[openbeos] Resampling algorithms for audio mixer
- From: "Stefano D'Angelo" <zanga.mail@xxxxxxxxx>
- To: openbeos@xxxxxxxxxxxxx
- Date: Sun, 25 Nov 2007 15:37:27 +0100
Hi guys,
I promised it a lot of time ago, but finally I had some time in the
last two days to check these resampling algorithms I wrote and do some
measurements.
I haven't adapted them to the Resampler API because I still haven't
managed to get some sound out of Haiku, so I hope someone else will
test them and do the necessary adjustments (as said, I haven't got
much time).
Then some optimizations are possible, like preventing calculations on
denormals (Intel P4) or check whether the # of output samples is a
multiple of the # of input samples (or viceversa), etc., but however
these are a good starting point, I guess.
The first one is a linear interpolator: it's incredibly fast and I get
circa 72-74 dB SNR.
The second one is a cubic spline interpolator (4 points at a time)
wihch is still fast and the quality is very good too: around 90-92 dB
SNR.
The third one is meant to be based on the Shannon interpolation
formula (sinc-based interpolation) which theoretically should give
even better results, but I think I've done something wrong and still
haven't got a clue of what isn't working. I put it here in case
someone knows how to fix it.
Here's the code, MIT licensed:
---
Copyright (c) 2007 Stefano D'Angelo
Permission is hereby granted, free of charge, to any person
obtaining a copy of this software and associated documentation
files (the "Software"), to deal in the Software without
restriction, including without limitation the rights to use,
copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following
conditions:
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.
#include <math.h>
#define PI 3.14159265358979323846264338327950288419716939937510
void
linear(float in_buf[], int n_in_samples, float out_buf[], int n_out_samples)
{
/* Position relative to the input buffer */
float x = (float) n_in_samples / (float) n_out_samples;
int i = x; /* Input buffer index */
int j = 1; /* Output buffer index */
/* The first sample is always the same. */
out_buf[0] = in_buf[0];
/* Interpolation cycle. */
while (i < (n_in_samples - 1))
{
out_buf[j] = in_buf[i] + (in_buf[i + 1] - in_buf[i])
* (x - (float) i);
j++;
/* Calculating the position each time gives much better results
* than adding a fixed 'step' value. */
x = j * (float) n_in_samples / (float) n_out_samples;
i = x;
}
/* Using the last slope for output samples beyond the last input
* sample. */
while (j < n_out_samples)
{
out_buf[j] = in_buf[n_in_samples - 1]
+ (in_buf[n_in_samples - 1]
- in_buf[n_in_samples - 2]) * (x - (float) i);
j++;
x = j * (float) n_in_samples / (float) n_out_samples;
i = x;
}
}
void
cubic_spline(float in_buf[], int n_in_samples, float out_buf[], int
n_out_samples)
{
/* Position relative to the input buffer */
float x = (float) n_in_samples / (float) n_out_samples;
int i = x; /* Input buffer index */
int j = 1; /* Output buffer index */
float a, b, c;
float rel_x, rel_x2, rel_x3;
out_buf[0] = in_buf[0];
/* Interpolation beetween the first and second input sample. */
while (!i)
{
a = + 1.666667e-1 * in_buf[i + 3] - 0.5 * in_buf[i + 2]
+ 0.5 * in_buf[i + 1] - 1.666667e-1 * in_buf[i];
b = - 0.5 * in_buf[i + 3] + 2.0 * in_buf[i + 2]
- 2.5 * in_buf[i + 1] + in_buf[i];
c = + 3.333333e-1 * in_buf[i + 3] - 1.5 * in_buf[i + 2]
+ 3.0 * in_buf[i + 1] - 1.833333 * in_buf[i];
rel_x = x - (float) i;
rel_x2 = rel_x * rel_x;
rel_x3 = rel_x2 * rel_x;
out_buf[j] = a * rel_x3 + b * rel_x2 + c * rel_x + in_buf[i];
j++;
x = j * (float) n_in_samples / (float) n_out_samples;
i = x;
}
/* Cubic spline interpolation. */
while (i < (n_in_samples - 2))
{
a = + 1.666667e-1 * in_buf[i + 2] - 0.5 * in_buf[i + 1]
+ 0.5 * in_buf[i] - 1.666667e-1 * in_buf[i - 1];
b = - 0.5 * in_buf[i + 2] + 2.0 * in_buf[i + 1]
- 2.5 * in_buf[i] + in_buf[i - 1];
c = + 3.333333e-1 * in_buf[i + 2] - 1.5 * in_buf[i + 1]
+ 3.0 * in_buf[i] - 1.833333 * in_buf[i - 1];
rel_x = 1.0 + x - (float) i;
rel_x2 = rel_x * rel_x;
rel_x3 = rel_x2 * rel_x;
out_buf[j] = a * rel_x3 + b * rel_x2 + c * rel_x +
in_buf[i - 1];
j++;
x = j * (float) n_in_samples / (float) n_out_samples;
i = x;
}
/* Interpolation beetween the last two input samples. */
while (i < (n_in_samples - 1))
{
a = + 1.666667e-1 * in_buf[i + 1] - 0.5 * in_buf[i]
+ 0.5 * in_buf[i - 1] - 1.666667e-1 * in_buf[i - 2];
b = - 0.5 * in_buf[i + 1] + 2.0 * in_buf[i]
- 2.5 * in_buf[i - 1] + in_buf[i - 2];
c = + 3.333333e-1 * in_buf[i + 1] - 1.5 * in_buf[i]
+ 3.0 * in_buf[i - 1] - 1.833333 * in_buf[i - 2];
rel_x = 2.0 + x - (float) i;
rel_x2 = rel_x * rel_x;
rel_x3 = rel_x2 * rel_x;
out_buf[j] = a * rel_x3 + b * rel_x2 + c * rel_x +
in_buf[i - 2];
j++;
x = j * (float) n_in_samples / (float) n_out_samples;
i = x;
}
/* Beyond the last sample. */
while (j < n_out_samples)
{
rel_x = 3.0 + (x - (float) (n_in_samples - 1));
rel_x2 = rel_x * rel_x;
rel_x3 = rel_x2 * rel_x;
out_buf[j] = a * rel_x3 + b * rel_x2 + c * rel_x +
in_buf[n_in_samples - 4];
j++;
x = j * (float) n_in_samples / (float) n_out_samples;
i = x;
}
}
/* FIXME: fix it. */
/* TODO: use splines and not linear interpolation where it is not possible to
* use sinc. */
void
sinc(float in_buf[], int n_in_samples, float out_buf[], int n_out_samples)
{
/* Position relative to the input buffer */
float x = (float) n_in_samples / (float) n_out_samples;
int i = x; /* Input buffer index */
int j = 1; /* Output buffer index */
float rel_x;
out_buf[0] = in_buf[0];
/* Sinc interpolation starts after the third sample. */
while (i < 2)
{
/* Linear interpolation */
out_buf[j] = in_buf[0] + (in_buf[1] - in_buf[0]) * x;
j++;
x = j * (float) n_in_samples / (float) n_out_samples;
i = x;
}
/* Sinc interpolation */
while (i < (n_in_samples - 2))
{
rel_x = x - (float) i;
if (rel_x < 1e-10)
out_buf[j] = in_buf[i];
else
out_buf[j] = in_buf[i + 2] * sin(PI * (rel_x -
2.0)) / (PI * (rel_x - 2.0))
+ in_buf[i + 1] * sin(PI * (rel_x
- 1.0)) / (PI * (rel_x - 1.0))
+ in_buf[i] * sin(PI * rel_x) /
(PI * rel_x)
+ in_buf[i - 1] * sin(PI * (rel_x
+ 1.0)) / (PI * (rel_x + 1.0))
+ in_buf[i - 2] * sin(PI * (rel_x
+ 2.0)) / (PI * (rel_x + 2.0));
j++;
x = j * (float) n_in_samples / (float) n_out_samples;
i = x;
}
/* Linear interoplation again here. */
while (i < (n_in_samples - 1))
{
out_buf[j] = in_buf[i] + (in_buf[i + 1] - in_buf[i])
* (x - (float) i);
j++;
x = j * (float) n_in_samples / (float) n_out_samples;
i = x;
}
/* Using the last slope for samples beyond the last input sample. */
while (j < n_out_samples)
{
out_buf[j] = in_buf[n_in_samples - 1]
+ (in_buf[n_in_samples - 1]
- in_buf[n_in_samples - 2]) * (x - (float) i);
j++;
x = j * (float) n_in_samples / (float) n_out_samples;
i = x;
}
}
----
Hope you find it useful. For anything, I'm always here.
Stefano
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