Re: Music decompression and resampling

"cr88192" <cr88192@xxxxxxxxxxxxxxxxxx> wrote in message
news:ed8a5$443dabbb$ca83b3d3$22993@xxxxxxxxxxxxx

"Pete Fraser" <pfraser@xxxxxxxxx> wrote in message
news:123r4m9nip4h360@xxxxxxxxxxxxxxxxxxxxx
"cr88192" <cr88192@xxxxxxxxxxxxxxxxxx> wrote in message
news:529e5$443d886c$ca83b3d3$10342@xxxxxxxxxxxxx

also, you are doing upsampling, which is fairly easy to implement and
fairly cheap using linear interpolation.

slightly higher quality might be to use quadratic or cubic
interpolation, but this is more complicated and slower (more samples
need to be taken into account and there is more involved math),
likewise, there is no real guerantee that the guessed curve is much more
accurate than a straight line anyways.

There certainly is.
You know precisely from the interpolation coefficients what the frequency
response will be, and from that you know exactly how much high frequency
droop and aliasing is going to occur.


yeah, but if the goal is being fast, then I wonder if that is enough to
justify the extra math involved.

Perhaps not, but higher order is audibly (and mathematically) better.


my testing with predictors and filtering implied that much beyond a
quadratic curve was not able to produce that good of predictions (and,
that said, quadratic was usually only best with 44kHz 16bit audio, vs the
11kHz 8bit audio I typically work with where often linear and half-line
prediction was best...). cubic curves were not that great, and quartic
curves were usually about useless...

Prediction is trickier. As the order of the predictor goes up, things get
better
for low frequencies, and worse close to Nyquist.

so, just on this, I would guess quadratic interpolation would be best in
general, or is cubic better in this case?... (eg, since we know the
following samples as well).

I think higher order is alway better. It has been 30 years since I dealt
with digital audio, but I can't think of any reason (other than complexity,
group delay, etc, that higher order shouldn't be better.)
Also, it doesn't need to be a polynomial. That's a good way of visualizing
what you're doing, but it just gives you a low-pass filter. Other approaches
will give different coefficients that are equally good (or better) but don't
represent interpolating polynomials.



.

Relevant Pages

  • Re: Music decompression and resampling
    ... Linear interpolation from 44.1 to 48KHz results is really poor ... And I'm not anal-retentive about my sound quality (I use ... g is the prediction (a modified linear prediction, ...
    (comp.compression)
  • Re: Secant method vs Newtons method
    ... It is found that the Secant Method is obtained using zero order NIH and higher order methods with increasingly higher order error terms are obtained by using First or Second Order NIH. ... The simple innovation which I am using in NIH, and which is indicated by the word Normalized, is that I am using for interpolation the two point Hermite Interpolating Polynomial interpolating the function and some of its derivatives on a normalized interval by simply mapping the bracketing interval to the normalized interval each iteration. ... This allows use of the same interpolation formula every step of the iterative search for the root by evaluating the root of the Hermite polynomial interpolating the inverse function and its first or even second derivatives on two points within the normalized interval. ... I have described this on my website www.numerical-algorithms.com under the section "Root Finding Using Inverse Normalized Hermite Interpolation" and present an example where I compute the roots of the Legendre polynomials. ...
    (sci.math.num-analysis)
  • Re: compression knee interpolation
    ... i don't happen to agree that the interpolation doesn't ... compressors if you know what you're listening for... ... difference between the linear law and the compression curve. ... smooth curve; many users of pro-audio gear believe that a smooth curve ...
    (comp.dsp)
  • Re: Secant method vs Newtons method
    ... The natural generalization of the Secant Method to higher order is obtained by using Normalized Inverse Hermite interpolation. ... It is found that the Secant Method is obtained using zero order NIH and higher order methods with increasingly higher order error terms are obtained by using First or Second Order NIH. ... The simple innovation which I am using in NIH, and which is indicated by the word Normalized, is that I am using for interpolation the two point Hermite Interpolating Polynomial interpolating the function and some of its derivatives on a normalized interval by simply mapping the bracketing interval to the normalized interval each iteration. ... This allows use of the same interpolation formula every step of the iterative search for the root by evaluating the root of the Hermite polynomial interpolating the inverse function and its first or even second derivatives on two points within the normalized interval. ...
    (sci.math.num-analysis)
  • Re: Confusion about splitting classes to allow sharing of resources
    ... I have a working Spline ... >> Along with the splines for x and y, the Curve class also has one ... >> Adding new interpolation variables in subclasses of Curve will then ... instantiate the relevant Nodes and add them to the R5 ...
    (comp.object)