient algorithm for computing [h(mΔ)] from the sinusoidal crossings also is proposed and demonstrated.

© 1995 Optical Society of America

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