20 - Convolution, Filtering with the Window Method

Summary

The objective of this chapter is to demonstrate the linkage between convolution and filtering and to discuss preliminary filtering with examples. The simplest low-pass filtering that allows low frequency to pass to the output is a “moving average,” which is essentially through a computation involving a rectangular window function (in this case, it is a filter), with a length determined by the cutoff frequency. The filtering action is accomplished by a convolution between the filter and the time series. However, moving average has its drawbacks because of the rectangular window effect or the side lobe effect. It is considered as a “poor man’s filter” because of the lack of sophistication in getting rid of the leakage from side lobes. One improvement over the moving average is using a non-rectangular window function in the convolution to reduce the sharp change at the edges. The basic ideas and examples presented here are useful in demonstrating how to do filtering with several MATLAB functions. When a low-pass filter is designed, a high-pass filter can be defined. With two or more low-pass filters, one can also design band-pass and band-stop filters. There are also other filters that can have various controls on the results.