The discrete Gabor (1946) transform algorithm is introduced that provides an efficient method of calculating the complete set of discrete Gabor coefficients of a finite-duration discrete signal from finite summations and to reconstruct the original signal exactly from the computed expansion coefficients. The similarity of the formulas between the discrete Gabor transform and the discrete Fourier transform enables one to employ the FFT algorithms in the computation. The discrete 1-D Gabor transform algorithm can be extended to 2-D as well.

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This method aims to analyze rosmarinic acid (RA), caffeic acid (CA), ursolic acid (UA) and oleanolic acid (OA) in different organs of Salvia deserta Schang qualitatively and quantitatively by high-performance thin-layer chromatography. Using chloroform–methanol–formic acid (10: 2: 0.5, v/v/v) as mobile phase and silica gel plate as stationary phase to analyze RA and CA at 330 nm. Using cyclohexane–ethyl acetate–methanol (10: 2: 0.5, v/v/v) as mobile phase and silica gel F254 plate as stationary phase to analyze UA and OA at 550 nm. The linearity ranges of RA, CA, UA and OA were 0.1250–0.4375, 0.0145–0.0870, 0.5000–2.5000 and 0.5000–2.5000 mg, respectively, with corresponding correlation coefficients of 0.9938, 0.9981, 0.9971 and 0.9969, respectively. Good precision, stability, accuracy (recovery rates were between 95 and 105%) of the method were determined. The limits of detection and the limits of quantification of RA, CA, UA and OA were determined, respectively, as 50, 58, 25, 33 and 160, 191, 80, 106 ng. The established method is simple, rapid, effective and can be easily used to determine the contents of RA, CA, UA and OA in different parts of S. deserta Schang.

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