Design of two-dimensional finite impulse response digital filters a software implementation

Abstract

A Turbo-Pascal program is written to design circularly-symmetric, 2-Dimensional, finite impulse response (FIR) digital filters using the Kaiser window method. The filter specifications are given in the frequency domain and comprise the passband limit (s), the transition width (s) and the ripple. Given these specifications, the first approximations of the window order and window parameter (0:) are computed using expressions given by T.S. Speake and R.M. Mersereau [20]. The operation of inverse discrete Fourier transform (IDFT) is used to obtain the ideal impulse response. The window function and the ideal impulse response are then multiplied point by point to get the actual impulse response. The DFT operation is then performed to get the Forier transform at discrete points in space. The filter characteristics of the designed filter are made available n tabular forms once the frequency response is determined. This enables the user to compare them with the supplied specifications. If the user is satisfied with the designed filter, then he/she can have the filter impulse response in the form of tables or 3-dimensional graphs. If, on the other hand, the filter specifications are not met and the user wants to redesign the filter, he/she can supply new values for the window order and window parameter (a). Increasing the window parameter (a) has the effect of reducing the ripple but widening the transition width. With the new values of the window order and parameter (a), the filter is redesigned. The process can be repeated as many times as one wishes until the user is satisfied with the design. The 3-dimensional graphs can be printed on paper if the user so wishes. For most lowpass filter applications, a redesign of the filter is not required as the first round design produces filters that meet the specifications. For other types, however, redesigns are often required especially if the window order is low. Coded data for 65x65 images with 32 gray levels are used as input data for the image processing application. An image is displayed on the screen with 16 gray leveis (actual gray levels divided by ... 2). The image is then corrupted by impulse noise with 10% probability and displayed on the screen. The effect of the different standard filters on both the original image and the image corrupted with noise can then be studied by designing the required filters and filtering the images with these filters. To effect all these, one only needs to respond appropriately to prompts from the computer. The blurring effects of the lowpass filter can best be studied by applying it to an image corrupted with impulse noise while the edge sharpening effect of highpass filters can best be seen when applied to the original uncorrupted image.