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Barker codes of length N equal to 11 and 13 are used in direct-sequence spread spectrum and pulse compression radar systems because of their low autocorrelation properties (the sidelobe level of amplitude of the Barker codes is 1/N that of the peak signal). [15]
In receiving antennas, sidelobes may pick up interfering signals, and increase the noise level in the receiver. The power density in the sidelobes is generally much less than that in the main beam. It is generally desirable to minimize the sidelobe level (SLL), which is measured in decibels relative to the peak of the main beam. The main lobe ...
Autocorrelation analysis is used heavily in fluorescence correlation spectroscopy [14] to provide quantitative insight into molecular-level diffusion and chemical reactions. [ 15 ] Another application of autocorrelation is the measurement of optical spectra and the measurement of very-short-duration light pulses produced by lasers , both using ...
where denotes the conjugate transpose of , and denotes expectation (note that in case the noise has zero-mean, its auto-correlation matrix is equal to its covariance matrix). Let us call our output, y {\displaystyle y} , the inner product of our filter and the observed signal such that
Consequently, the time sidelobe levels of the compressed pulses were high with these early systems, even after spectral weighting, with results no better than those achieved by phase coding or chip coding at that time. [30] Typically, sidelobe levels were in the range −20 to −25 dB [23] a poor result when compared to later achievements.
The autocorrelation technique is a method for estimating the dominating frequency in a complex signal, as well as its variance. Specifically, it calculates the first two moments of the power spectrum, namely the mean and variance. It is also known as the pulse-pair algorithm in radar theory.
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Classification of the different kinds of optical autocorrelation. In optics, various autocorrelation functions can be experimentally realized. The field autocorrelation may be used to calculate the spectrum of a source of light, while the intensity autocorrelation and the interferometric autocorrelation are commonly used to estimate the duration of ultrashort pulses produced by modelocked lasers.