Distortions phase and temporal effects audio systems

Transcription

1 Distortions phase and temporal effects audio systems Samuel Harsch 114th AES Swiss section meeting

2 Phase & group delay H (f) is the transfer function of an audio system Phase ph (f) = arg (H (f)) * 180 / ft Group delay TGR (f) = - (1/360) * ( d ph (f) / d f) The best way to observe and test the effects of phase distortion is to use an all-pass filter. An all-pass filter has a constant amplitude, but produces only a phase rotation: - A 1st order filter produces no phase rotation. - An all-pass filter of the first order producing a 180 phase shift as a filter of 2nd order. - An all-pass filter of the second order produces a 360 phase shift as a filter of the 4th order.

3 Phase & group delay All-pass 2nd order 1kHz Q = nd order all-pass 1kHz Q = 7

4 Phase & group delay All-pass 2nd order 1kHz Q = nd order all-pass 1kHz Q = 7

5 Audibility of phase distortion Seems more audible at low frequencies The time effect is more pronounced with a high quality factor The perception is very individual Ref: On the Perception of Phase Distortion Hideo Suzuki Shigeru Morita, and Takeo Shindo JAES September 1980 Vol 28, Nr 9

6 Sources of phase distortion pregnant the low cutoff Filtered Resonances (modes) of the workpiece

7 pregnant the low cutoff The effect is more pronounced with the boxes using a resonator (bass reflex, transmission line etc...) Cleavage at low frequency is similar to a filter of second order for a closed box and 3rd order for a vented enclosure.

8 Speaker Peerless in XXLS10 different types of caissons Bass reflex Quasi Butterworth (42l; 28Hz) Bass reflex extended low (100l; 25Hz) Close box (60l; 39Hz QTc 0.53) Amplitude (db)

9 Speaker Peerless in XXLS10 different types of caissons Bass reflex Quasi Butterworth (42l; 28Hz) Bass reflex extended low (100l; 25Hz) Close box (60l; 39Hz) group delay (ms)

10 Phase & group delay Simulation of this effect using an all-pass filter of the second order 30Hz Q = 1.5

11 Phase & group delay All-pass 2nd order 30Hz Q = 1.5 applied to a recording of a bass drum kick original after his His treatment

12 Stage & Group Delay All-pass second order 50Hz Q = 1.5 applied to a burst of 100ms 50Hz 500Hz + original after his His treatment

13 Linkwitz Transform and equalization similar to a sealed enclosure Equalizer Result Response original frequency Here, the equalizer is a second order low-shlef

14 Linkwitz Transform and equalization similar to a sealed enclosure Result Response original stage Equalizer

15 Speaker Peerless in XXLS10 different types of caissons Bass reflex Quasi Butterworth (42l; 28Hz) Bass reflex extended low (100l; 25Hz) Close + box Linkwitz transform Amplitude (db)

16 Speaker Peerless in XXLS10 different types of caissons Bass reflex Quasi Butterworth (42l; 28Hz) Bass reflex extended low (100l; 25Hz) Close + box Linkwitz transform group delay (ms)

17 Speaker Peerless in XXLS10 different types of caissons Bass reflex Quasi Butterworth (42l; 28Hz) Bass reflex extended low (100l; 25Hz) Close + box Linkwitz transform Deflection of the membrane

18 filter Phase Distortion Example with Linkwitz-Riley filter 2 th order Polarity reversal

19 filter Phase Distortion Example with Linkwitz-Riley filter 2 th Example with Linkwitz-Riley filter 2 th order

20 filter Phase Distortion Example with Linkwitz-Riley filter 4 th order No polarity reversal

21 filter Phase Distortion Example with Linkwitz-Riley filter 4 th Example with Linkwitz-Riley filter 4 th order

22 filter Phase Distortion Linearization of the phase using the method S.Harsch: 1. Select fc where the speaker phase is linear 2. Low Pass Butterworth 4 th order calculated for fc 3. High Pass: Bessel 2 th order calculated for fc 4. Create a constant delay to the high-pass section calculated by t = (1 / fc) * No polarity reversal Fc = 1 khz for example: Butterworth Low Pass = 4 th Passing 1kHz order Bessel high = 2 th 1kHz order Behind the high-pass section = (1/1000) * 0.5 = 0.5ms

23 filter Phase Distortion Linearization of the phase using the method S.Harsch:

24 filter Phase Distortion Linearization of the phase using the method S.Harsch:

25 filter Phase Distortion Linearization of the phase using the method S.Harsch Comparison with Linkwitz-Riley filters 2 th and 4 th order Method S.Harsch Linkwitz-Riley 2 nd Linkwitz-Riley 4 th

26 filter Phase Distortion Linearization of the phase using the method S.Harsch Comparison with Linkwitz-Riley filters 2 th and 4 th order Linkwitz-Riley 4 th Linkwitz-Riley 2 nd Method S.Harsch

27 filter Phase Distortion Linearization of the phase using the method S.Harsch: Advantages: - Usable with any digital filter having the ability to configure Bessel and Butterworth filters and add a constant delay - Usable on existing IIR systems with a simple parameterization - Used with passive filters or active analog filters if the delay can be implemented by a physical offset of the speakers. - Uses few DSP - Low latency disadvantages: - Not a true linear phase filter - The polar diagram may include hollow around the cutoff frequency depending on the angle

28 Results Example: 2-way box with equalization of low frequency filter method S.Harsch 400Hz

29 Using this method The use is free If someone wants to use a commercial product, I would be happy to put it as a reference on my website. For those interested in the audibility of phase distortion, I made a plug-in for Audacity with which we can introduce all pass to an audio file