durwood

Filters / Crossovers are not all Equal

This is under construction so bear with me until I get all my wording correct and try to condense this down into something that makes sense. This is highly mathematical and very difficult to explain in simple terms. I will try to define as much as possible. (for help see definitions below)

What is a crossover? A crossover divides frequencies into sections that different speakers can handle. For example a small speaker like a 1" tweeter cannot reproduce low frequencies that a 12" subwoofer can handle.

Why do I need one?
So you don't get distortion caused by the speaker failing to reproduce frequencies it wasn;t designed to handle. You get higher power handling, less distortion which sets you on a path for better sound.

Digital vs. Analog Crossovers

Analog crossovers are made of 4 electronic components -resistors, capacitors, inductors and opamps. The first three determine the value of the crossover and when used without opamps they are passive. The 4 component is optional- Opamps are used in active crossovers or ones that are powered by an external power source. Analog crossovers have a 90 degree phase shift for every 6db/octave due to the properties of capacitors and inductors.

Passive vs. Active

Digital Crossovers are peformed by mathematics. Depending on how they are designed, they can be modeled by the analog circuits (IIR) or more complex forms such as FIR filters. If they are modeled as analog crossovers in the digital domain, they still suffer from the 90 degree phase shift. It's easier to create filters with steeper cutoff's or higher order i.e. 60 or 72db/octave cutoff slope.

Digital IIR

Digital FIR

Examples

Definitions:

IIR
is a property of signal processing systems. Systems with that property are known as IIR systems or if we are dealing with electronic filter systems IIR filters. They have an impulse response function which is non-zero over an infinite length of time. This is in contrast to finite impulse response filters (FIR) which have fixed-duration impulse responses. The simplest analog IIR filter is an RC filter made up of a single resistor (R) feeding into a node shared with a single capacitor (C). This filter has an exponential impulse response characterized by an RC time constant.

FIR
is a type of a digital filter. It is 'finite' because its response to an impulse ultimately settles to zero. This is in contrast to infinite impulse response filters which have internal feedback and may continue to respond indefinitely.

Phase / Phase shift
Instantaneous phase
the current position in the cycle of something that changes cyclically
Phase shift
a constant difference/offset between two instantaneous phases, particularly when one is a standard reference

Discretization
concerns the process of transferring continuous models and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. In order to be processed on a digital computer another process named quantization is essential.

Quantization
is the process of approximating a continuous range of values (or a very large set of possible discrete values) by a relatively-small set of discrete symbols or integer values. More specifically, a signal can be multi-dimensional and quantization need not be applied to all dimensions. Discrete signals (a common mathematical model) need not be quantized, which can be a point of confusion.

Resistor / Resistance (R)
Resists the flow of current.

Inductor / Inductance (L)
is a measure of the amount of magnetic flux produced for a given electric current.

Capacitor / Capacitance (C)
is a measure of the amount of electric charge stored (or separated) for a given electric potential.

Operational Amplifier / Opamp

Frequency response

Impulse

Butterworth

Linkwitz Riley / LW4

Chebyshev


References

http://en.wikipedia.org/wiki/IIR
http://www.dspguru.com/info/faqs/iirfaq.htm
http://en.wikipedia.org/wiki/Finite_impulse_response
http://www.dspguru.com/info/faqs/firfaq.htm
http://en.wikipedia.org/wiki/Chebyshev_filter
http://en.wikipedia.org/wiki/Bessel_filter
http://en.wikipedia.org/wiki/Butterworth_filter
http://en.wikipedia.org/wiki/Comb_filter
http://en.wikipedia.org/wiki/Elliptic_filter
http://en.wikipedia.org/wiki/Quantiz..._processing%29
http://en.wikipedia.org/wiki/Discretization

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durwood

IIR (infinite impulse response)

• Explanation
Based on analog LRC crossover circuits and then modeled in mathematics using discretization or approximations. Quantization comes into play when using a computer. Since it has feedback controlling it, the response to an impulse goes on indefinitely (rounding errors of the approximations). Instead of using decimal numbers it uses fixed numbers (i.e.-1,2,3 instead of 1.234, 1.9845, 3.1467).

Discretization – using mathematical formulas to create models of an analog circuit

Quantization – rounding decimals to whole numbers for example an analog to digital converter. There exists debate about this between 16 bit and 24 bit audio and the ability to distinguish between quiet/soft passages of music and louder counterparts. The overall loudness of newer music has begun to increase due to portable devices, so the varying levels of sound are not as important as older music was once mastered. This is what is considered the “loudness war”. The dynamics of newer recordings are much less than recordings from years ago.

Phase shift of 90 degrees for every 6db/octave
Chebyshev filter, Butterworth filter, Elliptic filter

• Advantages
Fast and Cheap
Easy to implement due to analog counterparts

• Disadvantages
Poorer bandpass filtering
Stability issues
Phase shift
Rounding errors constantly increase due to feedback or feeding the rounded value back into the system.

• Programs/Software/Hardware using this type
KX project
Foobar DSP
Most car audio crossovers
Frequency Allocator

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durwood

FIR (finite impulse response)

• Explanation
There is no feedback controlling it so when it responds to an impulse (short burst of sound/energy) it eventually settles to zero.

• Advantages
Are inherently stable. This is due to the fact that all the poles are located at the origin and thus are located within the unit circle.
Require no feedback. This means that any rounding errors are not compounded by summed iterations. The same relative error occurs in each calculation.

Can have linear phase
Can have minimum phase

• Disadvantages
-Requires a great deal of resources to make an FIR filter and they have fixed values.
-Pre-ringin can occur in frequencies at 3000Hz and above.

• Programs/Software/Hardware using this type
Not FIR but Frequency Allocator+Frequency Arbitrator maintains correct linear phase
BruteFIR - Better have some programming skills.
AKAI PRO Quad Comp VSTplugin- more of a compressor plugin but might work as crossovers with multiple instances.

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durwood

Examples go here

and here

and here too.

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Abmolech

Great thread.

Problem with phase linear crossovers is "pre-ringing", most of the time this not audiable, however hit 3000 Hz and above and your "asking" for trouble.




http://freerider.dyndns.org/anlage/M...eo-Systems.zip

Time alighment



http://freerider.dyndns.org/anlage/M...-Alignment.zip

durwood

Excellent! I will add this info in about the ringing. I am still gathering information so it will take some time to get this organized. I just thought I would get it started.

Also, something is wrong with your links.

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Abmolech

Passive versus active filters..

Passive is as the name implies, is a filter reacting directly with its source. That is it is effected by driver impedance and reactance. There is a rather large band of people who swear by this as the ultimate solution. For us it is simply the cheapest(normally supplied by the manufacturer) and easiest to setup.
They provide "reasonable" driver protection from pops etc.

Caveats are
1\It requires amplifier power to run it, (up to 6 dB loss over active)
2\ Picks up every bit of inductance and RF going. see http://www.mp3car.com/vbulletin/car-audio/90240-alt-whine-i-dont-think-there-before-amps-off-even.html
as an example.
3\ Individual drivers cannot be time aligned.(OK yes their are passive delay circuits, but in the real world)
4\ lack of flexibility, these are designed for one set of drivers only. Change the driver and the parameters change.
5\ If one driver is shorted or forms an open circuit (wire falls off, coil destructs) it will present a short circuit to the amp ... at the particular LC resonant frequency of the crossover. (Usually 12 or 24 degree slopes)

Active
Require a external power source to operate and are generally before the amplifier. (Inbuilt into some amps are active crossovers)
Advantage is flexibility in driver choice.
Easier on the amp (doesn't have to power the passive crossover) so possibly less distortion depending on the crossover duties. Plus the amp is dedicated to a smaller frequency bandwidth.

caveats
Expense
Knowledge of crossover filters for the drivers.
No protection for drivers for pops etc.

furball69

What OS you runnin on that?

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homebrew sound deadening + sub and amp install... 04 Dakota QC

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durwood

Windows xp pro...not optimized. One of these days I will get around to removing what is not needed using nlite and a re-install. Also using Roadrunner as my frontend

hahaha...its from the old days 1992/1993...just kidding. I don't know what I was thinking. Fixed. thanks for pointing it out.

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durwood

Frequency Allocator uses IIR filtering only, however when teamed with frequency arbitrator the phase is supposed to remain intact and speaker frequency response is unaffected. These two programs are looking very promising! Now back to the software thread.

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