Filter Basics

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

As shown in Figs. 1-5, 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 used for phase shaping or equalization.

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

Figure 6: The ideal low-pass filter magnitude response.

Figure 7: A practical low-pass filter magnitude response.