High-pass filter

[1] High-pass filters have many uses, such as blocking DC from circuitry sensitive to non-zero average voltages or radio frequency devices.

High-pass and low-pass have the opposite meanings, with a "high-pass" filter (more commonly "short-pass") passing only shorter wavelengths (higher frequencies), and vice versa for "low-pass" (more commonly "long-pass").

In electronics, a filter is a two-port electronic circuit which removes frequency components from a signal (time-varying voltage or current) applied to its input port.

In optics a high pass filter is a transparent or translucent window of colored material that allows light longer than a certain wavelength to pass through and attenuates light of shorter wavelengths.

A resistor and either a capacitor or an inductor can be configured as a first-order high-pass filter.

The simple first-order capacitive high-pass filter shown in Figure 1 is implemented by placing an input voltage across the series combination of a capacitor and a resistor and using the voltage across the resistor as an output.

The transfer function of this linear time-invariant system is: The product of the resistance and capacitance (R×C) is the time constant (τ); it is inversely proportional to the cutoff frequency fc, that is, where fc is in hertz, τ is in seconds, R is in ohms, and C is in farads.

Figure 2 shows an active electronic implementation of a first-order high-pass filter using an operational amplifier.

The transfer function of this linear time-invariant system is: In this case, the filter has a passband gain of −R2/R1 and has a cutoff frequency of Because this filter is active, it may have non-unity passband gain.

While impedance matching and loading must be taken into account when chaining passive filters, active filters can be easily chained because the signal is restored by the output of the op amp at each stage.

For simplicity, assume that samples of the input and output are taken at evenly spaced points in time separated by

Making these substitutions: And rearranging terms gives the recurrence relation That is, this discrete-time implementation of a simple continuous-time RC high-pass filter is By definition,

The following pseudocode algorithm will simulate the effect of a high-pass filter on a series of digital samples, assuming equally spaced samples: The loop which calculates each of the

outputs can be refactored into the equivalent: However, the earlier form shows how the parameter α changes the impact of the prior output y[i-1] and current change in input (x[i] - x[i-1]).

They are used as part of an audio crossover to direct high frequencies to a tweeter while attenuating bass signals which could interfere with, or damage, the speaker.

As an example, the formula above, applied to a tweeter with a resistance of 10 Ω, will determine the capacitor value for a cut-off frequency of 5 kHz.

An alternative, which provides good quality sound without inductors (which are prone to parasitic coupling, are expensive, and may have significant internal resistance) is to employ bi-amplification with active RC filters or active digital filters with separate power amplifiers for each loudspeaker.

For example, noises (e.g., footsteps, or motor noises from record players and tape decks) may be removed because they are undesired or may overload the RIAA equalization circuit of the preamp.

One amplifier, the professional audio model DC300 made by Crown International beginning in the 1960s, did not have high-pass filtering at all, and could be used to amplify the DC signal of a common 9-volt battery at the input to supply 18 volts DC in an emergency for mixing console power.

[2] However, that model's basic design has been superseded by newer designs such as the Crown Macro-Tech series developed in the late 1980s which included 10 Hz high-pass filtering on the inputs and switchable 35 Hz high-pass filtering on the outputs.

[3] Another example is the QSC Audio PLX amplifier series which includes an internal 5 Hz high-pass filter which is applied to the inputs whenever the optional 50 and 30 Hz high-pass filters are turned off.

[4] Mixing consoles often include high-pass filtering at each channel strip.

Some models have fixed-slope, fixed-frequency high-pass filters at 80 or 100 Hz that can be engaged; other models have sweepable high-pass filters, filters of fixed slope that can be set within a specified frequency range, such as from 20 to 400 Hz on the Midas Heritage 3000, or 20 to 20,000 Hz on the Yamaha M7CL digital mixing console.

Veteran systems engineer and live sound mixer Bruce Main recommends that high-pass filters be engaged for most mixer input sources, except for those such as kick drum, bass guitar and piano, sources which will have useful low-frequency sounds.

Main writes that DI unit inputs (as opposed to microphone inputs) do not need high-pass filtering as they are not subject to modulation by low-frequency stage wash—low frequency sounds coming from the subwoofers or the public address system and wrapping around to the stage.

Main indicates that high-pass filters are commonly used for directional microphones which have a proximity effect—a low-frequency boost for very close sources.

[5] High-pass and low-pass filters are also used in digital image processing to perform image modifications, enhancements, noise reduction, etc., using designs done in either the spatial domain or the frequency domain.

[6] The unsharp masking, or sharpening, operation used in image editing software is a high-boost filter, a generalization of high-pass.