Band-stop filter

In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a range to very low levels. It is the opposite of a band-pass filter. A notch filter is a band-stop filter with a narrow stopband (high Q factor).

Other names include band limit filter, T-notch filter, band-elimination filter, and band-rejection filter.

Typically, the width of the stopband is less than 1 to 2 decades (that is, the highest frequency attenuated is less than 10 to 100 times the lowest frequency attenuated). In the audio band, a notch filter uses high and low frequencies that may be only semitones apart.

RF example 1: Non-linearities of power amplifiers For instance, when measuring non-linearities of power amplifiers a very narrow notch filter could be very useful to avoid the carrier so maximum input power will not be exceeded.

High-pass filter

A high-pass filter is a filter that passes high frequencies well, but attenuates (or reduces) frequencies lower than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a low-cut filter; the terms bass-cut filter or rumble filter are also used in audio applications. A high-pass filter is the opposite of a low-pass filter, and a bandpass filter is a combination of a high-pass and a low-pass.

It is useful as a filter to block any unwanted low frequency components of a complex signal while passing the higher frequencies. Of course, the meanings of low and high frequencies are relative to the cutoff frequency chosen by the filter designer.

Applications: Such a filter could be used to direct high frequencies to a tweeter speaker while blocking bass signals which could interfere with or damage the speaker. A low-pass filter, using a coil instead of a capacitor, could simultaneously be used to direct low frequencies to the woofer. See audio crossover.

High-pass and low-pass filters are also used in digital image processing to perform transformations in the frequency domain.

Most high-pass filters have zero gain (-inf dB) at DC. Such a high-pass filter with very low cutoff frequency can be used to block DC from a signal that is undesired in that signal (and pass nearly everything else). These are sometimes called DC blocking filters.

Low-pass filter

A low-pass filter is a filter that passes low frequencies well, but attenuates (or reduces) frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter when used in audio applications.

A high-pass filter is the opposite, and a bandpass filter is a combination of a high-pass and a low-pass.

The concept of a low-pass filter exists in many different forms, including electronic circuits (like a hiss filter used in audio), digital algorithms for smoothing sets of data, acoustic barriers, blurring of images, and so on. Low-pass filters play the same role in signal processing that moving averages do in some other fields, such as finance; both tools provide a smoother form of a signal which removes the short-term oscillations, leaving only the long-term trend.

Band-pass filter

A band-pass filter is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range. An example of an analogue electronic band-pass filter is an RLC circuit (a resistor-inductor-capacitor circuit). These filters can also be created by combining a low-pass filter with a high-pass filter.

An ideal filter would have a completely flat passband (e.g. with no gain/attenuation throughout) and would completely attenuate all frequencies outside the passband. Additionally, the transition out of the passband would be instantaneous in frequency. In practice, no bandpass filter is ideal. The filter does not attenuate all frequencies outside the desired frequency range completely; in particular, there is a region just outside the intended passband where frequencies are attenuated, but not rejected. This is known as the filter roll-off, and it is usually expressed in dB of attenuation per octave of frequency. Generally, the design of a filter seeks to make the roll-off as narrow as possible, thus allowing the filter to perform as close as possible to its intended design. However, as the roll-off is made narrower, the passband is no longer flat and begins to “ripple.” This effect is particularly pronounced at the edge of the passband in an effect known as the Gibbs phenomenon.