timefilter: internally compute feedback factors.

The feedback factors for the timefilter are directly computed from
the expected period. This commit changes the init function to accept
the period itself and compute the feedback factors internally,
rather than having all client code duplicate the formulas.

This commit also actually fixes the formulas: the current code had
sqrt(2*o), but the correct formula, both theoretically and according
to experimental testing, is sqrt(2)*o.

Furthermore, it adds an exponential to feedback factors larger than
1 with large periods.

4 files changed, 22 insertions, 17 deletions

diff --git a/libavdevice/alsa-audio-dec.c b/libavdevice/alsa-audio-dec.c
index f2dd21655b..62bf42d272 100644
--- a/libavdevice/alsa-audio-dec.c
+++ b/libavdevice/alsa-audio-dec.c
@@ -59,7 +59,6 @@ static av_cold int audio_read_header(AVFormatContext *s1)
     AVStream *st;
     int ret;
     enum CodecID codec_id;
-    double o;
 
     st = avformat_new_stream(s1, NULL);
     if (!st) {
@@ -81,9 +80,9 @@ static av_cold int audio_read_header(AVFormatContext *s1)
     st->codec->sample_rate = s->sample_rate;
     st->codec->channels    = s->channels;
     avpriv_set_pts_info(st, 64, 1, 1000000);  /* 64 bits pts in us */
-    o = 2 * M_PI * s->period_size / s->sample_rate * 1.5; // bandwidth: 1.5Hz
+    /* microseconds instead of seconds, MHz instead of Hz */
     s->timefilter = ff_timefilter_new(1000000.0 / s->sample_rate,
-                                      sqrt(2 * o), o * o);
+                                      s->period_size, 1.5E-6);
     if (!s->timefilter)
         goto fail;
 
diff --git a/libavdevice/jack_audio.c b/libavdevice/jack_audio.c
index 257a291758..1fa4f86724 100644
--- a/libavdevice/jack_audio.c
+++ b/libavdevice/jack_audio.c
@@ -145,7 +145,6 @@ static int start_jack(AVFormatContext *context)
     JackData *self = context->priv_data;
     jack_status_t status;
     int i, test;
-    double o, period;
 
     /* Register as a JACK client, using the context filename as client name. */
     self->client = jack_client_open(context->filename, JackNullOption, &status);
@@ -181,9 +180,7 @@ static int start_jack(AVFormatContext *context)
     jack_set_xrun_callback(self->client, xrun_callback, self);
 
     /* Create time filter */
-    period            = (double) self->buffer_size / self->sample_rate;
-    o                 = 2 * M_PI * 1.5 * period; /// bandwidth: 1.5Hz
-    self->timefilter  = ff_timefilter_new (1.0 / self->sample_rate, sqrt(2 * o), o * o);
+    self->timefilter  = ff_timefilter_new (1.0 / self->sample_rate, self->buffer_size, 1.5);
 
     /* Create FIFO buffers */
     self->filled_pkts = av_fifo_alloc(FIFO_PACKETS_NUM * sizeof(AVPacket));
diff --git a/libavdevice/timefilter.c b/libavdevice/timefilter.c
index e225ed11a9..4b8a10cb40 100644
--- a/libavdevice/timefilter.c
+++ b/libavdevice/timefilter.c
@@ -36,14 +36,21 @@ struct TimeFilter {
     int count;
 };
 
-TimeFilter *ff_timefilter_new(double clock_period,
-                              double feedback2_factor,
-                              double feedback3_factor)
+/* 1 - exp(-x) using a 3-order power series */
+static double qexpneg(double x)
+{
+    return 1 - 1 / (1 + x * (1 + x / 2 * (1 + x / 3)));
+}
+
+TimeFilter *ff_timefilter_new(double time_base,
+                              double period,
+                              double bandwidth)
 {
     TimeFilter *self       = av_mallocz(sizeof(TimeFilter));
-    self->clock_period     = clock_period;
-    self->feedback2_factor = feedback2_factor;
-    self->feedback3_factor = feedback3_factor;
+    double o               = 2 * M_PI * bandwidth * period * time_base;
+    self->clock_period     = time_base;
+    self->feedback2_factor = qexpneg(M_SQRT2 * o);
+    self->feedback3_factor = qexpneg(o * o);
     return self;
 }
 
diff --git a/libavdevice/timefilter.h b/libavdevice/timefilter.h
index 2a77946e99..33862f63bb 100644
--- a/libavdevice/timefilter.h
+++ b/libavdevice/timefilter.h
@@ -45,16 +45,18 @@ typedef struct TimeFilter TimeFilter;
  *
  * Unless you know what you are doing, you should set these as follow:
  *
- * o = 2 * M_PI * bandwidth * period
- * feedback2_factor = sqrt(2 * o)
+ * o = 2 * M_PI * bandwidth * period_in_seconds
+ * feedback2_factor = sqrt(2) * o
  * feedback3_factor = o * o
  *
  * Where bandwidth is up to you to choose. Smaller values will filter out more
  * of the jitter, but also take a longer time for the loop to settle. A good
  * starting point is something between 0.3 and 3 Hz.
  *
- * @param clock_period period of the hardware clock in seconds
- *        (for example 1.0/44100)
+ * @param time_base   period of the hardware clock in seconds
+ *                    (for example 1.0/44100)
+ * @param period      expected update interval, in input units
+ * @param brandwidth  filtering bandwidth, in Hz
  *
  * For more details about these parameters and background concepts please see:
  * http://www.kokkinizita.net/papers/usingdll.pdf