Add Slice 5 ADAU1701 runtime audio control (firmware 0.5.0).

Safeload mixer/EQ/master on the ADAU1701, persist AudioProfile in NVS,
expose /api/audio routes and web UI controls, with host tests and manual sync.

Co-authored-by: Cursor <cursoragent@cursor.com>

Software/components/core/src/BiquadDesign.cpp

@@ -0,0 +1,94 @@
+/**
+ * @file    BiquadDesign.cpp
+ * @brief   Biquad coefficient design and ADAU fixpoint helpers.
+ *
+ * DigiRadio firmware — https://github.com/manvalan/DigiRadio
+ *
+ * Copyright 2026 Michele Bigi
+ * SPDX-License-Identifier: Apache-2.0
+ *
+ * @author  Michele Bigi
+ * @date    2026-07-06
+ */
+
+#include "core/BiquadDesign.hpp"
+
+#include <cmath>
+#include <numbers>
+
+namespace core {
+
+namespace {
+
+constexpr float kPi = std::numbers::pi_v<float>;
+
+[[nodiscard]] float clampQ(float q) noexcept
+{
+    if (q < 0.2F) {
+        return 0.2F;
+    }
+    if (q > 10.0F) {
+        return 10.0F;
+    }
+    return q;
+}
+
+} // namespace
+
+std::int32_t floatToFixpoint823(float value) noexcept
+{
+    const double scaled =
+        static_cast<double>(value) * static_cast<double>(1U << 23);
+    const auto rounded = static_cast<std::int64_t>(std::llround(scaled));
+    return static_cast<std::int32_t>(rounded);
+}
+
+std::int32_t gainDbToLinearFixpoint(GainDb gain) noexcept
+{
+    return floatToFixpoint823(gain.linear());
+}
+
+BiquadCoefficients designFlatEq() noexcept
+{
+    return BiquadCoefficients{
+        .b0 = 1.0F,
+        .b1 = 0.0F,
+        .b2 = 0.0F,
+        .a0 = 0.0F,
+        .a1 = 0.0F,
+    };
+}
+
+BiquadCoefficients designPeakingEq(FrequencyHz center, GainDb gain,
+                                   float q) noexcept
+{
+    if (std::fabs(gain.value()) < 0.001F) {
+        return designFlatEq();
+    }
+
+    const float qClamped = clampQ(q);
+    const float fs = static_cast<float>(kAdauSampleRateHz);
+    const float f0 = static_cast<float>(center.value());
+    const float a = std::pow(10.0F, gain.value() / 40.0F);
+    const float omega = 2.0F * kPi * f0 / fs;
+    const float sinOmega = std::sin(omega);
+    const float cosOmega = std::cos(omega);
+    const float alpha = sinOmega / (2.0F * qClamped);
+
+    const float b0 = 1.0F + alpha * a;
+    const float b1 = -2.0F * cosOmega;
+    const float b2 = 1.0F - alpha * a;
+    const float a0 = 1.0F + alpha / a;
+    const float a1 = -2.0F * cosOmega;
+    const float a2 = 1.0F - alpha / a;
+
+    return BiquadCoefficients{
+        .b0 = b0 / a0,
+        .b1 = b1 / a0,
+        .b2 = b2 / a0,
+        .a0 = a1 / a0,
+        .a1 = a2 / a0,
+    };
+}
+
+} // namespace core