sub specie aeternitatis

Audio Filter Intro

April 18, 2004

In an attempt to educate myself on all things electroacoustic, I have been scrounging around for various sources of knowledge and studying them. Since the internet is full of curious people who happen upon little known places randomly, I thought I might reciprocate some of this knowledge. Please understand I am NOT an expert on this subject matter and that there very well may be mistakes that I am not aware of. But if you are curious about audio filters, then read on…

Technically speaking, an audio filter can be any operation performed on a given signal. Most applications don’t have such a wide range of use, but only deal with the boosting or attenuating of a specific spectrum of an audio signal. In other words, if a signal covers a large spectrum of sound (say from 20Hz to 20KHz), it can be put through a filter and a certain region(s) of its sound spectrum can be altered. Different filters will affect different regions in different ways.

An easy way to distinguish different types of filters is to look at the filter’s amplitude-versus-frequency response curve. If you have dealt with audio equipment you may be familiar with the term “frequency response”, which is simply a shorter way of saying it. A frequency response graph visually shows how much attenuation or boosting happens on a specific frequency. An ideal frequency response curve would be a straight line across all frequencies, meaning no changes in amplitude occur at any frequency. Of course, it is impossible to get a completely flat frequency response in real life, although high end audio systems can come close to hitting that mark.

An almost flat response curve for a high end audio system. It does not represent a real life audio system (I drew it in mspaint, so gimmie a break, ok?), but in this theoretical system, some lower frequencies would be boosted, while other higher frequencies are attenuated. In this sense, this imaginary audio equipment acts as a kind of small filter, which is why high end equipment would try to get as close to flat as possible so as not to negatively affect the sound.

An audio filter introduces extreme changes in frequency response in order to change the quality of the sound. Below are four pictures of basic types of filters: lowpass, highpass, bandpass, and bandreject.

Notice how each type of filter drastically changes the amplitude of certain frequencies to achieve the desired affect. Low and highpass filters allow either low or high frequencies through while cutting the opposite end. Bandpass and reject filters attenutate or boost a small portion of the sound spectrum, but leave the rest of the spectrum cut out of the sound.

All four of these filters have certain properties that help further define them. One important property is its cutoff frequency. Curtis Roads in his book, The Computer Music Tutorial, says that the cutoff frequency,

by convention, is the point in the frequency range at which the filter reduces the signal to 0.707 of its maximum value. Why 0.707? The power of the signal at the cutoff frequency is proportional to the amplitude of the signal squared, since 0.7072 = 0.5. Thus, the cutoff frequency is also called the half-power point. Yet another term for the cutoff frequency is the 3 dB point. This is because 0.707 relative to 1.0 is close to – 3dB.

Okay, so that’s a mouthful. I think you could say that the cutoff point is the point at which the filter starts working to do its stuff. In the ideal world, a filter would be a sort of a brick wall. You would set the desired cutoff frequency and anything beyond that frequency would either be cut (attenuated) or boosted. In reality, the point leading up to the cutoff frequency is not linear, but slopes down gradually. This is called the transition band. Those frequencies which are above the cutoff frequency (half-power point) are said to be in the passband of the filter, while frequencies below that point are in the stopband of the filter. In a bandpass or reject filter, the difference between the higher and lower cutoff frequencies is called the bandwidth of the filter.

The degree of slope or steepness in the transition band is defined in terms of decibels of attenuation or boost per octave, or “dB/octave”. (A new octave occurs anytime you double or half the frequency. In the musical scale, it is going from one note to the same note higher up in the scale. Think going from a c to a c on a piano) A filter with an 8dB/octave slope would have a nice gradual transition band, while a filter with a 75dB/octave slope would be quite sharp cutoff.

There are many, many types/uses of filters. This is really just a basic introduction to audio filters meant more for the sake of review for myself than as a true tutorial. If you want to start learning about filters, a really good idea is to jump in and get your hands wet. Playing with free software like Audacity is a great way to learn firsthand what a filter can do to sound. Other professional programs like Soundforge or Audition offer demo versions which are useful for experimentation. Or possibly one of the best ways to learn is to find someone who knows about audio technology and grill them about it. I would take an experienced teacher over a book any day.