XOVER Linkwitz-Riley

[steph_tsf]

This is a typical application of the 4-channel FFT-based Audio Analyzer and IIR BiQuad filters. See the attached .fsm

ch1 : reference channel (no need to graph it)
ch2 : lowpass signal
ch3 : highpass signal
ch4 : reconstruction (lowpass + higpass)

reference : ch1
impulse response graph : ch4 (we can also graph ch2 or ch3 impulse response)

For implementing a crossover operating at 2 kHz, we need to configure the LR Xover :
2000 Hz
2nd-order (actually each speaker is going to be filtered 4th-order, as there are two Butterworth cells in series)

The resulting graph illustrates the LR Xover behaviour and properties.
The Lowpass slope in the transition band looks adequate.
The -6 dB point of the Lowpass is 2 kHz.
The Highpass slope looks adequate.
The -6 dB point of the Highpass is 2 kHz.

The Lowpass phase is a typical double Butterworth one, far from linear.
The Highpass phase looks essentially the same as the Lowpass. This guarantees that the speaker drivers operate in-phase from DC to 20 kHz. The multiway loudspeaker wont "beam" particular frequencies at particular angles. The radiation pattern stays homogeneous.

The Lowpass + Highpass sum delivers a signal exhibiting a distorted phase inherited from the twin Butterworth. The magnitude is flat from DC to 22 kHz. Such Xover produces a severe phase distortion. A pulse signal won't show as a pulse signal after the crossover. A pulse signal will appear as a burst extending over time. This is the green curve obtained from channel 4 setup as the Lowpass + Highpass sum. Such phase distortion is a serious disadvantage compared a Lipshitz-Vanderkooy Xover relying on a Bessel Lowpass inside.

The Lipshitz-Vanderkooy Xover is illustrated here http://www.dsprobotics.com/support/viewtopic.php?f=3&t=1505

Cheers,
Steph

[jjs]

Great, thanks !