# Introduction to Filtering

The filtering process alters the frequency content of a signal. For example, the bass control on a stereo system alters the low-frequency content of a signal, while the treble control alters the high-frequency content. Changing the bass and treble controls filters the audio signal. Two common filtering applications are removing noise and decimation. Decimation consists of lowpass filtering and reducing the sample rate.

The filtering process assumes that you can separate the signal content of interest from the raw signal. Classical linear filtering assumes that the signal content of interest is distinct from the remainder of the signal in the frequency domain.

## Advantages of Digital Filtering Compared to Analog Filtering

An analog filter has an analog signal at both its input x(t) and its output y(t). Both x(t) and y(t) are functions of a continuous variable t and can have an infinite number of values. Analog filter design requires advanced mathematical knowledge and an understanding of the processes involved in the system affecting the filter.

Because of modern sampling and digital signal processing tools, you can replace analog filters with digital filters in applications that require flexibility and programmability, such as audio, telecommunications, geophysics, and medical monitoring applications.

Digital filters have the following advantages compared to analog filters:

- Digital filters are software programmable, which makes them easy to build and test.
- Digital filters require only the arithmetic operations of multiplication and addition/subtraction.
- Digital filters do not drift with temperature or humidity or require precision components.
- Digital filters have a superior performance-to-cost ratio.
- Digital filters do not suffer from manufacturing variations or aging.