[AUD-008][High] Correct band IIR section capacity and gain normalization

[gabrielsantosphilips]

Audit finding

• ID: AUD-008
• Status: Verified defect
• Severity: High
• Confidence: High
• Audited revision: 2f479320d805a1f9f35ebe4afaaeeded48913a94

Problem

Band transforms create 2 * order poles, but storage remains ceil(MaxOrder/2) sections. BuildSections() silently stops at capacity. Band-pass and band-stop also hardcode scalar gain 1.

Source:

numerical-toolbox-cpp/numerical/filters/passive/IirFilterDesign.hpp

Lines 47 to 49 in 2f47932

	static constexpr std::size_t kMaxSections{ (MaxOrder + 1) / 2 };
	using ComplexT = math::Complex<T>;

,

numerical-toolbox-cpp/numerical/filters/passive/IirFilterDesign.hpp

Lines 246 to 278 in 2f47932

	while (ai < numA && count < kMaxSections)
	{
	T a1{};
	T a2{};
	T b0{};
	T b1{};
	T b2{};
	PairPole(az, numA, aUsed, ai, a1, a2);
	PairZero(bz, numB, bUsed, bi, b0, b1, b2);
	const T sectionGain{ (count == 0) ? gain : T{ 1 } };
	if (math::Abs(a2) < static_cast<T>(1e-10))
	out[count] = { sectionGain * b0, sectionGain * b1, T{ 0 }, a1, T{ 0 } };
	else
	out[count] = { sectionGain * b0, sectionGain * b1, sectionGain * b2, a1, a2 };
	++count;
	while (ai < numA && aUsed[ai])
	++ai;
	}
	}
	template<typename T, std::size_t MaxOrder>
	OPTIMIZE_FOR_SPEED std::size_t IirFilterDesign<T, MaxOrder>::DesignLowPass(std::size_t order, T wc, T fs,
	const std::array<ComplexT, 16>& protoPoles) noexcept
	{
	std::array<ComplexT, 32> az{};
	std::array<ComplexT, 32> bz{};
	const std::size_t numA{ order };
	const std::size_t numB{ order };

, and

numerical-toolbox-cpp/numerical/filters/passive/IirFilterDesign.hpp

Lines 375 to 409 in 2f47932

	const T gain{ T{ 1 } };
	BuildSections(bz, numB, az, numA, gain, sections, sectionCount);
	return sectionCount;
	}
	template<typename T, std::size_t MaxOrder>
	OPTIMIZE_FOR_SPEED std::size_t IirFilterDesign<T, MaxOrder>::DesignBandStop(std::size_t order, T wc, T fs,
	const std::array<ComplexT, 16>& protoPoles) noexcept
	{
	const T bw{ wc };
	const T wc0{ wc };
	std::array<ComplexT, 32> az{};
	std::array<ComplexT, 32> bz{};
	std::size_t numA{ 0 };
	std::size_t numB{ 0 };
	for (std::size_t k{ 0 }; k < order; ++k)
	{
	const T mag2{ protoPoles[k].Real() * protoPoles[k].Real() + protoPoles[k].Imaginary() * protoPoles[k].Imaginary() };
	const ComplexT invLp{ protoPoles[k].Real() / mag2, -protoPoles[k].Imaginary() / mag2 };
	const ComplexT bsLp{ invLp.Real() * bw / T{ 2 }, invLp.Imaginary() * bw / T{ 2 } };
	const T discRe{ bsLp.Real() * bsLp.Real() - bsLp.Imaginary() * bsLp.Imaginary() - wc0 * wc0 };
	const T discIm{ T{ 2 } * bsLp.Real() * bsLp.Imaginary() };
	const T discMag{ math::Sqrt(math::Sqrt(discRe * discRe + discIm * discIm)) };
	const T discAngle{ math::Atan2(discIm, discRe) / T{ 2 } };
	const ComplexT sqrtDisc{ discMag * math::Cos(discAngle), discMag * math::Sin(discAngle) };
	az[numA++] = BilinearS2Z(bsLp + sqrtDisc, fs);
	az[numA++] = BilinearS2Z(bsLp - sqrtDisc, fs);
	bz[numB++] = BilinearS2Z({ T{ 0 }, wc0 }, fs);
	bz[numB++] = BilinearS2Z({ T{ 0 }, -wc0 }, fs);
	}
	const T gain{ T{ 1 } };

Reproduction

• Prototype order 8 band-pass returns four sections instead of eight.
• First-order Butterworth band-pass center gain is approximately 4.4026, not unity.

Acceptance criteria

• Define whether order is prototype or final digital order.
• Allocate sufficient bounded section storage or reject unsupported transformed order without truncation.
• Normalize band-pass/band-stop gain at documented reference frequencies.
• Add section-count and absolute response tests for low and maximum orders.