Digital Filters
Chunyan Li · Cambridge University Press eBooks · 2022
The objective of this chapter is to discuss digital filters. We start from a review of theory of Fourier Transform for continuous functions. The continuous Fourier Transform is then discretized. The discretized Fourier Transform and inverse Fourier Transform, however, are not approximate equations – they are exact. Using the shifting theorem, a filter can easily be expressed in the frequency domain. A Finite Impulse Response (FIR) filter is then defined. By adding another implicit convolution to the original convolution for FIR filter, the filtered data depends on not only the input (the original time series) but also the output (the filtered data). This is an iterative relation that forms the Infinite Impulse Response (IIR) filter. These filters are examples of so-called linear systems that have an input and output. The gain is defined by the filter, which is the ratio between the input and output in the frequency domain. Several FIR and IIR filter functions in MATLAB are discussed.