Three band crossover filter (part 1)

What are crossover filters?

Due to mechanical / physical constraints it is near impossible for a single speaker cone to accurately reproduce the full audio range. Carefully designed small speakers may work adequately for low power use such as portable radios, but for larger, higher power and higher sound quality speakers, multiple “driver” units are invariably used. Typically for domestic “hi-fi” systems,  small “tweeters” reproduce the high frequencies, while much larger “woofers” handle the high power and air shifting requirements of low frequencies. These days it is increasingly common to also have a “sub” (sub-bass) speaker to produce the lowest frequencies.

“Crossover” filters are used in loudspeakers so that each speaker driver receives audio frequencies appropriate to its capabilities.  Splitting the audio frequencies into multiple frequency bands has benefits of increasing the power handling of the speaker system, improving efficiency, and improving the overall sound quality. For low to medium power systems, passive filters built into the loudspeaker enclosure provides an inexpensive and effective means of splitting the audio frequencies into two or three bands (low and high, or low, mid and high). However, passive crossovers have their limitations, and for larger, more powerful or higher quality systems, active electronic circuits may be employed to split the audio signal and feed separate amplifiers to power the speaker drive units.

Crossover filters may also be used in music production to allow different effects to be applied according to the frequency range. This technique is commonly used in conjunction with dynamic compression effects but could be used creatively with other types of effects.

Design considerations:

For an “ideal” three way crossover filter, we would want to split the audio into three frequency bands (low, mid and high frequencies) in such a way that the three audio bands may be recombined to recreate the original full range audio signal.

A simple approach.

The simplest way in Audacity to split an audio track into three frequency ranges is:

  1. Duplicate the track twice (Ctrl+D) so that there are three identical tracks.
  2. Apply the Low Pass filter  to one track to create the “low” (bass) track.
  3. Apply the High Pass filter to another track to create the “high” (treble) track.
  4. Apply the Low Pass filter, and then the High Pass filter (or the other way round – the order is unimportant) to create the mid-range track.

While this manual method will work, it has some limitations and is rather fiddly to perform.

Making the task easier.

Rather than using two separate effects and apply each of them twice, we can simplify the task by creating a single Nyquist script to handle each of the filter steps. If we know in advance what frequencies we want to split at, then the task becomes simpler still.

The basic filters.

Nyquist has several convenient filters built in. There are a series of high pass filters, and a series of low pass filters.

The high pass filters:

The example code lines above may be used in the Nyquist Prompt effect. The keyword *track* means “the selected audio”.

The low pass filters:

The “order” of the filter refers to the steepness of the filter cut-off.

For a 1st order filter, the cut-off slope is 6dB per octave. That means that for a high pass filter with a corner frequency of 1000 Hz, one octave below 1000 Hz (500 Hz), the audio will be reduce by 6dB (half its original amplitude, and two octaves below (250 Hz) the audio is reduce by a further 6dB (-12 dB = 1/4 of its original amplitude), and so on.

For a 2nd order filter, the cut-off is twice as steep as a 1st order filter; that is, frequencies are rolled off by 12 dB per octave. For 4th order filters the slope is even steeper -24 dB per octave, and for 8th order the steepness is a massive 48 dB per octave. An absolute “dead cutoff” is never possible, though with advanced filtering techniques it is possible to produce even steeper cut-off slopes, but that’s another discussion.

To be continued…

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