Gabor transform has recently been exploited to do texture analysis, including texture edge detection, texture segmentation/discrimination, and texture synthesis. For most of the applications using Gabor transform, people convolve the given texture image with a set of Gabor filters with some user specified parameters. Although the mathematical formulation of applications involve the Fourier transform, few have investigated mathematical properties of the relationship between Gabor filters and their Fourier transform. This paper mainly studies mathematical properties of real Gabor filters and their corresponding Fourier transform. The goal is to select a set of `interesting' Gabor filters, or say, a set of parameters for Gabor filters to do texture analysis. We demonstrate, by means of 3-D graphical displays, that a Gabor filter or its corresponding Fourier transform may have a single peak or double peaks according to different parameters. Experiments for texture discrimination are given to demonstrate the applications of Gabor transform.