equalizer: use shelfing filters for first and last band

Refactor the filter setup. Add two new filters with shelf characteristics for
first and last band. Change gain calculation as recommended in the quoted
document (no qrt needed). Rename variables to match the formulas in the
document.

diff --git a/gst/equalizer/gstiirequalizer.c b/gst/equalizer/gstiirequalizer.c
index b671b24..0e481c6 100644 (file)
--- a/gst/equalizer/gstiirequalizer.c
+++ b/gst/equalizer/gstiirequalizer.c
@@ -121,10 +121,6 @@ struct _GstIirEqualizerBandClass
 
 static GType gst_iir_equalizer_band_get_type (void);
 
-static void setup_filter (GstIirEqualizer * equ, GstIirEqualizerBand * band);
-
-static void set_passthrough (GstIirEqualizer * equ);
-
 static void
 gst_iir_equalizer_band_set_property (GObject * object, guint prop_id,
     const GValue * value, GParamSpec * pspec)
@@ -357,12 +353,6 @@ gst_iir_equalizer_finalize (GObject * object)
   G_OBJECT_CLASS (parent_class)->finalize (object);
 }
 
-static inline gdouble
-arg_to_scale (gdouble arg)
-{
-  return (pow (10.0, arg / 20.0));
-}
-
 /* Filter taken from
  *
  * The Equivalence of Various Methods of Computing
@@ -372,66 +362,163 @@ arg_to_scale (gdouble arg)
  *
  * http://www.aes.org/e-lib/browse.cfm?elib=6326
  * http://www.musicdsp.org/files/EQ-Coefficients.pdf
+ * http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt
  *
  * The bandwidth method that we use here is the preferred
  * one from this article transformed from octaves to frequency
  * in Hz.
  */
+static inline gdouble
+arg_to_scale (gdouble arg)
+{
+  return (pow (10.0, arg / 40.0));
+}
+
+static gdouble
+calculate_omega (gdouble freq, gint rate)
+{
+  gdouble omega;
+
+  if (freq / rate >= 0.5)
+    omega = M_PI;
+  else if (freq <= 0.0)
+    omega = 0.0;
+  else
+    omega = 2.0 * M_PI * (freq / rate);
+
+  return omega;
+}
+
+static gdouble
+calculate_bw (GstIirEqualizerBand * band, gint rate)
+{
+  gdouble bw = 0.0;
+
+  if (band->width / rate >= 0.5) {
+    /* If bandwidth == 0.5 the calculation below fails as tan(M_PI/2)
+     * is undefined. So set the bandwidth to a slightly smaller value.
+     */
+    bw = M_PI - 0.00000001;
+  } else if (band->width <= 0.0) {
+    /* If bandwidth == 0 this band won't change anything so set
+     * the coefficients accordingly. The coefficient calculation
+     * below would create coefficients that for some reason amplify
+     * the band.
+     */
+    band->a0 = 1.0;
+    band->a1 = 0.0;
+    band->a2 = 0.0;
+    band->b1 = 0.0;
+    band->b2 = 0.0;
+  } else {
+    bw = 2.0 * M_PI * (band->width / rate);
+  }
+  return bw;
+}
+
 static void
-setup_filter (GstIirEqualizer * equ, GstIirEqualizerBand * band)
+setup_peak_filter (GstIirEqualizer * equ, GstIirEqualizerBand * band)
+{
+  g_return_if_fail (GST_AUDIO_FILTER (equ)->format.rate);
+
+  {
+    gdouble gain, omega, bw;
+    gdouble alpha, alpha1, alpha2, b0;
+
+    gain = arg_to_scale (band->gain);
+    omega = calculate_omega (band->freq, GST_AUDIO_FILTER (equ)->format.rate);
+    bw = calculate_bw (band, GST_AUDIO_FILTER (equ)->format.rate);
+    if (bw == 0.0)
+      goto out;
+
+    alpha = tan (bw / 2.0);
+
+    alpha1 = alpha * gain;
+    alpha2 = alpha / gain;
+
+    b0 = (1.0 + alpha2);
+
+    band->a0 = (1.0 + alpha1) / b0;
+    band->a1 = (-2.0 * cos (omega)) / b0;
+    band->a2 = (1.0 - alpha1) / b0;
+    band->b1 = (2.0 * cos (omega)) / b0;
+    band->b2 = -(1.0 - alpha2) / b0;
+
+  out:
+    GST_INFO
+        ("gain = %5.1f, width= %7.2f, freq = %7.2f, a0 = %7.5g, a1 = %7.5g, a2=%7.5g b1 = %7.5g, b2 = %7.5g",
+        band->gain, band->width, band->freq, band->a0, band->a1, band->a2,
+        band->b1, band->b2);
+  }
+}
+
+static void
+setup_low_shelf_filter (GstIirEqualizer * equ, GstIirEqualizerBand * band)
 {
   g_return_if_fail (GST_AUDIO_FILTER (equ)->format.rate);
 
-  /* FIXME: we need better filters
-   * - we need shelf-filter for 1st and last band
-   */
   {
     gdouble gain, omega, bw;
-    gdouble edge_gain, gamma;
-    gdouble alpha, beta;
+    gdouble alpha, delta, b0;
+    gdouble egp, egm;
 
     gain = arg_to_scale (band->gain);
+    omega = calculate_omega (band->freq, GST_AUDIO_FILTER (equ)->format.rate);
+    bw = calculate_bw (band, GST_AUDIO_FILTER (equ)->format.rate);
+    if (bw == 0.0)
+      goto out;
+
+    egm = gain - 1.0;
+    egp = gain + 1.0;
+    alpha = tan (bw / 2.0);
+
+    delta = 2.0 * sqrt (gain) * alpha;
+    b0 = egp + egm * cos (omega) + delta;
+
+    band->a0 = ((egp - egm * cos (omega) + delta) * gain) / b0;
+    band->a1 = ((egm - egp * cos (omega)) * 2.0 * gain) / b0;
+    band->a2 = ((egp - egm * cos (omega) - delta) * gain) / b0;
+    band->b1 = ((egm + egp * cos (omega)) * 2.0) / b0;
+    band->b2 = -((egp + egm * cos (omega) - delta)) / b0;
 
-    if (band->freq / GST_AUDIO_FILTER (equ)->format.rate >= 0.5)
-      omega = M_PI;
-    else if (band->freq <= 0.0)
-      omega = 0.0;
-    else
-      omega = 2.0 * M_PI * (band->freq / GST_AUDIO_FILTER (equ)->format.rate);
-
-    if (band->width / GST_AUDIO_FILTER (equ)->format.rate >= 0.5) {
-      /* If bandwidth == 0.5 the calculation below fails as tan(M_PI/2)
-       * is undefined. So set the bandwidth to a slightly smaller value.
-       */
-      bw = M_PI - 0.00000001;
-    } else if (band->width <= 0.0) {
-      /* If bandwidth == 0 this band won't change anything so set
-       * the coefficients accordingly. The coefficient calculation
-       * below would create coefficients that for some reason amplify
-       * the band.
-       */
-      band->a0 = 1.0;
-      band->a1 = 0.0;
-      band->a2 = 0.0;
-      band->b1 = 0.0;
-      band->b2 = 0.0;
-      gain = 1.0;
+
+  out:
+    GST_INFO
+        ("gain = %5.1f, width= %7.2f, freq = %7.2f, a0 = %7.5g, a1 = %7.5g, a2=%7.5g b1 = %7.5g, b2 = %7.5g",
+        band->gain, band->width, band->freq, band->a0, band->a1, band->a2,
+        band->b1, band->b2);
+  }
+}
+
+static void
+setup_high_shelf_filter (GstIirEqualizer * equ, GstIirEqualizerBand * band)
+{
+  g_return_if_fail (GST_AUDIO_FILTER (equ)->format.rate);
+
+  {
+    gdouble gain, omega, bw;
+    gdouble alpha, delta, b0;
+    gdouble egp, egm;
+
+    gain = arg_to_scale (band->gain);
+    omega = calculate_omega (band->freq, GST_AUDIO_FILTER (equ)->format.rate);
+    bw = calculate_bw (band, GST_AUDIO_FILTER (equ)->format.rate);
+    if (bw == 0.0)
       goto out;
-    } else {
-      bw = 2.0 * M_PI * (band->width / GST_AUDIO_FILTER (equ)->format.rate);
-    }
 
-    edge_gain = sqrt (gain);
-    gamma = tan (bw / 2.0);
+    egm = gain - 1.0;
+    egp = gain + 1.0;
+    alpha = tan (bw / 2.0);
 
-    alpha = gamma * edge_gain;
-    beta = gamma / edge_gain;
+    delta = 2.0 * sqrt (gain) * alpha;
+    b0 = egp - egm * cos (omega) + delta;
+
+    band->a0 = ((egp + egm * cos (omega) + delta) * gain) / b0;
+    band->a1 = ((egm + egp * cos (omega)) * -2.0 * gain) / b0;
+    band->a2 = ((egp + egm * cos (omega) - delta) * gain) / b0;
+    band->b1 = ((egm - egp * cos (omega)) * -2.0) / b0;
+    band->b2 = -((egp - egm * cos (omega) - delta)) / b0;
 
-    band->a0 = (1.0 + alpha) / (1.0 + beta);
-    band->a1 = (-2.0 * cos (omega)) / (1.0 + beta);
-    band->a2 = (1.0 - alpha) / (1.0 + beta);
-    band->b1 = (2.0 * cos (omega)) / (1.0 + beta);
-    band->b2 = -(1.0 - beta) / (1.0 + beta);
 
   out:
     GST_INFO
@@ -459,11 +546,14 @@ set_passthrough (GstIirEqualizer * equ)
 static void
 update_coefficients (GstIirEqualizer * equ)
 {
-  gint i;
+  gint i, n = equ->freq_band_count;
 
-  for (i = 0; i < equ->freq_band_count; i++) {
-    setup_filter (equ, equ->bands[i]);
+  setup_low_shelf_filter (equ, equ->bands[0]);
+  for (i = 1; i < n - 1; i++) {
+    setup_peak_filter (equ, equ->bands[i]);
   }
+  setup_high_shelf_filter (equ, equ->bands[n - 1]);
+
   equ->need_new_coefficients = FALSE;
 }