Filter Slope
Canonical Definition
Filter slope describes how rapidly a filter attenuates signal outside its passband, commonly stated in decibels per octave or decade. The stated asymptotic rate does not by itself define the local corner shape or final acoustic slope.
Order And Asymptotic Rate
| Filter order | Common asymptotic rate | Basic implication |
|---|---|---|
| 1st order | 6 dB/octave | Wide overlap and limited out-of-band protection |
| 2nd order | 12 dB/octave | More separation and phase rotation |
| 3rd order | 18 dB/octave | Stronger attenuation with alignment-specific behavior |
| 4th order | 24 dB/octave | Common active-crossover starting point with tighter overlap |
These rates describe the far-out attenuation trend of an ideal electrical filter. The exact response near the corner depends on the alignment, Q values, and implementation.
Four Numbers People Mix Together
| Property | What it tells you |
|---|---|
| Order | Number of poles and the eventual attenuation rate |
| Alignment | How pole Q values are arranged, such as Butterworth, Bessel, or Linkwitz-Riley |
| Corner frequency | The filter's defined reference frequency; its attenuation there depends on the filter type |
| Acoustic slope | The measured installed response after driver, mounting, enclosure, EQ, and electrical filter combine |
The Corner Is Not Always -3 dB
A single Butterworth low-pass or high-pass section is commonly -3 dB at its cutoff. A Linkwitz-Riley crossover path is commonly -6 dB at the transition frequency. Other alignments and filter types use different corner behavior.
Therefore, do not infer the alignment from the dB-per-octave rate alone, and do not assume every software “frequency” field means the same measured point.
Electrical Slope Times Driver Response
Acoustic transfer ≈ electrical filter × driver / enclosure / mounting responseIf a tweeter is already rolling off acoustically near the selected high-pass region, adding a steep electrical filter can produce an acoustic slope much steeper than the DSP label. If a driver has breakup or a broad response rise, the same electrical filter may not produce a clean target at all.
The correction is not automatically “move the frequency higher.” Measure the installed driver and choose the filter that creates the intended acoustic result while preserving safe operation.
Steeper Is A Tradeoff, Not A Ranking
| Potential benefit | Potential cost or requirement |
|---|---|
| Faster out-of-band attenuation | More phase rotation and tighter need for acoustic alignment |
| Reduced driver excursion outside the passband | More abrupt handoff and possible directivity discontinuity |
| Less overlap with breakup or distortion | Greater sensitivity to frequency, delay, and acoustic-center errors |
| Cleaner channel separation | Possible group-delay concentration near the transition |
How To Measure A Slope
- Measure the driver alone with the intended filter active.
- Use a graph span wide enough to see the response trend over one or more octaves.
- Record the electrical filter type, order, alignment, frequency, Q, sample rate, and platform.
- Compare the measured acoustic attenuation with the intended target.
- Check phase, group delay, distortion, and excursion before deciding that the slope is acceptable.
Being 12 dB down at one frequency does not prove a 12 dB-per-octave response. The rate is derived from change across frequency.