Filters

A filter is a device or algorithm that selectively passes or attenuates components of a signal according to frequency or other criteria. Filters are used to remove noise, extract desired components, or shape the spectral content of signals. They can be implemented as analog hardware, such as electronic circuits, or as digital algorithms running on processors.

In frequency-based terms, filters are commonly categorized as low-pass, high-pass, band-pass, or band-stop (notch). A low-pass filter passes low frequencies and attenuates higher ones, while a high-pass filter does the opposite. Band-pass filters pass a specific range of frequencies, and notch filters suppress a narrow range. Spatial filters in image processing operate similarly on spatial frequencies to blur or sharpen images.

Implementation and design vary by domain. Analog filters rely on circuit topologies (for example, RC, RLC, or op-amp configurations) to realize a desired transfer function. Digital filters process discrete samples and are described by difference equations. They are broadly divided into finite impulse response (FIR) and infinite impulse response (IIR) types. Key concepts include the frequency response, cutoff frequency, filter order, attenuation, and ripple. In digital design, methods such as windowing, optimization, or transform-based approaches (for example bilinear transform) are used to achieve desired characteristics and stability, including linear phase in some applications.

Applications span audio processing, communications, control systems, and image processing. Filters are used for anti-aliasing before sampling, noise reduction, signal extraction, and feature enhancement. The choice of filter reflects trade-offs among attenuation, phase behavior, computational resources, and real-time requirements.