# compare of two interpolation method

Started by April 23, 2007
```Hi all,

As I know there are two interpolation method:

1. As many DSP book said, pading (L-1) zero points into space
between two primitive samples, then lowpass filter it. Then we get the
result.

2. linear cubic langerange interpolation.

What is difference between those two method? Which has better
performance?

As my understanding first method always apply to the rational number
upsample (include L or L/M). The second method always apply to nonrational
number upsample. Am I right?

When rational nember upsampling, two method can be used. The
performance of first method depends on the lp filter. If the filter has
perfect frequency response the first method will achieve optimal
performance. Whereas the performance of second method depends on the
numbers of interperlation (8th langerange interpolation achieve better
than 4th langerange interpolation). Am I right?

Is there any quantantive relationship between taps of lp filter and
number of langerange interpolation?

_____________________________________
Do you know a company who employs DSP engineers?
Is it already listed at http://dsprelated.com/employers.php ?
```
```On Apr 23, 2:03 pm, "HouYongmin" <houyong...@hotmail.com> wrote:

>       As I know there are two interpolation method:
>
>         1. As many DSP book said, pading (L-1) zero points into space
> between two primitive samples, then lowpass filter it. Then we get the
> result.
>
>         2. linear cubic langerange interpolation.

well, there are many more than only these two.

>       What is difference between those two method? Which has better
> performance?
>
>       As my understanding first method always apply to the rational number
> upsample (include L or L/M). The second method always apply to nonrational
> number upsample. Am I right?
>
>       When rational nember upsampling, two method can be used. The
> performance of first method depends on the lp filter.

both of these methods have an impulse function and corresponding LPF
of which the performance (usually the stop-band attenuation) can be
compared.

in a sense, Hou, there *are* two fundamental methods of interpolating
(of which there are many variants of each).  the rational number
interpolation is really upsampling by a known _integer_ and then
decimating (downsampling by another integer) by picking out the
samples you want (the samples you do not want are best not calculated
in the first place).  this is polyphase filtering and the sample-rate
conversion (SRC) ratio *is* a rational number and you are restricted
to that (meaning the interpolated times land exactly on the sampling
instances of the intermediate upsampled signal).  however, you can use
opitimization like Parks-McClellan algorithm to design a really good
LPF and pick out the interpolation coefficients from the FIR that
results.  that finite set of FIR coefficients would live in a table
somewhere.

interpolating using Lagrange or Hermite or B-spline or any other
polynomial interpolation is when your new sampling instances can be
*any* value of time; not restricted to integer values of your
upsampled signal.  actually linear interpolation and drop-sample
interpolation are 1st and 0th order polynomial interpolation.  from
knowing the interpolating polynomial, you can determine a continuous-
time impulse response and from that, a frequency response of an LPF to
judge the quality of interpolation.  i can send you a few papers
describing some of this if you want.

now these two methods can be combined: upsample by an integer ratio of
128 or 256 or 512 and then interpolate, using a polynomial, the
adjacent micro-samples.  usually linear interpolation is fine.

r b-j

```
```Method 1 uses sinc function as its core (assuming rectangular window is
used), while method 2 uses cubic Lagrange.

>Hi all,
>
>      As I know there are two interpolation method:
>
>        1. As many DSP book said, pading (L-1) zero points into space
>between two primitive samples, then lowpass filter it. Then we get the
>result.
>
>        2. linear cubic langerange interpolation.
>
>
>      What is difference between those two method? Which has better
>performance?
>
>      As my understanding first method always apply to the rational
number
>upsample (include L or L/M). The second method always apply to
nonrational
>number upsample. Am I right?
>
>      When rational nember upsampling, two method can be used. The
>performance of first method depends on the lp filter. If the filter has
>perfect frequency response the first method will achieve optimal
>performance. Whereas the performance of second method depends on the
>numbers of interperlation (8th langerange interpolation achieve better
>than 4th langerange interpolation). Am I right?
>
>      Is there any quantantive relationship between taps of lp filter
and
>number of langerange interpolation?
>
>
>
>
>
>
>
>
>_____________________________________
>Do you know a company who employs DSP engineers?
>Is it already listed at http://dsprelated.com/employers.php ?
>

_____________________________________
Do you know a company who employs DSP engineers?
Is it already listed at http://dsprelated.com/employers.php ?
```