CrossoverFilterFract32

Overview

General crossover designer

Discussion

This subsystem implements N-way crossover filters of either Linkwitz-Riley or Butterworth design. Internally, the crossovers are constructed out of two other subsystems: a 1in-2out crossover which divides the input into two separate frequency bands and an allpass phase compensation network. The 1in-2out crossover consists of lowpass (first output) and highpass (second output) filters. The lowpass and highpass filters are designed such that the sum of their responses equals an allpass filter with unity gain - and this allpass response equals the response of the allphase phase compensation network. An N-way crossover is constructed by cascading these subsystems.

The subsystem .className is generated using the crossover type, number of outputs, and order. For Linkwitz-Riley crossovers, the .className equals "LRXoverN%dOrder%d" where the first integer is the number of bands and the second integer is the order. Similarly, for Butterworth crossovers, the .className equals "ButterXoverN%dOrder%d" where the first integer is the number of bands and the second integer is the order.

The number of 1in-2out crossovers required to make an N-way crossover equals N-1. The number of allpass phase compensation filters grows as O(NxN), so beware, there may be quite a large number of filters! The table below shows the number of 1in-2out crossovers and the number of allpass filters as a function of N, the number of output channels.

N 1in-2out Allpass

2 1 0

3 2 1

4 3 3

5 4 6

6 5 10

See some of the example below for the topology of the crossover system.

In the Linkwitz-Rily design, the lowpass and highpass splitting filters are always 4th order. The splitting filters are each formed as a cascade of 2 second order Butterworth filters. The allpass compensating filter is 2nd order based on a Butterworth design.

In the Butterworth filter design, the lowpass and highpass filters are each standard Butterworth designs and the order must be odd. The odd order requirement ensures that the sum of the splitting filters is an allpass, and the allpass compensation filter equals the the sum of the splitting filters. The order of the allpass compensation filter matches the order of the splitting filters. Thus, 5th order splitting filters require a 5th order allpass network

Type Definition

-Not Shown-

Variables

Properties

Pins

Input Pins

Name: in

Description: audio input

Data type: fract32

Channel range: Unrestricted

Block size range: Unrestricted

Sample rate range: Unrestricted

Complex support: Real

Output Pins

Name: out1

Description: Audio output

Data type: fract32

Name: out2

Description: Audio output

Data type: fract32

Name: out3

Description: Audio output

Data type: fract32

Scratch Pins

Channel count: 1

Block size: 32

Sample rate: 48000

Channel count: 1

Block size: 32

Sample rate: 48000

Channel count: 1

Block size: 32

Sample rate: 48000

MATLAB Usage

File Name: xover_nway_fract32_subsystem.m

 SYS=xover_nway_fract32_subsystem(NAME, TYPE, N, ORDER)
 Creates a subsystem that implements N-way crossovers of various types.
 The module has a single input pin and N output pins.  Each pin can
 be multichannel.  The subsystem divides the input signal into N
 distinct frequency bands.  The first band extends from DC to
 cutoff(1) Hz; the second band extends from cutoff(1) to cutoff(2) Hz;
 the last band extends from cutoff(N-1) to Nyquist.  Arguments:
   NAME - name of the subsystem
   TYPE - a string specifying what filter is used in the crossover.
          Allowable values are:
              'lr' - Linkwitz Riley design (default).
              'butter' - Butterworth filters.
   N - number of output bands.  This should be in the range 
      2 to 10 (default=3).
   ORDER - order of each of the crossover filters (default = 2).
 The TYPE and ORDER are tied together.  For Linkwitz-Riley designs, the
 ORDER is always 4.  (In fact, the ORDER argument is ignored for this
 type of design).  Each lowpass or highpass filter consists of two
 second order Butterworth files yielding a net order of 4 per stage.
 For Butterworth type crossovers, the ORDER must be odd:  1, 3, 5, etc.
 The function returns a subsystem that implements the crossover.  The
 subsystem's input pin is named '.in' and the outputs are named
 '.out1', '.out2', etc.