[AUD-015][High] Compute finite-length window power for PSD normalization

[gabrielsantosphilips]

Audit finding

• ID: AUD-015
• Status: Verified defect
• Severity: High
• Confidence: High
• Audited revision: 2f479320d805a1f9f35ebe4afaaeeded48913a94

Problem

Hann, Hamming, and Blackman windows return hardcoded asymptotic power constants, while PSD normalization requires the actual finite-length mean-square power U = sum(w[n]^2)/N for the implemented window convention.

Source:

numerical-toolbox-cpp/numerical/analysis/windowing/Windowing.hpp

Lines 26 to 72 in 2f47932

	class HammingWindow
	: public Window<QNumberType>
	{
	public:
	QNumberType operator()(std::size_t n, std::size_t order) override
	{
	return QNumberType((0.54f - 0.46f * static_cast<float>(math::Cos(2.0 * math::pi * static_cast<double>(n) / static_cast<double>(order)))) * 0.9999f);
	}
	QNumberType Power([[maybe_unused]] std::size_t order) override
	{
	return QNumberType(0.397f);
	}
	};
	template<typename QNumberType>
	class HanningWindow
	: public Window<QNumberType>
	{
	public:
	QNumberType operator()(std::size_t n, std::size_t order) override
	{
	return QNumberType(0.5f * (1.0f - static_cast<float>(math::Cos(2.0 * math::pi * static_cast<double>(n) / static_cast<double>(order)))) * 0.9999f);
	}
	QNumberType Power([[maybe_unused]] std::size_t order) override
	{
	return QNumberType(0.375f);
	}
	};
	template<typename QNumberType>
	class BlackmanWindow
	: public Window<QNumberType>
	{
	public:
	QNumberType operator()(std::size_t n, std::size_t order) override
	{
	return QNumberType(
	(0.42f - 0.5f * static_cast<float>(math::Cos(2.0 * math::pi * static_cast<double>(n) / static_cast<double>(order))) + 0.08f * static_cast<float>(math::Cos(4.0 * math::pi * static_cast<double>(n) / static_cast<double>(order)))) * 0.9999f);
	}
	QNumberType Power([[maybe_unused]] std::size_t order) override
	{
	return QNumberType(0.305f);
	}
	};

Reproduction

For the implemented two-point Hann window, direct mean-square power is 0.499899983; Power(2) returns 0.375. Welch density is therefore about 33.3% high for this valid segment length.

Acceptance criteria

• Power(N) equals the direct finite sum for every supported window and length.
• Define and document periodic versus symmetric window semantics.
• PSD integrated power agrees with an independent signal-variance reference.
• Replace tests that only repeat the hardcoded constants.