@GrantBrown said:

Thanks @wforwumbo for your work on this. Acoustics is a hobby of mine also. I'd like to mention that after years of tinkering with playback equipment and setups, using a minimum-phase response resampler has made the biggest difference in terms of warmth and authenticity. Any thoughts from you (and others) about this topic? By the way, for anyone interested, Foobar 's SOX resampler has a minimum phase setting, which is what I use. Thanks.

Yes I can talk about resampling quite a bit, given my bread-and-butter is audio DSP.

Before digging into that, a brief note - there are two types of approaches to designing digital filters and layouts: finite impulse response (FIR) and infinite impulse response (IIR). FIR when designed right gives you a linear phase distortion, with the downside being that by nature of its design it requires additional computation power and induces an inherent lag into your signal path (which is fine for post or offline work, but for things like live mixing or trying to actively change parameters on the fly during tracking/mixing can prove problematic). IIR filters are immediate in their response, however it is impossible to generate a truly linear phase response with them; so we instead design systems that mitigate the phase distortion - so-called “minimum phase systems”.

Why do we care about this? Let’s analyze what I mean by “distorting the phase” first. Going back to basic waves, envision a sine wave for a moment. Clean, starts with value 0 at time t=0 and completing its cycle in some period T, extending (for all intents and purposes, for analysis at the periodic cycle from 0->T) infinitely long in either direction. If we have a system that allows it through with no attenuation or gain, but shift its phase in either direction and then add it back to the initial sine wave, we get destructive interference. Which is all fine and dandy if you have just a single tone you are analyzing because you can compensate for that delay, but in IIR systems the phase distorts in a non-linear fashion across different frequencies, making it impossible to correctly compensate across the board. This is what we call “phase distortion” and can affect things such as stereo imaging and will additionally produce a comb filter effect in the frequency magnitude.

For filters in particular, we additionally analyze something called “group delay,” which is computed by taking the negative derivative of the phase of the system. From this we can analyze how the filter will respond to different tones in the steady state (long, sustained vowel tones). Accordingly, we can also compute an approximation of an idealized de-warping filter to compensate for phase distortion, however those de-warping filters will induce inherent lag and will never truly de-warp the phase fully. Likewise, for impulsive sounds (drums, or the pluck of a guitar string, for example), all transients get smeared non-linearly by this system and the attack sounds both softened by the spread-out and decorrelated phase; it’s possible to try and fix this but I’ve yet to hear any minimum phase algorithm that gets anywhere close.

Resampling as a practice isn’t usually something I recommend. Depending on the conversion process and calculations used (for audio, sigma-delta is usually the best), there is always an inherent Gaussian error induced in the signal. Basically, you are trying to approximate information that wasn’t there to begin with, and it’s very rarely going to be 100% accurate for real signals that aren’t pure sines or 100% linear functions (which, I’d note, sines and cosines are not linear). So then why do it? Well there are actually sometimes benefits to doing so. For one thing, output converters are usually for cost reasons designed to be optimized at a very specific sampling frequency. They have reduced “jitter” (basically, how far they deviate from being on time - which if not true can induce further phase distortion) at these specific sample rates. For another, digital filters will be more accurate in their computations when the sample rate is higher. This can produce a perceived “better sound”.

At the end of the day there’s no right answer. Trust your ears and do what you think sounds best when listening.