audioconvert: add optional hilbert transform to rear channels

Add an option to do a hilbert transform on the generated rear channels
to do a 90 degree pahse shift on them. This can improve spacialization
of the rear channels.

See #861

spa/plugins/audioconvert/hilbert.h

@@ -0,0 +1,69 @@
+/* Hilbert function
+ *
+ * Copyright © 2021 Wim Taymans
+ *
+ * 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 (including the next
+ * paragraph) 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.
+ */
+
+#ifndef HILBERT_H
+#define HILBERT_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <errno.h>
+#include <stddef.h>
+#include <math.h>
+
+static inline void blackman_window(float *taps, int n_taps)
+{
+	int n;
+	for (n = 0; n < n_taps; n++) {
+		float w = 2 * M_PI * n / (n_taps-1);
+		taps[n] = 0.3635819 - 0.4891775 * cos(w)
+			+ 0.1365995 * cos(2 * w) - 0.0106411 * cos(3 * w);
+	}
+}
+
+static inline int hilbert_generate(float *taps, int n_taps)
+{
+	int i;
+
+	if ((n_taps & 1) == 0)
+		return -EINVAL;
+
+	for (i = 0; i < n_taps; i++) {
+		int k = -(n_taps / 2) + i;
+		if (k & 1) {
+			float pk = M_PI * k;
+			taps[i] *= (1.0f - cosf(pk)) / pk;
+		} else {
+			taps[i] = 0.0f;
+		}
+	}
+	return 0;
+}
+
+#ifdef __cplusplus
+} /* extern "C" */
+#endif
+
+#endif /* HILBERT_H */