posted 13 May 2003 10:06            

phasecomp-retardbass.kym

This set of filters provides crisper highs without killing the mid-bass response. If anything, you should notice a bass extended response. But the effect doesn't hit you in the face. It is subtle, as it probably ought to be.

The trick here is realizing that a low-shelving filter in boost mode produces a phase retardation of the bass. But you don't want huge boost, so to compensate, I had my computer derive an empirical fit to a 2-pole sort-of-allpass response that lifted the highs, but more importantly, it produced a phase retardation of the bass by a small amount. Hence the all-pass enhances the effect, instead of fighting it.

The phase compensating all-pass has real zeros at around 1.03 and -49, and a pair of complex conjugate poles at around 0.23+/-0.23i. This filter alone produces about 800 usec of phase retardation in the bass (not much). But it really kills off the bass response -- about 30 dB or so. So this is perfect for a major bass phase retarding low-shelf filter whose parameters are: boost = 35 dB (!!), Fc = 400 Hz, Q = 0.313, all at 44.1 KHz sample rate.

The result exhibits a bathtub EQ curve with about 3.5 ms of phase retardation in the bass region below 100 Hz. and rapidly declining to around 0 above 1 KHz.

It really does enhance the highs and extend the bass response a little bit, but like I said, the effect is not "obvious". Given that my headphone measurements showed the phase of the bass already retarded coming out of the headphones, I have to wonder if the phase retardation has any real effect. Perhaps it is the subtle bathtub EQ that contributes most to the enhancement?

Enjoy!

- DM

[PS: Since the low-shelving filter produces so much boost (35 dB!) it is very important to process the signal first through the phase bender followed by the low-shelf boost filter. Going the other way around will lead to massive clipping distortion unless you severely attenuate the input signal. But then you'd need compensating gain on the output side, and meanwhile you've thrown away at least 5-6 bits of signal to noise ratio. ]

[umm... sorry, I keep saying "phase delay". What I really meant to say was "group delay". That delay of 3.5 ms near 20 Hz is real physical delay.]