# Is Spline Interpolation an FIR Filter

Mentor
Hi Guys

This question came up in the new supposed big thing in audio called MQA (Master Quality Authenticated). Here is a technical overview and a link to its patent:
https://www.soundonsound.com/techniques/mqa-time-domain-accuracy-digital-audio-quality
https://patentscope.wipo.int/search...A34392194DDAEFDDC7.wapp2nA?docId=WO2014108677

They talk about explaining it with triangular sampling and linear interpolation in approximating what was lost in the sampling. This of course is an example of a spline of order 1 - pretty trivial really. But it is claimed better results are obtained using higher order splines:
'Even better results are possible using higher-order ‘B-spline’ kernels, which allow both the position and intensity to be identified of two or more separate pulses occurring within the same sampling period!'

The MQA guys are bit coy about exactly what they do, but the conjecture is they do an an analysis of the music, decide from that what order of spline to use in sampling it down to 96k and put the best way to upsample it in metadata encoded in the bit-stream in some way.

The reason is they claim to want to reduce time smear as much as possible ie when fed a Dirac impulse it has the shortest time response.

OK so far. But in the discussion I am having, some guys claim that above order 1 spline reconstruction is not a FIR (Finite Impulse Response) filter. I know polynomial reconstruction is:
https://www.dsprelated.com/freebooks/pasp/Lagrange_Interpolation.html

I know splines are polynomials between points - but not exactly the same as Lagrange interpolation. However since the whole object of this is to keep the time response as short as possible I cant see how it can be anything but FIR.

Does anyone know the answer - is it a FIR filter? If not why so?

The person I was discussing this with posted the following links:
http://bigwww.epfl.ch/publications/unser9301.pdf
http://bigwww.epfl.ch/publications/unser9302.pdf

It seems as the order of the spline increases it approaches a Gaussian filter (an example of the central limit theorem at work?).

Thanks
Bill

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## Answers and Replies

Baluncore
Science Advisor
This of course is an example of a spline of order 1 - pretty trivial really. But it is claimed better results are obtained using higher order splines:
'Even better results are possible using higher-order ‘B-spline’ kernels, which allow both the position and intensity to be identified of two or more separate pulses occurring within the same sampling period!'
I think they are kidding themselves. The higher the order of the spline, the higher the frequency components it will introduce, it is nothing more than a higher order polynomial. The bandwidth is limited by sample rate. There is no information on which to base the hunch that the rate of change is higher near the sample points.

Data compression may benefit from the use of higher order splines. Is that what they think they are doing.

Any order spline can always be FIR. The greater the order of spline, the greater the delay needed to perform the computation in the pipeline.

bhobba
Mentor
I think they are kidding themselves.

So do I and a number of others in the audio area are reaching the same view - but that is a different thread. Audiophiles are a funny lot (they must be because I am one ), so it will be interesting to see what eventuates.

Some are going ga ga over it - some don't like it. I have heard it with their spline up-sampling and just using an apodising filter. MQA sound's a bit thin and too clean to me - I don't mind it personally - but a big advance - not quite - and besides the apodising filter sounds to me just as good.

Just so those reading this know what an apodising filter is, when music hits a linear phase brick-wall filter you use to prevent aliasing components in digital audio you get pre and post ringing. Pre-ringing sounds unnatural - you don't hear bells ring before they are hit. It is conjectured this is why digital audio doesn't sound as good as analogue masters - and having heard those its painfully only too true. Apodising filters have no pre-ringing so supposedly sound better - post ringing occurs all the time in nature so its not a worry. I have heard the effect - its not BS - but I think the MQA guys are overall having themselves on - other ways such as the apodising filter can solve the issue. Still even better is simply not let happen in the first place by making the filter above the maximum musical frequency above which is nothing but noise - but how to do that is a whole different story - there are a number of ideas/ways I can think of - and that's just me.

Anyway I appreciate you confirming its a FIR - I thought it must be.

Thanks
Bill