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Three questions:

  1. What are all the metrics one can use to measure audio interpolation quality, objectively? (but also in terms of psychoacoustics if possible)

  2. By those metrics, what is the current state of the art in audio interpolation?

  3. Suppose I were to render two files from a sequence of notes from virtual instruments in two resolutions and then compare an upsampling of one file with the high-frequency rendered version, what software could one use to compare these objectively? - ideally using the before-mentioned metrics

So far, from I've been able to gather, these resamplers provide some of the best quality

  1. http://www.mega-nerd.com/SRC/
  2. http://sox.sourceforge.net/SoX/
  3. http://www.izotope.com/tech/src/

One of the problems that these resamplers seem to have is pre- and post ringing.

I should note that of key interest is signal reconstruction (insofar as that term makes sense), so upsampling more than downsampling.

Edit: Interpolation time efficiency is irrelevant in this context.

Best regards, The curious :-)

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Regarding the "problem" you note with resamplers:

Many resampling algorithms use a linear-phase low-pass filter poly-phase interpolation kernel. A minimum-phase filter interpolation kernel, as opposed to linear-phase interpolation kernel (with the same frequency response), would produce less pre-ringing during resampling to a higher sample rate, which may objectively measure as less accurate, but possibly psycho-acoustically sound "better" to humans.

Here's a note on creating minimum phase filters for filtering with potentially less pre-ringing: http://www.music.columbia.edu/pipermail/music-dsp/2004-February/059372.html

Also, a Remez (Parks-McClellan) designed low-pass filter may have a clear periodic ripple in the frequency domain, which might also produce a pre-ring impulse in the time-domain. So you might want to instead try a windowed Sinc, or a derivation of a classic analog filter, for the low-pass filter design (the latter usually resulting in something closer to minimum phase) for the resampling interpolation kernel.

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  • $\begingroup$ Regarding your point about minimum phase filters: I'm not sure about the first two links, but iZotope's SRC allows for continuously variable phase between minimum and linear. In listening tests, people do tend to like somewhere in-between minimum phase and linear phase. $\endgroup$
    – schnarf
    Jan 31, 2012 at 3:04
  • $\begingroup$ A windowed-sinc filter wouldn't necessarily be any better than an equiripple (designed via Remez exchange) filter with respect to time-domain ringing. The ringing effect is called the Gibbs phenomenon and is observed when you bandlimit a signal that contains discontinuities (e.g. a square wave). It is not caused by the frequency-domain ripple of an equiripple filter. The effect is more noticeable when you use filters with very sharp cutoff; increasing the transition width can mitigate it somewhat. $\endgroup$
    – Jason R
    Jan 31, 2012 at 12:48
  • $\begingroup$ @Jason R : sinusoid in time domain = impulse in the frequency domain, position depending on ripple rate of the sinusoid. Now reverse the 2 domains and put a sinusoidal-like ripple in a frequency domain response. The impulse goes into the time domain, position depending on ripple characteristics. $\endgroup$
    – hotpaw2
    Jan 31, 2012 at 13:18
  • $\begingroup$ @hotpaw2: I see your analogy. I misunderstood the intent of your term "pre-ring impulse." $\endgroup$
    – Jason R
    Jan 31, 2012 at 13:24
  • $\begingroup$ Also, a smooth window in the time domain reproduces its non-discontinuous shape around discontinuities in the frequency domain by convolution, thus reducing Gibbs overshoot. $\endgroup$
    – hotpaw2
    Jan 31, 2012 at 13:32
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There is this pretty thorough comparison of resampling algorithms: http://src.infinitewave.ca/

You can see the tests they used there. Aliasing is a big one, and is easy to visualize with a spectrogram of a sine sweep. There's also high frequency response -- SRC can roll off high frequencies in addition to allowing them to cause aliasing. You can visualize phase response with the impulse response graph, or with a plot of the phase response.

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  • $\begingroup$ Yes, I know this excellent resource. I just wanted to know all the parameters that are worth measuring when measuring resampling (in particular upsampling) performance. $\endgroup$
    – Bent Rasmussen
    Jan 31, 2012 at 20:24

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