Technical analysis of the Meridian Apodizing filter

Following the unsatisfactory experience with the apodizing filter I decided to try to create my own filter that would have the advantages of the apodizing filter without the disadvantages. The first step was to analyze the old linear and new apodizing filters.

I started out looking for software that can analyze filters, but did not find anything besides the software that Ayre also uses (QEDesign2000). That seems to be able to load filter coefficients, but the file format is not documented (there are no docs at all) and the company did not respond to my question about it. So I decided to write something myself that can both analyze and generate filters.

Let’s first take a look at the impulse response of the filters, as John Atkinson also did in his review of the 808.2.

Linear Impulse Response Apodizing Impulse Response

The difference is pretty clear: the new filter does not have a pre-echo, but has a much bigger post-echo. This is supposed to be one of the main advantages. Pre-echos are not natural (there is nothing that ‘announces’ a sound), post-echos are natural (reverberation). The bigger post-echo should be no problem because the cycles are lower than the impulse and the masking effect of the ear will hide them.

Now let’s take a look at the amplitude and phase response of the filters:
(Amplitude scale from -144dB to +144dB. Phase scale is normalized per frequency from -0.5 to +0.5 cycle)

Linear Amplitude and Phase Response

Apodizing Amplitude and Phase Response

Meridian is using the term ‘apodizing’ to indicate the removal of the pre-echo (which resides at the nyquist frequency of 22.05kHz) and side-effects caused by brick-wall filters from the original recording. Apodizing itself means a gradual falloff, and is the way the above is accomplished: we see that the amplitude gradually decreases to -100dB from 20kHz to 22kHz. But now comes the interesting part: also the old linear filters has this apodizing falloff! Apodizing is thus not the discriminating feature of the new filter!

The difference between the old and new filters is clearly not in the amplitude response, but in the phase behavior: the old filter is linear to 22kHz, but the new filter has a gradually increasing phase shift that increases with the frequency. This is caused by the minimal phase behavior of the filter. Although the resolution of the picture is not high enough to see, the phase shift starts already from the lowest frequency and increases more as the frequency goes up (logarithmic).

So the absence of the pre-echo comes at the cost of an increasing phase shift across the entire frequency range. People may argue that the shift is only small, and this may be good enough for normal audio applications, but for high-end it seems a serious issue. For one the human brain uses phase information of frequencies up to 3kHz for spacial localization. The inner ear itself has an amplification around 3kHz, which makes the ear most sensitive in the 2 to 5 kHz range (for human speech). And the most important one, instruments and voices are not just limited to a single frequency, they operate on a range. For instance drums even operate on the entire range from low to high. Every frequency component of the sound will get a different shift in time with this filter, it is like smearing the sound over the frequency range, with lows first and highs last. This might also explain why the lows are more pronounced.

On the HitchHikers forum it is mentioned countless times that there is (must be?) a special sauce in the Meridian filter. However, from this analysis there is no indication that this is the case. The old linear filter is just an equiripple lowpass filter, and the new apodizing filter is a minimal phase version of this linear filter. With a bit of Googling you can find a mathlab script to convert a linear filter into a minimal phase filter.

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