Design protocols for time-dependent finite impulse response digital filters based on regression analysis of Fourier transform infrared interferograms

A protocol for the design of time-dependent finite impulse response (FIR) digital filters is described for use in extraction of frequency information from Fourier transform infrared (FT-IR) interferogram data. Building upon previous work that devised a multiple linear regression (MLR) approach to the filter design, the current work develops a design protocol that produces filters with narrow frequency responses, high attenuation, and better performance than conventional FIR filters with a similar number of coefficients. The five variables that influence the frequency response characteristics of filters designed with this method are: (1) entrance criterion that determines the number of significant filter coefficients in the stepwise MLR analysis, (2) the offset values that represent which interferogram points before and after the point that is to be filtered are included in the convolution sum, (3) the target width of the filter passband, (4) the filter position, and (5) the number of interferograms used in the regression. A full factorial experimental design is used to study the main and interaction effects of these factors and their contribution to determining the frequency response function of the computed filter. It is found that an interaction exists between the offset range and the target width of the passband, necessitating a joint study of these parameters. However, the entrance criterion, the number of interferograms, and the filter position can be studied independently. The effect of each of these variables on the performance of the computed filters is explored in detail. The results of this study provide a set of guidelines for choosing values of the five variables that allow the desired tradeoffs to be achieved between the number of filter coefficients, passband width, stopband attenuation, and filter phase response.