Finite Impulse Response Filters

One way of classifying linear time-invariant filters is by the duration of their impulse response. If the impulse response is of a finite duration, then it is called a finite impulse response (FIR) filter. This chapter presents the characterization of ideal digital filters. A causal FIR filter is characterized by a difference equation that is a linear combination of the products of the impulse response (filter coefficients) with present and past input samples only. Filters are classified according to their frequency responses, such as lowpass, highpass, and bandpass filter. These types of filters are introduced through their ideal frequency-response characteristics. The chapter analyzes the required symmetry of the impulse response of linear-phase FIR filters. The requirement of linear phase response is essential for major applications such as signal transmission and image processing. Finally, the chapter presents typical frequency responses of filters used in the discrete wavelet transform (DWT).