A filter suppress unwanted components or features from a signal. Most often, this means removing some frequencies. As a result, the Fourier transform is an often used tool for analyzing filters as it converts signals into frequency domain.
The behavior of a filter can be described in two ways:
- In the time domain, as a convolution of the time-domain input with the filter’s impulse response function
- In the frequency domain, using either the transfer function or frequency response based on the convolution theorem
Classification of Filters
There are many ways to classify filters and these can overlap in many different ways. Filters may be:
- non-linear or linear
- time-variant or time-invariant
- causal or non-causal
- analog or digital
- discrete-time or continuous-time
By Frequency Response
- Low-pass filter: retain low frequency and eliminate others
- High pass filter: retain high frequency and eliminate others
- Band pass filter: retain frequencies in a certain band
- Notch filter (or the band-reject or band-stop filter): attenuates frequencies within a specific range and retains others
- All-pass filter: Passes all frequencies equally in magnitude, but may alter phase
By Transfer Function
- Gaussian filter: Uses a Gaussian function for smoothing; can be low-pass in image processing
- Moving average filter (boxcar filter): Smooths data by averaging neighbors