What Are High-Pass and Low-Pass Filters?

Solution 1:

Here is how you implement a low-pass filter using convolution:

double[] signal = (some 1d signal);
double[] filter = [0.25 0.25 0.25 0.25]; // box-car filter
double[] result = new double[signal.Length + filter.Length + 1];

// Set result to zero:
for (int i=0; i < result.Length; i++) result[i] = 0;

// Do convolution:
for (int i=0; i < signal.Length; i++) 
  for (int j=0; j < filter.Length; j++)
    result[i+j] = result[i+j] + signal[i] * filter[j];

Note that the example is extremely simplified. It does not do range checks and does not handle the edges properly. The filter used (box-car) is a particularly bad lowpass filter, because it will cause a lot of artifacts (ringing). Read up on filter design.

You can also implement the filters in the frequency domain. Here is how you implement a high-pass filter using FFT:

double[] signal = (some 1d signal);
// Do FFT:
double[] real;
double[] imag;
[real, imag] = fft(signal)

// Set the first quarter of the real part to zero to attenuate the low frequencies
for (int i=0; i < real.Length / 4; i++) 
  real[i] = 0;

// Do inverse FFT:
double[] highfrequencysignal = inversefft(real, imag);

Again, this is simplified, but you get the idea. The code does not look as complicated as the math.

Solution 2:

Wikipedia:

• High-pass filter
• Low-pass filter
• Band-pass filter

These "high", "low", and "band" terms refer to frequencies. In high-pass, you try to remove low frequencies. In low-pass, you try to remove high. In band pass, you only allow a continuous frequency range to remain.

Choosing the cut-off frequency depends upon your application. Coding these filters can either be done by simulating RC circuits or by playing around with Fourier transforms of your time-based data. See the wikipedia articles for code examples.

Solution 3:

They are generally Electrical circuits that tend to pass parts of analog signals. High pass tends to transmit more of the high frequency parts and low pass tends to pass more of the low frequency parts.

They can be simulated in software. A walking average can act as a low pass filter for instance and the difference between a walking average and it's input can work as a high pass filter.

Solution 4:

High-pass filter lets high-frequency (detailed/local information) pass.
Low-pass filter lets low-frequency (coarse/rough/global information) pass.