From c5c6c5ff728fbcbf3acce2faa409d2c5d63c1e67 Mon Sep 17 00:00:00 2001
From: Thomas Harte <thomas.harte@gmail.com>
Date: Wed, 12 Nov 2025 22:06:48 -0500
Subject: [PATCH] Add textbook filter construction.

---
 Components/SID/SID.cpp                        |   2 +-
 .../xcschemes/Clock Signal.xcscheme           |   2 +-
 SignalProcessing/BiquadFilter.hpp             | 123 ++++++++++++++++++
 3 files changed, 125 insertions(+), 2 deletions(-)

diff --git a/Components/SID/SID.cpp b/Components/SID/SID.cpp
index 318c8cf1f..d30b927fa 100644
--- a/Components/SID/SID.cpp
+++ b/Components/SID/SID.cpp
@@ -81,7 +81,7 @@ void SID::write(const Numeric::SizedInt<5> address, const uint8_t value) {
 }
 
 void SID::update_filter() {
-
+	// TODO!
 }
 
 uint8_t SID::read(const Numeric::SizedInt<5> address) {
diff --git a/OSBindings/Mac/Clock Signal.xcodeproj/xcshareddata/xcschemes/Clock Signal.xcscheme b/OSBindings/Mac/Clock Signal.xcodeproj/xcshareddata/xcschemes/Clock Signal.xcscheme
index 14b3f64d2..9c1a3c3d1 100644
--- a/OSBindings/Mac/Clock Signal.xcodeproj/xcshareddata/xcschemes/Clock Signal.xcscheme	
+++ b/OSBindings/Mac/Clock Signal.xcodeproj/xcshareddata/xcschemes/Clock Signal.xcscheme	
@@ -62,7 +62,7 @@
       </Testables>
    </TestAction>
    <LaunchAction
-      buildConfiguration = "Release"
+      buildConfiguration = "Debug"
       selectedDebuggerIdentifier = "Xcode.DebuggerFoundation.Debugger.LLDB"
       selectedLauncherIdentifier = "Xcode.DebuggerFoundation.Launcher.LLDB"
       enableASanStackUseAfterReturn = "YES"
diff --git a/SignalProcessing/BiquadFilter.hpp b/SignalProcessing/BiquadFilter.hpp
index e5b336f35..3969c98fb 100644
--- a/SignalProcessing/BiquadFilter.hpp
+++ b/SignalProcessing/BiquadFilter.hpp
@@ -8,6 +8,9 @@
 
 #pragma once
 
+#include <cmath>
+#include <numbers>
+
 namespace SignalProcessing {
 
 class BiquadFilter {
@@ -17,6 +20,126 @@ public:
 		coefficients_[0] = int16_t(1 << 15);
 	}
 
+	enum class Type {
+		LowPass,
+		HighPass,
+		BandPass,
+		Notch,
+		AllPass,
+		Peaking,
+		LowShelf,
+		HighShelf
+	};
+	BiquadFilter(
+		const Type type,
+		const float sample_rate,
+		const float frequency,
+		const float resonance,
+		const float gain,
+		const bool normalise
+	) {
+		const float w0 = 2.0f * std::numbers::pi_v<float> * frequency / sample_rate;
+		const float alpha = std::sin(w0) / (2.0f * resonance);
+		const float cos_w0 = std::cos(w0);
+
+		float coefficients[5];
+		float magnitude = 1.0f;
+		switch(type) {
+			case Type::LowPass:
+				coefficients[0] = (1.0f - cos_w0) / 2.0f;
+				coefficients[1] = 1.0f + cos_w0;
+				coefficients[2] = (1.0f - cos_w0) / 2.0f;
+				magnitude = 1.0f + alpha;
+				coefficients[3] = -2.0f * cos_w0;
+				coefficients[4] = 1.0f - alpha;
+			break;
+
+			case Type::HighPass:
+				coefficients[0] = (1.0f - cos_w0) / 2.0f;
+				coefficients[1] = -(1.0f + cos_w0);
+				coefficients[2] = (1.0f - cos_w0) / 2.0f;
+				magnitude = 1.0f + alpha;
+				coefficients[3] = -2.0f * cos_w0;
+				coefficients[4] = 1.0f - alpha;
+			break;
+
+			case Type::BandPass:
+				coefficients[0] = alpha;
+				coefficients[1] = 0.0f;
+				coefficients[2] = -alpha;
+				magnitude = 1.0f + alpha;
+				coefficients[3] = -2.0f * cos_w0;
+				coefficients[0] = 1.0f - alpha;
+			break;
+
+			case Type::Notch:
+				coefficients[0] = 1.0f;
+				coefficients[1] = -2.0f * cos_w0;
+				coefficients[2] = 1.0f;
+				magnitude = 1.0f + alpha;
+				coefficients[3] = -2.0f * cos_w0;
+				coefficients[4] = 1.0f - alpha;
+			break;
+
+			case Type::AllPass:
+				coefficients[0] = 1.0f - alpha;
+				coefficients[1] = -2.0f * cos_w0;
+				coefficients[2] = 1.0f + alpha;
+				magnitude = 1.0f + alpha;
+				coefficients[3] = -2.0f * cos_w0;
+				coefficients[4] = 1.0f - alpha;
+			break;
+
+			case Type::Peaking: {
+				const float a = std::pow(10.0f, gain / 40.0f);
+
+				coefficients[0] = 1.0f + (alpha * a);
+				coefficients[1] = -2.0f * cos_w0;
+				coefficients[2] = 1.0f - (alpha * a);
+				magnitude = 1.0f + (alpha / a);
+				coefficients[3] = -2.0f * cos_w0;
+				coefficients[4] = 1.0f - (alpha / a);
+			} break;
+
+			case Type::LowShelf: {
+				const float a_ls = std::pow(10.0f, gain / 40.0f);
+				const float sqrt_a = std::sqrt(a_ls);
+				const float alpha_ls =
+					std::sin(w0) / 2.0f * std::sqrt((a_ls + 1.0f / a_ls) * (1.0f / resonance - 1.0f) + 2.0f);
+
+				coefficients[0] = a_ls * ((a_ls + 1.0f) - (a_ls - 1.0f) * cos_w0 + 2.0f * sqrt_a * alpha_ls);
+				coefficients[1] = 2.0f * a_ls * ((a_ls - 1.0f) - (a_ls + 1.0f) * cos_w0);
+				coefficients[2] = a_ls * ((a_ls + 1.0f) - (a_ls - 1.0f) * cos_w0 - 2.0f * sqrt_a * alpha_ls);
+				magnitude = (a_ls + 1.0f) + (a_ls - 1.0f) * cos_w0 + 2.0f * sqrt_a * alpha_ls;
+				coefficients[3] = -2.0f * ((a_ls - 1) + (a_ls + 1) * cos_w0);
+				coefficients[4] = (a_ls + 1.0f) + (a_ls - 1.0f) * cos_w0 - 2.0f * sqrt_a * alpha_ls;
+			} break;
+
+			case Type::HighShelf: {
+				const float a_hs = std::pow(10.0f, gain / 40.0f);
+				const float sqrt_a_hs = std::sqrt(a_hs);
+				const float alpha_hs =
+					std::sin(w0) / 2.0f * std::sqrt((a_hs + 1.0f / a_hs) * (1.0f / resonance - 1.0f) + 2.0f);
+
+				coefficients[0] = a_hs * ((a_hs + 1.0f) + (a_hs - 1.0f) * cos_w0 + 2.0f * sqrt_a_hs * alpha_hs);
+				coefficients[1] = -2.0f * a_hs * ((a_hs - 1.0f) + (a_hs + 1.0f) * cos_w0);
+				coefficients[2] = a_hs * ((a_hs + 1.0f) + (a_hs - 1.0f) * cos_w0 - 2.0f * sqrt_a_hs * alpha_hs);
+				magnitude = (a_hs + 1.0f) - (a_hs - 1.0f) * cos_w0 + 2.0f * sqrt_a_hs * alpha_hs;
+				coefficients[3] = 2.0f * ((a_hs - 1.0f) - (a_hs + 1.0f) * cos_w0);
+				coefficients[4] = (a_hs + 1.0f) - (a_hs - 1.0f) * cos_w0 - 2.0f * sqrt_a_hs * alpha_hs;
+			} break;
+		}
+
+		if(normalise) {
+			for(int c = 0; c < 5; c++) {
+				coefficients[c] /= magnitude;
+			}
+		}
+		for(int c = 0; c < 5; c++) {
+			coefficients_[c] = int16_t(coefficients[c] * 32767.0f);
+		}
+	}
+
 	int16_t apply(const int16_t input) {
 		const int16_t output = (
 			coefficients_[0] * input +