biquad: Add {low,high}pass_transform filters.

linkwitz_transform is now an alias for highpass_transform.

Author: bmc0

README.md

@@ -185,8 +185,16 @@ Example:
 	Second-order lowshelf filter.
 * `highshelf f0[k] width[q|s|d|o|h|k] gain`  
 	Second-order highshelf filter.
+* `lowpass_transform fz[k] qz fp[k] qp`  
+	Second-order lowpass transformation filter. Cancels the poles defined by
+	`fz` and `qz` and replaces them with new poles defined by `fp` and `qp`.
+	Gain is unity at DC.
+* `highpass_transform fz[k] qz fp[k] qp`  
+	Second-order highpass transformation filter. Also known as a Linkwitz
+	transform (see http://www.linkwitzlab.com/filters.htm#9). Same as
+	`lowpass_transform` except the gain is unity at Fs/2.
 * `linkwitz_transform fz[k] qz fp[k] qp`  
-	Linkwitz transform (see http://www.linkwitzlab.com/filters.htm#9).
+	Alias for `highpass_transform`.
 * `deemph`  
 	Compact Disc de-emphasis filter.
 * `biquad b0 b1 b2 a0 a1 a2`  

biquad.c

@@ -79,14 +79,15 @@ void biquad_reset(struct biquad_state *state)
 void biquad_init_using_type(struct biquad_state *b, int type, double fs, double arg0, double arg1, double arg2, double arg3, int width_type)
 {
 	double b0 = 1.0, b1 = 0.0, b2 = 0.0, a0 = 1.0, a1 = 0.0, a2 = 0.0;
-	if (type == BIQUAD_LINKWITZ_TRANSFORM) {
+	if (type == BIQUAD_LOWPASS_TRANSFORM || type == BIQUAD_HIGHPASS_TRANSFORM) {
 		const double fz = arg0, qz = arg1;
 		const double fp = arg2, qp = arg3;
 
 		const double w0z = 2*M_PI*fz / fs, w0p = 2*M_PI*fp / fs;
 		const double cos_w0z = cos(w0z), cos_w0p = cos(w0p);
 		const double alpha_z = sin(w0z) / (2.0*qz), alpha_p = sin(w0p) / (2.0*qp);
-		const double kz = 2.0/(1.0+cos_w0z), kp = 2.0/(1.0+cos_w0p);
+		const double kz = (type == BIQUAD_LOWPASS_TRANSFORM) ? 2.0/(1.0-cos_w0z) : 2.0/(1.0+cos_w0z);
+		const double kp = (type == BIQUAD_LOWPASS_TRANSFORM) ? 2.0/(1.0-cos_w0p) : 2.0/(1.0+cos_w0p);
 
 		b0 = (1.0 + alpha_z)*kz;
 		b1 = (-2.0 * cos_w0z)*kz;
@@ -109,7 +110,7 @@ void biquad_init_using_type(struct biquad_state *b, int type, double fs, double
 		}
 
 		const double a = pow(10.0, gain / 40.0);
-		const double w0 = 2.0*M_PI*f0 / fs;
+		const double w0 = 2*M_PI*f0 / fs;
 		const double sin_w0 = sin(w0), cos_w0 = cos(w0);
 
 		switch (width_type) {
@@ -422,8 +423,9 @@ struct effect * biquad_effect_init(const struct effect_info *ei, const struct st
 		if (ei->effect_number == BIQUAD_PEAK) CHECK_WIDTH_TYPE(BIQUAD_WIDTH_TEST_NO_SLOPE);
 		GET_ARG(arg2, argv[3], "gain");
 		break;
-	case BIQUAD_LINKWITZ_TRANSFORM:
-		INIT_COMMON(4, BIQUAD_LINKWITZ_TRANSFORM);
+	case BIQUAD_LOWPASS_TRANSFORM:
+	case BIQUAD_HIGHPASS_TRANSFORM:
+		INIT_COMMON(4, ei->effect_number);
 		GET_FREQ_ARG(arg0, argv[1], "fz");
 		GET_ARG(arg1, argv[2], "qz");
 		CHECK_RANGE(arg1 > 0.0, "qz", return NULL);

biquad.h

@@ -44,7 +44,8 @@ enum {
 	BIQUAD_PEAK,
 	BIQUAD_LOWSHELF,
 	BIQUAD_HIGHSHELF,
-	BIQUAD_LINKWITZ_TRANSFORM,
+	BIQUAD_LOWPASS_TRANSFORM,
+	BIQUAD_HIGHPASS_TRANSFORM,
 	/* Only for effect_info->effect_number */
 	BIQUAD_DEEMPH,
 	BIQUAD_BIQUAD,

dsp.1

@@ -168,8 +168,18 @@ Second-order lowshelf filter.
 \fBhighshelf\fR \fIf0\fR[\fBk\fR] \fIwidth\fR[\fBq\fR|\fBs\fR|\fBd\fR|\fBo\fR|\fBh\fR|\fBk\fR] \fIgain\fR
 Second-order highshelf filter.
 .TP
+\fBlowpass_transform\fR \fIfz\fR[\fBk\fR] \fIqz\fR \fIfp\fR[\fBk\fR] \fIqp\fR
+Second-order lowpass transformation filter. Cancels the poles defined by
+\fIfz\fR and \fIqz\fR and replaces them with new poles defined by \fIfp\fR and \fIqp\fR.
+Gain is unity at DC.
+.TP
+\fBhighpass_transform\fR \fIfz\fR[\fBk\fR] \fIqz\fR \fIfp\fR[\fBk\fR] \fIqp\fR
+Second-order highpass transformation filter. Also known as a Linkwitz
+transform (see http://www.linkwitzlab.com/filters.htm#9). Same as
+\fBlowpass_transform\fR except the gain is unity at Fs/2.
+.TP
 \fBlinkwitz_transform\fR \fIfz\fR[\fBk\fR] \fIqz\fR \fIfp\fR[\fBk\fR] \fIqp\fR
-Linkwitz transform (see http://www.linkwitzlab.com/filters.htm#9).
+Alias for \fBhighpass_transform\fR.
 .TP
 \fBdeemph\fR
 Compact Disc de-emphasis filter.

effect.c

@@ -59,7 +59,9 @@ static const struct effect_info effects[] = {
 	{ "eq",                 "eq f0[k] width[q|o|h|k] gain",            biquad_effect_init,    BIQUAD_PEAK },
 	{ "lowshelf",           "lowshelf f0[k] width[q|s|d|o|h|k] gain",  biquad_effect_init,    BIQUAD_LOWSHELF },
 	{ "highshelf",          "highshelf f0[k] width[q|s|d|o|h|k] gain", biquad_effect_init,    BIQUAD_HIGHSHELF },
-	{ "linkwitz_transform", "linkwitz_transform fz[k] qz fp[k] qp",    biquad_effect_init,    BIQUAD_LINKWITZ_TRANSFORM },
+	{ "lowpass_transform",  "lowpass_transform fz[k] qz fp[k] qp",     biquad_effect_init,    BIQUAD_LOWPASS_TRANSFORM },
+	{ "highpass_transform", "highpass_transform fz[k] qz fp[k] qp",    biquad_effect_init,    BIQUAD_HIGHPASS_TRANSFORM },
+	{ "linkwitz_transform", "linkwitz_transform fz[k] qz fp[k] qp",    biquad_effect_init,    BIQUAD_HIGHPASS_TRANSFORM },
 	{ "deemph",             "deemph",                                  biquad_effect_init,    BIQUAD_DEEMPH },
 	{ "biquad",             "biquad b0 b1 b2 a0 a1 a2",                biquad_effect_init,    BIQUAD_BIQUAD },
 	{ "gain",               "gain gain_dB",                            gain_effect_init,      GAIN_EFFECT_NUMBER_GAIN },