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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<html>
<head>
<title>Zita-resampler.</title>
<meta name="Author" content="Fons Adriaensen (fons@linuxaudio.org)">
<meta name="Description" content="The zita-resampler library.">
<meta name="Keywords" content="resampling sound audio dsp linux">
<link rel=StyleSheet href="zitadocs.css" type="text/css" media="all">
</head>
<body>
<h1>Libzita-resampler</h1>
<ul>
<li><a href = "#introduction">Introduction</a>
<li><a href = "#algorithm">The algorithm</a>
<li><a href = "#description">API description</a>
<li><a href = "#reference">API reference</a>
</ul>
<br>
<a name = "introduction"></a>
<h2>Introduction</h2>
<p>
Libzita-resampler is a C++ library for resampling audio signals. It is designed
to be used within a real-time processing context, to be fast, and to provide
high-quality sample rate conversion.
</p>
<p>
The library operates on signals represented in single-precision floating point
format. For multichannel operation both the input and output signals are
assumed to be stored as interleaved samples.
</p>
<p>
The API allows a trade-off between quality and CPU load. For the latter
a range of approximately 1:6 is available. Even at the highest quality
setting libzita-resampler will be faster than most similar libraries
providing the same quality, e.g. libsamplerate.
</p>
<p>
In many real-time resampling applications (e.g. an audio player), processing
is driven by the ouput sample rate: each processing period requires a fixed
number of output samples, and the input side has to adapt, providing whatever
number of samples required. The inverse situation (less common, but possible)
would be e.g. a recording application that writes an audio file at a rate that
is different from the hardware sample rate. In that case the number of input
samples is fixed for each processing period. The API provided by libzita-resampler
is fully symmetric in this respect - it handles both situations in the exactly the
same way, using the same application code.
</p>
<p>
Libzita-resampler provides two classes:
</p>
<p>
The <b>Resampler</b> class performs resampling at a fixed ratio <b>F_out / F_in</b>
which is required to be <b>≥ 1/16</b> and be reducible to the form <b> b / a</b>
with <b>a, b</b> integer and <b>b ≤ 1000</b>. This includes all the 'standard'
ratios, e.g. 96000 / 44100 = 320 / 147. These restrictions allow for a more efficient
implementation.
</p>
<p>
The <b>VResampler</b> class provides an arbitrary ratio <b>r</b> in the range
<b>1/16 ≤ r ≤ 64</b> and which can variable within a range of <b>0.95 to
16.0</b> w.r.t. the originally configured one. The lower limit here is necessary
because this class still uses a fixed multiphase filter, with only the phase step
being variable. This class was developed for converting between two nominally fixed
sample rates with a ratio which is not known exactly and may even drift slowly, e.g.
when combining sound cards wich do not have a common word clock. This resampler is
somewhat less efficient than the fixed ratio one since it has to interpolate filter
coefficients, but the difference is marginal when used on multichannel signals.
</p>
<p>
Both classes provide essentially the same API, with only small differences
where necessary.
<br>
<a name = "algorithm"></a>
<h2>The algorithm</h2>
<p>
Libzita-resampler implements <b>constant bandwidth resampling</b>. In contrast
to e.g. cubic interpolation it does not consider the actual shape of the
waveform represented by the input samples, but rather operates in the spectral
domain.
</p>
<p>
Let
<ul>
<li><b>F_in, F_out</b>    be the input and output sample rates,</li>
<li><b>F_min</b>    the lower of the two,</li>
<li><b>F_lcm</b>    their lowest common multiple,</li>
<li><b>b = F_lcm / F_in</b>,</li>
<li><b>a = F_lcm / F_out</b></li>.
</ul>
<p>
Then the calculation performed by zita-resampler is equivalent to:
</p>
<ul>
<li>upsampling to a rate of <b>F_lcm</b> by inserting <b>b - 1</b>
zero-valued samples after each input sample,</li>
<li>low-pass filtering of the upsampled signal to remove everything
above <b>F_min / 2</b>,</li>
<li>retaining only the first of each series of <b>a</b> filtered
samples.</li>
</ul>
<p>
This is of course not how things are implemented in the resampler code.
Only those samples that are actually output are computed, and the inserted
zeros are never used. In practice this means there is a set of <b>b</b>
different FIR filters that each output one sample in turn, in round-robin
fashion. All these filters have the same frequency response, but different
delays that correspond to the relative position in time of the input and
output samples.
</p>
<p>
A real-world filter can't be perfect, it is always a compromise between
complexity (CPU load) and performance. In the context of resampling this
compromise manifests itself as deviations from the ideally flat frequency
response, and as aliasing - the same phenomenon that occurs with AD and
DA conversion. For aliasing, two cases need to be considered:
</p>
<p>
<b>Upsampling.</b> In this case <b>F_min = F_in</b>, and input signals
below but near to <b>F_in / 2</b> will also appear in the output
just above this frequency. This is similar to DA conversion.
</p>
<p>
<b>Downsampling.</b> In this case <b>F_min = F_out</b>, and input signals
above but near to <b>F_out / 2</b> will also appear in the output
just below this frequency. This is similar to AD conversion.
</p>
<p>
In the design of zita-resampler it was assumed that in most cases
conversion will be between the 'standard' audio sample rates (44.1,
48, 88.2, 96, 192 kHz), and that consequently frequency response
errors and aliasing will occur only above the upper limit of the
audible frequency range. Given this assumption, some pragmatic
trade-offs can be made.
</p>
<p>
The filter used by libzita-resampler is dimensioned to reach an
attenuation of 60dB at the Nyquist frequency. The initialisation
function takes a parameter named <b>hlen</b> that is in fact half
the length of the symmetrical FIR filter expressend in samples at
the rate <b>F_min</b>. The valid range for <b>hlen</b> is 16 to 96.
The figure below shows the filter responses for <b>hlen</b> = 32,
48, and 96. The <b>x</b> axis is <b>F / F_min</b>, the <b>y</b> axis
is in dB. The lower part of the traces is the mirrored continuation
of the response above the Nyquist frequency, i.e. the aliasing.
Note that 20 kHz corresponds to x = 0.416 for a sample rate of 48 kHz,
and to x = 0.454 for a sample rate of 44.1 kHz.
</p>
<p>
<img src="filt1.png">
</p>
<p>
<br>
The same traces with a reduced vertical range, showing the passband
response.
</p>
<p>
<img src="filt2.png">
</p>
<p>
From these figures it should be clear that <b>hlen = 32</b> should
provide very high quality for <b>F_min</b> equal to 48 kHz or higher,
while <b>hlen = 48</b> should be sufficient for an <b>F_min</b> of
44.1 kHz. The validity of these assumptions was confirmed by a series
of listening tests. If fact the conclusion of these test was that even
at 44.1 kHz the subjects (all audio specialists or musicians) could not
detect any significant difference between <b>hlen</b> values of 32 and 96.
</p>
<br>
<a name = "description"></a>
<h2>API description</h2>
<p>
The constructors of both classes do not initialise the object for a particular
resampling rate, quality or number of channels - this is done by a separate
function member which can be used as many times as necessary. This means you
can allocate <b>(V)Resampler</b> objects before the actual resampling parameters
are known.
</p>
<p>
The <b>setup ()</b> member initialises a resampler for a combination of input
sample rate, output sample rate, number of channels, and filter length. This
function allocates and computes the filter coefficient tables and is definitely
not RT-safe. The actual tables will be shared with other resampler instances if
possible - the library maintains a reference-counted collection of them. After
the initialisation by <b>setup ()</b>, the <b>process ()</b> member can be called
repeatedly to actually resample audio signals. This function is RT-safe and
can be used within e.g. a JACK callback. The <b>clear ()</b> member restores
the object to the initial state it has after construction, and is also called
from the destructor. You can safely call <b>setup ()</b> again without first
calling <b>clear ()</b> - doing this avoids recomputation of the filter
coefficients in some cases.
</p>
<p>
Both classes have four public data members which are used as input and output
parameters of <b>process ()</b>, in the same way as you would use a C struct
to pass parameters. These are:
</p>
<pre>
unsigned int inp_count; // number of frames in the input buffer
unsigned int out_count; // number of frames in the output buffer
float *inp_data; // pointer to first input frame
float *out_data; // pointer to first output frame
</pre>
<p>
As <b>process ()</b> does its work, it increments the pointers and decrements the
counts. The call returns when either of the counts is zero, i.e. when the input
buffer is empty or the output buffer is full. You should then take appropriate
action and if necessary call <b>process ()</b> again.
</p>
<p>
When <b>process ()</b> returns, the four parameter values exactly reflect
those parts of both buffers <b>that have not yet been used</b>.
One of them will be fully used, with the corresponding count being zero.
The remaining part of the other, pointed to by the returned pointer, can
always be replaced before the next call to <b>process ()</b>, but this is
entirely optional.
</p>
<p>
When for example <b>inp_count</b> is zero, you have to fill the input buffer
again, or provide a new one, and re-initialise the input count and pointer.
If at that time <b>out_count</b> is not zero, you can either leave the output
parameters as they are for the next call to <b>process ()</b>, or you could
empty the part of the output buffer that has been filled and re-use it from
the start, or provide a completely different one.
</p>
<p>
The same applies to the input buffer when it is not empty on return of
<b>process ()</b>: it can be left alone or be replaced. A number of input
samples is stored internally between <b>process ()</b> calls as part of the
resampler state, but this never includes samples that have not yet been used.
So you can 'revise' the input data, starting from the frame pointed to by the
returned <b>inp_data</b>, up to the last moment.
</p>
<p>
All this means that both classes will interface easily with fixed input and
output buffers, with dynamically generated input signals, and also with
lock-free circular buffers.
</p>
<p>
Either of the two pointers can be NULL. When <b>inp_data</b> is zero, the effect
is to insert zero-valued input samples, as if you had supplied a zero-filled
buffer of length <b>inp_count</b>. When <b>out_data</b> is zero, input samples
will be consumed, the internal state of the resampler will advance normally
and <b>out_count</b> will decrement, but no output samples are written (in
fact they are not even computed).
</p>
<a name = "padding"></a>
<p>
Note that libzita-resampler does <b>not</b> automatically insert zero-valued
input samples at the start and end of the resampling process. The API makes it
easy to add such padding, and doing this is left entirely up to the user.
</p>
<p>
The <b>inpsize ()</b> member returns the lenght of the FIR filter expressed in
input samples. At least this number of samples is required to produce an output
sample. If <b>k</b> is the value returned by this function, then
</p>
<ul>
<li>inserting <b>k / 2 - 1</b> zero-valued samples at the start will align the
first input and output samples,</li>
<li>inserting <b>k - 1</b> zero valued samples will ensure that the output
includes the full filter response for the first input sample.</li>
</ul>
<p>
Similar considerations apply at the end of the input data:
</p>
<ul>
<li>inserting <b>k / 2</b> zero-valued samples at the end will ensure
that the last output sample produced will correspond to a position as close
as possible but not past the last real input sample,</li>
<li>inserting <b>k - 1</b> zero valued samples will ensure that the output
includes the full filter response for the last real input sample.</li>
</ul>
<p>
<a name = "inpdist"></a>
The <b>inpdist ()</b> member returns the distance or delay expressed in sample
periods at the input rate, between the first output sample that will be ouput
by the next call to <b>process ()</b> and the first input sample that will be
read (i.e. that is not yet part of the internal state).
<br><br>
In the picture below, the red dots represent input samples and the blue ones
are the output. Solid dots are samples already used or output. After a call
to process () the resampler object remains in a state ready to produce the next
output sample, except that it may have to input one or more new samples first.
The filter is aligned with the next output sample. In this case one more input
sample is required to compute it, and the input distance is 2.7.
</p>
<p>
<img src="inpdist.png">
</p>
<p>
After a resampler is prefilled with <b>inpsize () / 2 - 1</b> samples as described
above, <b>inpdist ()</b> will be zero - the first output sample corresponds exactly
to the first input. Note that without prefilling the distance is negative, which
means that the first output sample corresponds to some point past the start of the
input data.
</p>
<p>
The 'resample' application supplied with the library sources provides
an example of how to use the <b>Resampler</b> class. For an example
using <b>VResampler</b> you can have a look at zita_a2j and zita_ja2.
</p>
<br>
<a name = "reference"></a>
<h2>API reference</h2>
<p>
Public function members of the <b>Resampler</b> and <b>VResampler</b> classes.
Functions listed without a class prefix are available for both classes.
</p>
<ul>
<li><a href = "#resampler">Resampler ()</a>
<li><a href = "#resampler">~Resampler ()</a>
<li><a href = "#vresampler">VResampler ()</a>
<li><a href = "#vresampler">~VResampler ()</a>
<li><a href = "#res_setup">Reampler::setup ()</a>
<li><a href = "#vres_setup">VResampler::setup ()</a>
<li><a href = "#clear">clear ()</a>
<li><a href = "#reset">reset ()</a>
<li><a href = "#process">process ()</a>
<li><a href = "#nchan">nchan ()</a>
<li><a href = "#inpsize">inpsize ()</a>
<li><a href = "#inpdist">inpdist ()</a>
<li><a href = "#vres_set_rratio">VResampler::set_rratio ()</a>
<li><a href = "#vres_set_rrfilt">VResampler::set_rrfilt ()</a>
</ul>
<p>
Public data members of the <b>Resampler</b> and <b>VResampler</b> classes.
</p>
<ul>
<li><a href = "#inp_count">inp_count</a>
<li><a href = "#out_count">out_count</a>
<li><a href = "#inp_data">inp_data</a>
<li><a href = "#out_data">out_data</a>
</ul>
<a name="resampler"></a>
<br><p class="apihdr">Resampler (void);<br>~Resampler (void);</p>
<p>
<b>Description:</b> Constructor and destructor. The constructor just creates an object that takes
almost no memory but needs to be configured by <a href="#setup"><b>setup ()</b></a> before it
can be used. The destructor calls <a href="#clear"><b>clear ()</b></a>.
<br><br>
<b>RT-safe:</b> No
</p>
<a name="vresampler"></a>
<br><p class="apihdr">VResampler (void);<br>~VResampler (void);</p>
<p>
<b>Description:</b> Constructor and destructor. The constructor just creates an object that takes
almost no memory but needs to be configured by <a href="#setup"><b>setup ()</b></a> before it
can be used. The destructor calls <a href="#clear"><b>clear ()</b></a>.
<br><br>
<b>RT-safe:</b> No
</p>
<a name="res_setup"></a>
<br><p class="apihdr">int   Resampler::setup (unsigned int   fs_inp, unsigned int fs_out, unsigned int nchan, unsigned int hlen);</p>
<p>
<b>Description:</b> Configures the object for a combination of input / output sample rates, number
of channels, and filter lenght.<br>If the parameters are OK, creates the filter coefficient tables
or re-uses existing ones, allocates some internal resources, and returns via <a href="#reset">
<b>reset ()</b></a>.
<br><br>
<b>Parameters:</b>
</p>
<p class="indent">
<b>fs_inp, fs_out:</b> The input and output sample rates. The ratio <b>fs_out
/ fs_inp</b> must be <b> ≥ 1/16</b> and reducible to the form <b>b / a</b>
with <b>a, b</b> integer and <b>b ≤ 1000</b>.
<br><br>
<b>nchan:</b> Number of channels, must not be zero.
<br><br>
<b>hlen:</b> Half the lenght of the filter expressed in samples at the lower of
input and output rates. This parameter determines the 'quality' as explained
<a href="#algorithm">here</a>. For any fixed combination of the other parameters,
cpu load will be roughly proportional to <b>hlen</b>. The valid range is
<b>16 ≤ hlen ≤ 96</b>.
</p>
<p>
<b>Returns:</b> Zero on success, non-zero otherwise.
<br><br>
<b>Remark:</b> It is perfectly safe to call this function again without
having called <a href="#clear"><b>clear ()</b></a> first. If only the number
of channels is changed, doing this will avoid recalculation of the filter tables
even if they are not shared.
<br><br>
<b>RT-safe:</b> No
</p>
<a name="vres_setup"></a>
<br><p class="apihdr">int   VResampler::setup (double ratio, unsigned int nchan, unsigned int hlen);</p>
<p>
<b>Description:</b> Configures the object for a combination of resampling ratio, number of channels,
and filter lenght.<br>If the parameters are OK, creates the filter coefficient tables or re-uses
existing ones, allocates some internal resources, and returns via <a href="#reset">
<b>reset ()</b></a>.
<br><br>
<b>Parameters:</b>
</p>
<p class="indent">
<b>ratio:</b> The resampling ratio wich must be between <b>1/16</b> and <b>64</b>.
<br><br>
<b>nchan:</b> Number of channels, must not be zero.
<br><br>
<b>hlen:</b> Half the lenght of the filter expressed in samples at the lower of
the input and output rates. This parameter determines the 'quality' as explained
<a href="#algorithm">here</a>. For any fixed combination of the other parameters,
cpu load will be roughly proportional to <b>hlen</b>. The valid range is
<b>16 ≤ hlen ≤ 96</b>.
</p>
<p>
<b>Returns:</b> Zero on success, non-zero otherwise.
<br><br>
<b>Remark:</b> It is perfectly safe to call this function again without
having called <a href="#clear"><b>clear ()</b></a> first. If only the number
of channels is changed, doing this will avoid recalculation of the filter tables
even if they are not shared.
<br><br>
<b>RT-safe:</b> No
</p>
<a name="clear"></a>
<br><p class="apihdr">void   clear (void);</p>
<p>
<b>Description:</b> Deallocates resources (if not shared) and returns the object to
the unconfigured state as after construction. Also called by the destructor.
<br><br>
<b>RT-safe:</b> No
</p>
<a name="reset"></a>
<br><p class="apihdr">int   reset (void);</p>
<p>
<b>Description:</b> Resets the internal state of the resampler. Any stored
input samples are cleared, the filter phase and the four <a href="#inp_count">
public data members</a> are set to zero. This should be called before starting
resampling a new stream with the same configuration as the previous one.
<br><br>
<b>Returns:</b> Zero if the resampler is configured , non-zero otherwise.
<br><br>
<b>RT-safe:</b> Yes.
</p>
<a name="process"></a>
<br><p class="apihdr">int   process (void);</p>
<p>
<b>Description:</b> Resamles the input signal until either the input buffer
is empty or the output buffer is full. Information on the input and output
buffers is passed to this function using the four <a href="#inp_count"> public
data members</a> described below. The same four values are updated on return.
<br><br>
<b>Returns:</b> Zero if the resampler is configured, non-zero otherwise.
<br><br>
<b>RT-safe:</b> Yes.
</p>
<a name="nchan"></a>
<br><p class="apihdr">int   nchan (void);</p>
<p>
<b>Description:</b> Accessor.
<br><br>
<b>Returns:</b> The number of channels the resampler is configured for,
or zero if it is unconfigured. Input and output buffers are assumed to contain
this number of channels in interleaved format.
<br><br>
<b>RT-safe:</b> Yes
</p>
<a name="inpsize"></a>
<br><p class="apihdr">int   inpisze (void);</p>
<p>
<b>Description:</b> Accessor.
<br><br>
<b>Returns:</b> If the resampler is configured, the lenght of the
finite impulse filter expressed in samples at the input sample rate,
or zero otherwise. This value may be used to determine the number of
silence samples to insert at the start and end when resampling e.g.
an impulse response. See <a href="#padding">here</a> for more about this.
This function was called 'filtlen ()' in previous releases.
<br><br>
<b>RT-safe:</b> Yes
</p>
<a name="inpdist"></a>
<br><p class="apihdr">double   inpdist (void);</p>
<p>
<b>Description:</b> Accessor.
<br><br>
<b>Returns:</b> If the resampler is configured, the distance between
the next output sample and the next input sample, expressed in sample
periods at the input rate, zero otherwise. See <a href="#inpdist">
here</a> for more about this.
<br><br>
<b>RT-safe:</b> Yes
</p>
<a name="vres_set_rratio"></a>
<br><p class="apihdr">void   VResampler::set_rratio (double ratio);</p>
<p>
<b>Description:</b> Sets the resampling ratio relative to the one configured
by <a href="#vres_setup"> setup ()</a>. The valid range is <b>0.95 ≤
ratio ≤ 16</b>.
<br><br>
<b>Parameters:</b>
</p>
<p class="indent">
<b>ratio:</b> The relative resampling ratio.
</p>
<p>
<b>RT-safe:</b> Yes
</p>
<a name="vres_set_rrfilt"></a>
<br><p class="apihdr">void   VResampler::set_rrfilt (double time);</p>
<p>
<b>Description:</b> Sets the time constant of the first order filter applied
on values set by <a href="#vres_set_rratio"> set_rratio ()</a>. The time is
expressed as sample periods at the output rate. The default is zero, which
means changes are applied instantly.
<br><br>
<b>Parameters:</b>
</p>
<p class="indent">
<b>time:</b> The filter time constant.
</p>
<p>
<b>RT-safe:</b> Yes
</p>
<a name="inp_count"></a>
<br><p class="apihdr">unsigned int   inp_count;</p>
<p>
<b>Description:</b> Data member, input / output parameter of the <a href="#process">
process ()</a> function. This value is always equal to the number of frames in the
input buffer that have not yet been read by the process () function. It should be set
to the number of available frames before calling process ().
</p>
<a name="out_count"></a>
<br><p class="apihdr">unsigned int   out_count;</p>
<p>
<b>Description:</b> Data member, input / output parameter of the <a href="#process">
process ()</a> function. This value is always equal to the number of frames in the
output buffer that have not yet been written by the process () function. It should be
set to the size of the output buffer before calling process ().
</p>
<a name="inp_data"></a>
<br><p class="apihdr">float   *inp_data;</p>
<p>
<b>Description:</b> Data member, input / output parameter of the <a href="#process">
process ()</a> function. If not zero (NULL), this points to the next frame in the
input buffer that will be read by process (). If set to zero (NULL), the resampler
will proceed normally but use zero-valued samples as input (still counted by
<b>inp_count</b>).
</p>
<a name="out_data"></a>
<br><p class="apihdr">float   *out_data;</p>
<p>
<b>Description:</b> Data member, input / output parameter of the <a href="#process">
process ()</a> function. If not zero (NULL), this points to the next frame in the
output buffer that will be written by process (). If set to zero (NULL), the resampler
will proceed normally but the output is discarded (but still counted by <b>out_count</b>).
</p>
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