[AUD-021][High] Correct FIR simulator band-pass construction

[gabrielsantosphilips]

Audit finding

• ID: AUD-021
• Status: Verified defect
• Severity: High
• Confidence: High
• Audited revision: 2f479320d805a1f9f35ebe4afaaeeded48913a94

Problem

The FIR simulator converts the low-cutoff low-pass kernel into a high-pass kernel, then computes LP(high) - HP(low). At DC this is approximately one, but a band-pass response must be zero. The spectral subtraction should be LP(high) - LP(low).

Source:

numerical-toolbox-cpp/simulator/filters/FirFilter/application/FirFilterSimulator.cpp

Lines 137 to 160 in 2f47932

	lowpass[mid] += 1.0f;
	return lowpass;
	}
	case FilterType::BandPass:
	{
	auto normalizedLow = design.cutoffHz / design.sampleRateHz;
	auto normalizedHigh = design.cutoffHighHz / design.sampleRateHz;
	auto highpass = WindowedSinc(design.order, normalizedHigh);
	auto lowpass = WindowedSinc(design.order, normalizedLow);
	auto mid = (design.order - 1) / 2;
	for (std::size_t i = 0; i < lowpass.size(); ++i)
	lowpass[i] = -lowpass[i];
	lowpass[mid] += 1.0f;
	std::vector<float> bandpass(design.order);
	for (std::size_t i = 0; i < design.order; ++i)
	bandpass[i] = highpass[i] - lowpass[i];
	return bandpass;
	}
	default:
	return WindowedSinc(design.order, normalizedCutoff);

Acceptance criteria

• Construct the band-pass from two low-pass prototypes with correct cutoff ordering.
• DC and Nyquist response are attenuated; center-band response matches an independent reference.
• Reject invalid cutoff ordering and cutoff above Nyquist.
• Add simulator-domain coefficient and response tests.

[gabrielfrasantos]

Fixed and merged in #325 (d71b05f on main).

The variable naming hid the bug: highpass was the low-pass kernel at the high cutoff, while lowpass had been negated in place into a high-pass at the low cutoff, so highpass[i] - lowpass[i] computed LP(high) - HP(low). That is not merely wrong at DC, it is the exact inverse of a band-pass. Evaluating the old and new kernels for order 65, cutoffs 0.1 and 0.3:

	DC	centre (0.2)	Nyquist
old	1.0000	0.0000	1.0005
new	0.0000	1.0000	0.0021

The old construction passed DC and Nyquist and rejected the centre of the band.

It now subtracts two low-pass prototypes, LP(high) - LP(low), with no in-place negation, and rejects invalid cutoff ordering (low not below high, high at or above Nyquist, non-positive low) by returning a zero kernel rather than producing a nonsense filter.

On the last criterion, simulator-domain coefficient and response tests: not added. The simulator has no test target and this environment has no Qt to build it, so the numbers above come from evaluating the kernel construction directly rather than from a checked-in test. That is a real gap, not a judgement that it was unnecessary.

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