Contents I. Introduction
Digital filters find various applications in signal processing. Digital filters can be broadly classified as the IIR (Infinite Impulse Response) or the FIR (Finite Impulse Response), based on the duration of the impulse response of the filter. FIR filters are always stable and can be designed to be linear phase, and hence have a preference over the IIR filters, where one needs to consider and ensure stability. Design of FIR filters is well established and few methods of design are usually included in the under graduate course on `Digital Signal Processing’. Prominent design techniques for the FIR digital filters are: 1) design using the Window method, 2) design through the frequency sampling method, and 3) optimization techniques. In the design of FIR filters using the Window method, one represents the desired frequency response using the Fourier series representation (which results in an impulse response of infinite duration), and use suitable Window functions to truncate and arrive at the desired FIR filter. With increase in the length of the filter, the error between the desired and the designed filter can be reduced. On the other hand, design using the frequency sampling method involves taking fixed frequency samples from the desired frequency response, and computing its inverse discrete Fourier transform to obtain the desired FIR filter coefficients. Here, there is an exact representation of the designed and the desired filter at the instants of sampling, and ripples in between. In this method also the error decreases with increase in the length of the filter. The third method of FIR filter design is based on applying optimization techniques to arrive at the desired filter.
