Filter Basics

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Filtering is the oldest and most common type of signal processing, usually in the form of frequency selectivity or phase shaping, or both. Some filter applications include (1) extracting a desired signal from other signals, (2) separating signals from noise, (3) anti-aliasing in analog-to-digital converters or smoothing in digital-to-analog converters, (4) phase equalization, and (5) limiting amplifier bandwidths for reducing noise.

Filter Types

We can classify filters based on frequency range selectivity as: (1) low-pass filters, (2) high-pass filters, (3) band-pass filters, (4) band-stop, band-reject, or notch filters, and (5) all-pass filters.

Figure 1: Low-pass filter magnitude response and symbol.
Figure 2: High-pass filter magnitude response and symbol.
Figure 3: Band-pass filter magnitude response and symbol.
Figure 4: Band-stop filter magnitude response and symbol.
Figure 5: All-pass filter magnitude response and symbol.


Ideal vs. Practical Filters

Magnitude and Frequency Metrics

Group Delay