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