On 8/18/15 11:46 PM, Ethan Duni wrote:
> for linear interpolation, if you are a delayed by 3.5 samples and you
keep that delay constant, the transfer function is
>
> H(z) = (1/2)*(1 + z^-1)*z^-3
>
>that filter goes to -inf dB as omega gets closer to pi.
Note that this holds for symmetric fractional delay filter of any odd
order (i.e., Lagrange interpolation filter, windowed sinc, etc). It's
not an artifact of the simple linear approach,
at precisely Nyquist, you're right. as you approach Nyquist, linear
interpolation is worser than cubic Hermite but better than cubic
B-spline (better in terms of less roll-off, worser in terms of killing
images).
it's a feature of the symmetric, finite nature of the fractional
interpolator. Since there are good reasons for the symmetry
constraint, we are left to trade off oversampling and filter
order/design to get the final passband as flat as we need.
My view is that if you are serious about maintaining fidelity across
the full bandwidth, you need to oversample by at least 2x.
i would say way more than 2x if you're using linear in between. if
memory is cheap, i might oversample by perhaps as much as 512x and then
use linear to get in between the subsamples (this will get you 120 dB S/N).
That way you can fit the transition band of your interpolation filter
above the signal band. In applications where you are less concerned
about full bandwidth fidelity, oversampling isn't required. Some argue
that 48kHz sample rate is already effectively oversampled for lots of
natural recordings, for example. If it's already at 96kHz or higher I
would not bother oversampling further.
i might **if** i want to resample by an arbitrary ratio and i am doing
linear interpolation between the new over-sampled samples.
remember, when we oversample for the purpose of resampling, if the
prototype LPF is FIR (you know, the polyphase thingie), then you need
not calculate all of the new over-sampled samples. only the two you
need to linear interpolate between. so oversampling by a large factor
only costs more in terms of memory for the coefficient storage. not in
computational effort.
Also this is recommended reading for this thread:
https://ccrma.stanford.edu/~jos/Interpolation/
<https://ccrma.stanford.edu/%7Ejos/Interpolation/>
quite familiar with it.
--
r b-j r...@audioimagination.com
"Imagination is more important than knowledge."
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