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Comparison of Real and Envelope Cross-Correlation Techniques

机译:实数和包络互相关技术的比较

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This document presents a summary and comparison of two different cross-correlation techniques: real correlation and envelope correlation by using the analytic signal. Data recorded in analog form are subsequently sampled and digitized for processing in a digital computer. The correlator operates on any real or complex signals and outputs the magnitude, phase, real part, and imaginary parts of the complex output. The digitized data can be directly input as real data for real correlation, or they can be input in the form of the complex-valued analytic signal for an envelope correlation. The data are input into the correlator with only real parts. The correlator assumes the imaginary part to be zero. The fast Fourier transform (FFT) of each channel is performed and the resulting complex spectra are Hermitian (real part exhibiting even symmetry; imaginary part exhibiting odd symmetry). One channel's spectrum then undergoes a complex conjugation. Since only the imaginary parts change their sign, the result is still Hermitian. Then the two spectra undergo a complex multiplication and the product is again Hermitian. Finally, the inverse fast Fourier transform (IFFT) of a Hermitian signal returns a real-valued sequence of data. Since the output is completely real, there are no phase angles other than 0

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