A high-pass filter (HPF) is a type of spectral effect. It is the complement of the low-pass filter. The HPF can be used to reduce the amplitude of low frequencies without changing the amplitude of high frequencies. In other words, the high frequencies pass through the filter and the low frequencies are cut.
One implementation of a HPF is based on a modification to the low-pass filter. Parallel processing is used with 1 sample of delay. For the HPF, a gain of -1 is used on the delayed path. This is equivalent to inverting the polarity of the signal. In other words, it flips the signal or reflects the waveform across the horizontal axis.
When the two paths are combined at the output, low frequencies will be canceled out due to destructive interference. High frequencies will pass through with constructive interference. This is the opposite result of the low-pass filter. Therefore, by having a gain of -1 on the delayed path, which frequencies have constructive versus destructive interference is reversed.
The impulse response of this HPF is: h = [1 -1]. The frequency response of the HPF can be plotted using the command: freqz(h).
Now let’s take a look at how to attenuate frequencies in the mid-range using a notch filter.