The Fourier analysis has been used to examine the exit amplitudes of the Lyot-type birefringent filter. It has been found that all of its Fourier coefficients are equal to (1/2)y N is the number of the elements. Therefore the equal Fourier coefficient birefringent filter has been invented. The new filter described in this paper consists of a number of birefringent crystal plates with equal thickness between two polarizers. Selecting the angles between plates, we can make the Fourier coefficients of the filter to be equal to l/(w + l),m is the number of the plates. When two polarizers are parallel and the angles increase gradually, the Fourier coefficients are not only equal in value, but also in sign. When the wave numbers of the retardation aro integral, the maxima transmission are available. When two polarizers are perpendicular and the angles change alternately sign, the Fourier coefficients are only equal in value, but signs change alternately. When the wave number of retardation are half integral, the transmission maxima are available. If (m-f-1) instead of 2N in the formula about Lyot-type filter is replaced by (in + 1), we can obtain the various similar characters of the new filter. For example, the band width AX~ z]Ai'2,/(m + l), the thickness of following element d2 = (m + 1) dx. Multiplying Fourier expressions of two equal Fourier coefficient filters with matched thickness, we can obtain the Fourier expression of the composition filter. According to our theory, we have found eleven kinds of strict combinations between the equal Fourier coefficient filter and, respectively, the equal Fourier coefficient filter, the Lyot filter, the Evans filter, Sole filter and the partial polarizer filter. From these combinations we can obtain various kinds of filters. The above properties have been justified by computation. Before then, because there was no theory of strict combination between Sole and other filters, the increased scattering light is inevitable. We have designed a program for calculating the angles between plates for m 100, and the angles for m 15 have been computed. The most important designing data then have been provided. At last, we give the formulae about for estimating the angle and thickness errors of the filter.