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.
The simplest electronic high-pass filter consists of a capacitor in series with the signal path in conjunction with a resistor in parallel with the signal path. The resistance times the capacitance (R×C) is the time constant (τ); it is inversely proportional to the cutoff frequency, at which the output power is half the input (−3 dB):
The effect of a high-pass filter can be simulated on a computer by analyzing its behavior in the time domain, and then discretizing the model.
Taking the time derivative of the second equation, . Combining this with the first equation:
Now we may discretize the equation. Let us represent by a series of samples . We will likewise represent by a series of sample at the same points in time. For simplicity we assume that the samples are taken at evenly-spaced points in time separated by . Making these substitutions:
And rearranging terms:
or more succinctly,
This gives us a way to determine the output samples in terms of the input samples and the preceding output. The following algorithm will simulate the effect of a high-pass filter on a series of digital samples:
// Return RC high-pass filter output samples, given input samples,
// time interval dt, and time constant RC
function highpass(real[0..n] x, real dt, real RC)
var real[0..n] y
var real alpha := RC / (RC + dt)
y := x
for i from 1 to n
y[i] := alpha*(y[i-1] + x[i] - x[i-1])
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 could be realized by using an inductor instead of a capacitor, to simultaneously direct low frequencies to the woofer. See audio crossover. However, inductors are prone to parasitic coupling; hence the RC low-pass filter.
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.
WIPO PUBLISHES PATENT OF HEAR IP FOR "A SIGNAL PROCESSING DEVICE FOR USE IN ELECTROENCEPHALOGRAPHY AND A CABLE SYSTEM INCORPORATING THE DEVICE" (AUSTRALIAN INVENTORS)
Mar 30, 2012; GENEVA, March 28 -- Publication No. WO/2012/034161 was published on March 22. Title of the invention: "A SIGNAL PROCESSING DEVICE...