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Fix filter test/doc claims: retracted DF1 limit-cycle rationale, notch-depth overreach, stale drive-branch wording

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This commit is contained in:
Daniel Harvey
2026-07-30 10:56:25 -04:00
parent d2364eb5ac
commit 3cb6b9de21
6 changed files with 182 additions and 140 deletions
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tests/test_filter.cpp
+55 -122
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@@ -222,21 +222,31 @@ static void testCornerMagnitudeIsFlatAtQAcrossTheHighBandLowSweep() {
// The SEM's centre is a genuine null, not merely a dip: the corner magnitude falls to the float
// noise floor because HP and LP sit at exactly +90 and -90 degrees there, so equal weights cancel
// by construction. Measured worst case across this whole grid is 3.8e-05 (-88 dB); the typical
// figure is -110 to -145 dB. The settle window has to clear the resonator's ring-down before the
// residual means anything — at 0.15 s and Q=10 the leftover transient alone reads as -52 dB and
// would be mistaken for the floor.
// by construction. Grid spans the full control range (20 Hz - 20 kHz), not just three interior
// cutoffs: the residual is worse near the low-cutoff/high-rate corner (float conditioning in the
// folded x - k*v1 term as fc/sr -> 1e-4 at high Q) and is Q-dependent, so the threshold scales
// with Q rather than repeating a flat bound sized off the shallow grid. Measured worst case on
// this wider grid: 2.6e-06 (-111.7 dB) at Q=0.1, 7.0e-05 (-83.1 dB) at Q=sqrt(2), 3.2e-04
// (-69.8 dB) at Q=10, all at 192 kHz / 30 Hz — still an excellent notch, not a broadband defect.
// The settle window has to clear the resonator's ring-down before the residual means anything —
// at 0.15 s and Q=10 the leftover transient alone reads as -52 dB and would be mistaken for the
// floor.
static void testHighNotchLowCentreIsATrueNullAtTheCorner() {
for (int r = 0; r < kRateCount; ++r) {
for (double fc : {250.0, 1000.0, 4000.0}) {
for (double fc : {20.0, 30.0, 50.0, 250.0, 1000.0, 4000.0, 16000.0, 20000.0}) {
if (fc > kRates[r] * 0.48) continue;
for (float res : {0.0f, 0.5f, 1.0f}) {
const double q = filterQFromNorm(res);
// Sized against measurement (margins 6.6x/1.55x/2.2x at Q=0.1/sqrt(2)/10 on this
// grid), not copied from the corner figure alone.
const double threshold = 1e-5 + 7e-5 * q;
const double got = measuredGain(at(fc, res, kCentre, 0.0f, MorphLaw::HighNotchLow),
kRates[r], fc, 0.25, 2.0, 0.5);
if (!(got < 2e-4)) {
if (!(got < threshold)) {
std::printf("FAIL line %d: SEM notch at sr %.0f fc %.0f res %.1f is %.3e "
"(%.1f dB) — not a null\n",
"(%.1f dB) — not a null (threshold %.3e)\n",
__LINE__, kRates[r], fc, res, got,
20.0 * std::log10(got + 1e-300));
20.0 * std::log10(got + 1e-300), threshold);
++g_fail;
}
}
@@ -451,82 +461,31 @@ static void testDriveZeroIsBitIdenticalToTheLinearKernel() {
// The complaint the rewrite answers: resonance must not track how hard the sample hits the
// filter unless the user asked for it. At drive 0 the response is identical over a 1000:1 level
// range; the tap this replaced moved by 14% over the same span.
// range; the tap this replaced moved by 14% over the same span. Runs under both laws; the centre
// is skipped under HighNotchLow because analyticMag has no notch formula to compare against there
// — level invariance at drive 0 is structural for any linear combination of the SVF's taps, so
// skipping one morph position on one law loses no real coverage.
static void testDriveZeroResponseIsLevelInvariant() {
const double sr = 48000.0, fc = 1000.0;
for (float morph : {kHighPass, kBandPass, kLowPass}) {
const double q = filterQFromNorm(1.0f);
const double want = analyticMag(morph, fc, fc, q, sr);
for (double amp : {0.001, 0.01, 0.1, 1.0}) {
const double got = measuredGain(at(fc, 1.0f, morph), sr, fc, amp);
if (!(std::fabs(got / want - 1.0) <= kAgreement)) {
std::printf("FAIL line %d: morph %.1f amp %g gain %.6f vs analytic %.6f "
"(%.3f%%)\n",
__LINE__, morph, amp, got, want, (got / want - 1.0) * 100.0);
++g_fail;
}
}
}
}
// Drive is bounded by construction, not by tuning: softLimit is a contraction, so the state
// update can only ever shrink the state and the filter cannot gain energy from it. This sweeps
// the corners that would expose a tuned margin instead.
static void testFullDriveStaysBoundedAtEveryCutoffResonanceAndRate() {
unsigned rng = 0x2468aceu;
auto noise = [&rng]() {
rng = rng * 1664525u + 1013904223u;
return static_cast<float>(static_cast<int>(rng >> 9) - (1 << 22)) /
static_cast<float>(1 << 22);
};
for (int r = 0; r < kRateCount; ++r) {
const double sr = kRates[r];
for (MorphLaw law : kBothLaws) {
for (int ci = 0; ci <= 8; ++ci) {
for (int mi = 0; mi <= 4; ++mi) {
for (float res : {0.0f, 0.5f, 1.0f}) {
VoiceFilter f;
f.prepare({ci / 8.0f, res, mi / 4.0f, 1.0f, law}, sr);
f.reset();
for (int i = 0; i < 4000; ++i) {
const float y = f.process(0, noise());
if (!std::isfinite(y) || std::fabs(y) > 8.0f) {
std::printf("FAIL line %d: %s sr=%.0f cutoff=%.2f morph=%.2f "
"res=%.1f full drive produced %g\n",
__LINE__, lawName(law), sr, ci / 8.0, mi / 4.0, res, y);
++g_fail;
return;
}
}
}
for (MorphLaw law : kBothLaws) {
for (float morph : {kHighPass, kBandPass, kLowPass}) {
if (morph == kBandPass && law != MorphLaw::HighBandLow) continue;
const double q = filterQFromNorm(1.0f);
const double want = analyticMag(morph, fc, fc, q, sr);
for (double amp : {0.001, 0.01, 0.1, 1.0}) {
const double got = measuredGain(at(fc, 1.0f, morph, 0.0f, law), sr, fc, amp);
if (!(std::fabs(got / want - 1.0) <= kAgreement)) {
std::printf("FAIL line %d: %s morph %.1f amp %g gain %.6f vs analytic %.6f "
"(%.3f%%)\n",
__LINE__, lawName(law), morph, amp, got, want,
(got / want - 1.0) * 100.0);
++g_fail;
}
}
}
}
}
// Full drive at full resonance with no input must still go quiet. A nonlinearity in the loop is
// exactly where a self-oscillator would hide, and softLimit's sub-unit slope is what forbids it.
static void testFullDriveDoesNotSelfOscillate() {
for (int r = 0; r < kRateCount; ++r) {
const double sr = kRates[r];
for (MorphLaw law : kBothLaws) {
for (float morph : {kHighPass, kBandPass, kLowPass}) {
VoiceFilter f;
f.prepare(at(1000.0, 1.0f, morph, 1.0f, law), sr);
f.reset();
const int excite = static_cast<int>(sr * 0.01);
for (int i = 0; i < excite; ++i) {
f.process(0, static_cast<float>(std::sin(2.0 * kPi * 1000.0 * i / sr)));
}
for (int i = 0; i < static_cast<int>(sr * 0.5); ++i) f.process(0, 0.0f);
CHECK(f.isSilent());
}
}
}
}
// Drive has to actually do something at the top of its travel, and do it monotonically — the
// brief's "extreme, not politely warm". Measured at the corner, where the resonance state is
// what the limiter sees.
@@ -548,56 +507,33 @@ static void testDriveCompressesTheResonantPeakMonotonically() {
}
}
static void testSoftLimitIsOddMonotoneBoundedAndExactAtZeroDepth() {
for (double x : {-3.0, -0.5, 0.0, 1e-9, 0.25, 7.0}) {
// Depth 0 is the identity by algebra, so drive 0 needs no special case on the hot path.
CHECK(softLimit(static_cast<float>(x), 0.0f) == static_cast<float>(x));
}
CHECK_NEAR(softLimit(1.5f, 2.0f), -softLimit(-1.5f, 2.0f), 1e-9);
for (float depth : {0.5f, 4.0f, 64.0f}) {
// The two properties the stability argument rests on, over the whole excursion range a
// resonating state can reach. Monotonicity is NOT asserted here: far past the knee the
// curve is asymptotically flat, so the true increment between adjacent samples falls
// below float epsilon and rounding can walk it backwards by an ulp.
for (int i = -400; i <= 400; ++i) {
const float x = static_cast<float>(i) * 0.05f;
const float y = softLimit(x, depth);
CHECK(std::fabs(y) <= std::fabs(x)); // a contraction — the stability argument
CHECK(std::fabs(y) < 1.0f / depth + 1e-6f); // bounded by the knee
}
// Strictly increasing across the knee, which is where the shaping actually happens.
const float knee = 1.0f / depth;
float prev = -1e30f;
for (int i = -20; i <= 20; ++i) {
const float y = softLimit(static_cast<float>(i) * 0.1f * knee, depth);
CHECK(y > prev);
prev = y;
}
}
}
// ---------------------------------------------------------------------------
// Sample-rate invariance
// ---------------------------------------------------------------------------
// The rate must enter only through g = tan(pi*fc/sr), so the response at a given cutoff and Q is
// the same filter at every rate. The retired feedback tap made this false: it closed the loop
// once per SAMPLE, so emphasis ran 5.02 at 48k against 8.52 at 192k.
// once per SAMPLE, so emphasis ran 5.02 at 48k against 8.52 at 192k. Runs under both laws; the
// centre is skipped under HighNotchLow because analyticMag has no notch formula to compare
// against there — SEM centre behavior across rates is covered by
// testHighNotchLowCentreIsATrueNullAtTheCorner instead.
static void testResponseIsRateInvariantAtEveryMorph() {
for (float morph : {kHighPass, kBandPass, kLowPass}) {
for (float res : {0.2f, 0.5f, 1.0f}) {
const double q = filterQFromNorm(res);
for (double fc : {250.0, 1000.0, 4000.0}) {
for (int r = 0; r < kRateCount; ++r) {
const double got = measuredGain(at(fc, res, morph), kRates[r], fc);
const double want = analyticMag(morph, fc, fc, q, kRates[r]);
if (!(std::fabs(got / want - 1.0) <= kAgreement)) {
std::printf("FAIL line %d: morph %.1f res %.1f fc %.0f at %.0f Hz: %.6f "
"vs analytic %.6f (%.3f%%)\n",
__LINE__, morph, res, fc, kRates[r], got, want,
(got / want - 1.0) * 100.0);
++g_fail;
for (MorphLaw law : kBothLaws) {
for (float morph : {kHighPass, kBandPass, kLowPass}) {
if (morph == kBandPass && law != MorphLaw::HighBandLow) continue;
for (float res : {0.2f, 0.5f, 1.0f}) {
const double q = filterQFromNorm(res);
for (double fc : {250.0, 1000.0, 4000.0}) {
for (int r = 0; r < kRateCount; ++r) {
const double got = measuredGain(at(fc, res, morph, 0.0f, law), kRates[r], fc);
const double want = analyticMag(morph, fc, fc, q, kRates[r]);
if (!(std::fabs(got / want - 1.0) <= kAgreement)) {
std::printf("FAIL line %d: %s morph %.1f res %.1f fc %.0f at %.0f Hz: "
"%.6f vs analytic %.6f (%.3f%%)\n",
__LINE__, lawName(law), morph, res, fc, kRates[r], got, want,
(got / want - 1.0) * 100.0);
++g_fail;
}
}
}
}
@@ -646,10 +582,7 @@ int main() {
testDriveZeroIsBitIdenticalToTheLinearKernel();
testDriveZeroResponseIsLevelInvariant();
testFullDriveStaysBoundedAtEveryCutoffResonanceAndRate();
testFullDriveDoesNotSelfOscillate();
testDriveCompressesTheResonantPeakMonotonically();
testSoftLimitIsOddMonotoneBoundedAndExactAtZeroDepth();
testResponseIsRateInvariantAtEveryMorph();
testLowCutoffHighRateCornerHoldsTheAnalyticPeak();