diff --git a/lib/trends_IIR/ema/ema.py b/lib/trends_IIR/ema/ema.py
new file mode 100644
index 00000000..02489c00
--- /dev/null
+++ b/lib/trends_IIR/ema/ema.py
@@ -0,0 +1,68 @@
+"""Exponential Moving Average — bias-compensated, NaN-safe.
+
+Algorithm (mirrors Ema.cs):
+
+    alpha  = 2 / (period + 1)
+    decay  = 1 - alpha
+
+    For each bar:
+        ema   = ema * decay + alpha * value
+        E    *= decay
+        result = ema / (1 - E)      while E > epsilon
+        result = ema                 after warmup
+"""
+
+import math
+
+import numpy as np
+
+__all__ = ["ema"]
+
+EPSILON = 1e-10  # bias-compensator cutoff
+
+
+def ema(source, period: int = 10, *, alpha: float | None = None) -> np.ndarray:
+    """Bias-compensated EMA.
+
+    Use *period* (default) or explicit *alpha* (keyword-only).
+    If *alpha* is given, *period* is ignored.
+    """
+    if alpha is not None:
+        if not (0.0 < alpha <= 1.0):
+            raise ValueError(f"alpha must be in (0, 1], got {alpha}")
+    else:
+        if period <= 0:
+            raise ValueError(f"period must be > 0, got {period}")
+        alpha = 2.0 / (period + 1)
+
+    src = np.asarray(source, dtype=np.float64)
+    if src.ndim == 0 or src.size == 0:
+        raise ValueError("source must not be empty")
+    src = src.ravel()
+
+    out = np.empty(len(src), dtype=np.float64)
+    decay = 1.0 - alpha
+    ema_val = 0.0
+    e = 1.0
+    last_valid = 0.0
+    has_valid = False
+
+    for i, v in enumerate(src):
+        if math.isfinite(v):
+            last_valid = v
+            has_valid = True
+        elif has_valid:
+            v = last_valid
+        else:
+            out[i] = math.nan
+            continue
+
+        ema_val = ema_val * decay + alpha * v
+
+        if e > EPSILON:
+            e *= decay
+            out[i] = ema_val / (1.0 - e)
+        else:
+            out[i] = ema_val
+
+    return out
diff --git a/lib/trends_IIR/ema/ema_test.py b/lib/trends_IIR/ema/ema_test.py
new file mode 100644
index 00000000..e0c28f0a
--- /dev/null
+++ b/lib/trends_IIR/ema/ema_test.py
@@ -0,0 +1,143 @@
+"""Unit tests for pure-Python EMA implementation.
+
+Per PYTHON_FALLBACK_SPEC §5: co-located <indicator>_test.py
+
+Run::
+
+    pytest lib/trends_IIR/ema/ema_test.py -v
+"""
+
+import math
+import sys
+from pathlib import Path
+
+import numpy as np
+import pytest
+
+# Import from co-located ema.py
+sys.path.insert(0, str(Path(__file__).parent))
+from ema import ema  # noqa: E402
+
+
+# ── basic correctness ──
+
+def test_known_values():
+    """Hand-calculated EMA(3) with bias compensation.
+
+    alpha=0.5, decay=0.5:
+    Bar 0: acc = 0.5*10 = 5,   E = 0.5,   result = 5/0.5 = 10.0
+    Bar 1: acc = 5*0.5 + 0.5*20 = 12.5,  E = 0.25,  result = 12.5/0.75 ≈ 16.667
+    Bar 2: acc = 12.5*0.5 + 0.5*30 = 21.25,  E = 0.125,  result = 21.25/0.875 ≈ 24.286
+    """
+    data = np.array([10.0, 20.0, 30.0, 40.0, 50.0])
+    result = ema(data, period=3)
+    assert result[0] == pytest.approx(10.0, rel=1e-12)
+    assert result[1] == pytest.approx(16.666666666666668, rel=1e-10)
+    assert result[2] == pytest.approx(24.285714285714285, rel=1e-10)
+
+
+def test_period_1():
+    """Period=1 → alpha=1.0 → output equals input (no smoothing)."""
+    data = np.array([10.0, 20.0, 30.0, 40.0, 50.0])
+    result = ema(data, period=1)
+    np.testing.assert_array_equal(result, data)
+
+
+def test_constant_input():
+    """Constant 100.0 through any EMA → always 100.0."""
+    data = np.full(100, 100.0)
+    result = ema(data, period=20)
+    np.testing.assert_allclose(result, 100.0, rtol=1e-12)
+
+
+# ── edge cases ──
+
+def test_empty_array():
+    """Empty input → raises ValueError."""
+    with pytest.raises(ValueError, match="must not be empty"):
+        ema(np.array([]), period=5)
+
+
+def test_invalid_period():
+    """Period ≤ 0 → raises ValueError."""
+    with pytest.raises(ValueError, match="period must be > 0"):
+        ema(np.array([1.0, 2.0, 3.0]), period=0)
+    with pytest.raises(ValueError, match="period must be > 0"):
+        ema(np.array([1.0, 2.0, 3.0]), period=-1)
+
+
+def test_single_element():
+    """Single-element input returns that element."""
+    result = ema([42.0], period=10)
+    assert len(result) == 1
+    assert result[0] == pytest.approx(42.0, rel=1e-12)
+
+
+# ── NaN handling ──
+
+def test_nan_in_input():
+    """NaN replaced with last valid value → output stays finite."""
+    data = np.array([10.0, 20.0, np.nan, 40.0, 50.0])
+    result = ema(data, period=3)
+    assert all(math.isfinite(v) for v in result)
+
+
+def test_all_nan_returns_nan():
+    """All-NaN input → all-NaN output."""
+    data = np.full(5, np.nan)
+    result = ema(data, period=3)
+    assert all(math.isnan(v) for v in result)
+
+
+def test_inf_handled():
+    """Inf replaced with last valid value."""
+    data = np.array([10.0, 20.0, np.inf, 40.0, 50.0])
+    result = ema(data, period=3)
+    assert all(math.isfinite(v) for v in result)
+
+
+# ── output shape & warmup ──
+
+def test_output_length_matches_input():
+    """len(output) == len(input)."""
+    data = np.random.default_rng(42).normal(100, 5, size=200)
+    result = ema(data, period=14)
+    assert len(result) == 200
+
+
+def test_first_bar_always_valid():
+    """Bias compensation means EMA produces valid output from bar 0."""
+    data = np.random.default_rng(42).normal(100, 5, size=50)
+    result = ema(data, period=50)
+    assert math.isfinite(result[0])
+
+
+# ── numerical precision ──
+
+def test_large_values():
+    """No overflow with 1e300 values."""
+    data = np.full(100, 1e300)
+    result = ema(data, period=10)
+    np.testing.assert_allclose(result, 1e300, rtol=1e-10)
+
+
+def test_tiny_values():
+    """No underflow with 1e-300 values."""
+    data = np.full(100, 1e-300)
+    result = ema(data, period=10)
+    np.testing.assert_allclose(result, 1e-300, rtol=1e-10)
+
+
+def test_10k_series_all_finite():
+    """Long series stays finite (no drift)."""
+    data = np.random.default_rng(42).normal(100, 10, size=10_000)
+    result = ema(data, period=20)
+    assert np.all(np.isfinite(result))
+
+
+def test_alpha_from_period_equivalence():
+    """ema(period=N) == ema(alpha=2/(N+1))."""
+    data = np.random.default_rng(42).normal(100, 5, size=200)
+    r1 = ema(data, period=14)
+    r2 = ema(data, alpha=2.0 / 15.0)
+    np.testing.assert_allclose(r1, r2, rtol=1e-14)
diff --git a/lib/trends_IIR/ema/tests/test_ema.py b/lib/trends_IIR/ema/tests/test_ema.py
new file mode 100644
index 00000000..30a2d753
--- /dev/null
+++ b/lib/trends_IIR/ema/tests/test_ema.py
@@ -0,0 +1,337 @@
+"""Tests for the pure-Python EMA implementation.
+
+Validates that ``ema.py`` produces results matching the C# ``Ema.Batch``
+algorithm, including bias compensation, NaN handling, and edge cases.
+
+Run with::
+
+    python -m pytest lib/trends_IIR/ema/tests/test_ema.py -v
+"""
+
+import math
+import sys
+from pathlib import Path
+
+import numpy as np
+import pytest
+
+# ── ensure the ema module is importable ──────────────────────────────────
+# The ema.py lives one directory up from tests/
+_EMA_DIR = Path(__file__).resolve().parent.parent
+if str(_EMA_DIR) not in sys.path:
+    sys.path.insert(0, str(_EMA_DIR))
+
+from ema import ema  # noqa: E402
+
+
+# ═════════════════════════════════════════════════════════════════════════
+#  Fixtures
+# ═════════════════════════════════════════════════════════════════════════
+
+@pytest.fixture
+def constant_series() -> np.ndarray:
+    """100 bars of constant value 50.0."""
+    return np.full(100, 50.0)
+
+
+@pytest.fixture
+def ramp_series() -> np.ndarray:
+    """50 bars ramping 1..50."""
+    return np.arange(1.0, 51.0)
+
+
+@pytest.fixture
+def short_series() -> np.ndarray:
+    """10 bars: [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]."""
+    return np.arange(10.0, 110.0, 10.0)
+
+
+# ═════════════════════════════════════════════════════════════════════════
+#  Input validation
+# ═════════════════════════════════════════════════════════════════════════
+
+class TestInputValidation:
+    """Guard clauses match C# ArgumentOutOfRangeException behavior."""
+
+    def test_period_zero_raises(self) -> None:
+        with pytest.raises(ValueError, match="period must be > 0"):
+            ema([1.0, 2.0], period=0)
+
+    def test_period_negative_raises(self) -> None:
+        with pytest.raises(ValueError, match="period must be > 0"):
+            ema([1.0, 2.0], period=-5)
+
+    def test_alpha_zero_raises(self) -> None:
+        with pytest.raises(ValueError, match="alpha must be in"):
+            ema([1.0, 2.0], alpha=0.0)
+
+    def test_alpha_negative_raises(self) -> None:
+        with pytest.raises(ValueError, match="alpha must be in"):
+            ema([1.0, 2.0], alpha=-0.1)
+
+    def test_alpha_above_one_raises(self) -> None:
+        with pytest.raises(ValueError, match="alpha must be in"):
+            ema([1.0, 2.0], alpha=1.01)
+
+    def test_alpha_exactly_one_ok(self) -> None:
+        result = ema([5.0, 10.0, 15.0], alpha=1.0)
+        # alpha=1 means output == input (no smoothing)
+        np.testing.assert_array_equal(result, [5.0, 10.0, 15.0])
+
+    def test_empty_source_raises(self) -> None:
+        with pytest.raises(ValueError, match="must not be empty"):
+            ema([], period=10)
+
+    def test_scalar_source_raises(self) -> None:
+        with pytest.raises(ValueError, match="must not be empty"):
+            ema(np.float64(5.0), period=10)
+
+
+# ═════════════════════════════════════════════════════════════════════════
+#  Output shape
+# ═════════════════════════════════════════════════════════════════════════
+
+class TestOutputShape:
+    """Output array must match input length exactly."""
+
+    def test_length_equals_input(self, ramp_series: np.ndarray) -> None:
+        result = ema(ramp_series, period=10)
+        assert len(result) == len(ramp_series)
+
+    def test_single_element(self) -> None:
+        result = ema([42.0], period=5)
+        assert len(result) == 1
+
+    def test_dtype_float64(self, ramp_series: np.ndarray) -> None:
+        result = ema(ramp_series, period=10)
+        assert result.dtype == np.float64
+
+    def test_accepts_list_input(self) -> None:
+        result = ema([1.0, 2.0, 3.0], period=2)
+        assert len(result) == 3
+
+    def test_accepts_tuple_input(self) -> None:
+        result = ema((1.0, 2.0, 3.0), period=2)
+        assert len(result) == 3
+
+
+# ═════════════════════════════════════════════════════════════════════════
+#  Bias compensation correctness
+# ═════════════════════════════════════════════════════════════════════════
+
+class TestBiasCompensation:
+    """Verify the warmup compensator E = (1-α)^t produces valid early values."""
+
+    def test_first_bar_equals_input(self) -> None:
+        """EMA(bar_0) must equal the input itself (compensated to 1×input)."""
+        result = ema([100.0, 200.0, 300.0], period=10)
+        # After compensation: ema_acc = alpha * 100, E = decay
+        # result[0] = (alpha * 100) / (1 - decay) = (alpha * 100) / alpha = 100
+        assert result[0] == pytest.approx(100.0, rel=1e-12)
+
+    def test_constant_series_converges_to_constant(
+        self, constant_series: np.ndarray
+    ) -> None:
+        """On constant input, every bar should equal the constant."""
+        result = ema(constant_series, period=10)
+        np.testing.assert_allclose(result, 50.0, rtol=1e-12)
+
+    def test_compensator_eliminates_zero_bias(self) -> None:
+        """Without compensation, starting from ema=0 would bias downward.
+        With compensation, bar 1 on a constant 100 series must be 100."""
+        result = ema(np.full(5, 100.0), period=20)
+        # Every value should be exactly 100.0 (constant input)
+        np.testing.assert_allclose(result, 100.0, rtol=1e-12)
+
+    def test_period_1_passthrough(self) -> None:
+        """Period=1 → alpha=1.0 → output equals input."""
+        data = np.array([10.0, 20.0, 30.0, 40.0, 50.0])
+        result = ema(data, period=1)
+        np.testing.assert_array_equal(result, data)
+
+
+# ═════════════════════════════════════════════════════════════════════════
+#  EMA mathematical properties
+# ═════════════════════════════════════════════════════════════════════════
+
+class TestMathProperties:
+    """Verify EMA satisfies known mathematical properties."""
+
+    def test_monotone_input_monotone_output(self, ramp_series: np.ndarray) -> None:
+        """Strictly increasing input → strictly increasing EMA."""
+        result = ema(ramp_series, period=10)
+        diffs = np.diff(result)
+        assert np.all(diffs > 0), "EMA of monotone-increasing input must increase"
+
+    def test_ema_lags_behind_ramp(self, ramp_series: np.ndarray) -> None:
+        """EMA of increasing ramp must be ≤ the source (lag property)."""
+        result = ema(ramp_series, period=10)
+        # After first bar, EMA should lag behind
+        assert np.all(result[1:] <= ramp_series[1:] + 1e-10)
+
+    def test_ema_between_min_and_max(self, ramp_series: np.ndarray) -> None:
+        """EMA output must lie within [min(source), max(source)]."""
+        result = ema(ramp_series, period=10)
+        assert np.all(result >= ramp_series.min() - 1e-10)
+        assert np.all(result <= ramp_series.max() + 1e-10)
+
+    def test_alpha_from_period(self) -> None:
+        """ema(period=N) must equal ema(alpha=2/(N+1))."""
+        data = np.random.default_rng(42).normal(100, 5, size=200)
+        r1 = ema(data, period=14)
+        r2 = ema(data, alpha=2.0 / 15.0)
+        np.testing.assert_allclose(r1, r2, rtol=1e-14)
+
+    def test_larger_period_smoother(self) -> None:
+        """Larger period → less variance in the output."""
+        data = np.random.default_rng(99).normal(100, 10, size=500)
+        r5 = ema(data, period=5)
+        r50 = ema(data, period=50)
+        # Skip warmup region; use last 300 bars
+        assert np.std(r50[-300:]) < np.std(r5[-300:])
+
+
+# ═════════════════════════════════════════════════════════════════════════
+#  NaN / Inf handling
+# ═════════════════════════════════════════════════════════════════════════
+
+class TestNanHandling:
+    """NaN/Inf inputs are replaced with last valid value (C# GetValidValue)."""
+
+    def test_nan_in_middle(self) -> None:
+        data = np.array([10.0, 20.0, np.nan, 40.0, 50.0])
+        result = ema(data, period=3)
+        assert all(math.isfinite(v) for v in result)
+
+    def test_inf_in_middle(self) -> None:
+        data = np.array([10.0, 20.0, np.inf, 40.0, 50.0])
+        result = ema(data, period=3)
+        assert all(math.isfinite(v) for v in result)
+
+    def test_neg_inf_in_middle(self) -> None:
+        data = np.array([10.0, 20.0, -np.inf, 40.0, 50.0])
+        result = ema(data, period=3)
+        assert all(math.isfinite(v) for v in result)
+
+    def test_nan_at_start_skipped(self) -> None:
+        """Leading NaNs use last_valid = 0 until a finite value arrives."""
+        data = np.array([np.nan, np.nan, 100.0, 200.0, 300.0])
+        result = ema(data, period=3)
+        # First two bars use last_valid=0 initially, then seed
+        # After 100.0 arrives, behavior normalizes
+        assert math.isfinite(result[2])
+        assert math.isfinite(result[4])
+
+    def test_all_nan_returns_nan(self) -> None:
+        """If every value is NaN, output must be all NaN."""
+        data = np.full(5, np.nan)
+        result = ema(data, period=3)
+        assert all(math.isnan(v) for v in result)
+
+    def test_all_inf_returns_nan(self) -> None:
+        """If every value is Inf, no valid seed → all NaN."""
+        data = np.full(5, np.inf)
+        result = ema(data, period=3)
+        assert all(math.isnan(v) for v in result)
+
+
+# ═════════════════════════════════════════════════════════════════════════
+#  Golden values (hand-calculated reference)
+# ═════════════════════════════════════════════════════════════════════════
+
+class TestGoldenValues:
+    """Verify against hand-calculated EMA with bias compensation.
+
+    For period=3, alpha=0.5, decay=0.5:
+    Bar 0: ema_acc = 0.5*10 = 5,   E = 0.5,   result = 5/(1-0.5) = 10.0
+    Bar 1: ema_acc = 5*0.5 + 0.5*20 = 12.5,  E = 0.25,  result = 12.5/0.75 ≈ 16.6667
+    Bar 2: ema_acc = 12.5*0.5 + 0.5*30 = 21.25,  E = 0.125,  result = 21.25/0.875 ≈ 24.2857
+    """
+
+    def test_period_3_first_three_bars(self) -> None:
+        data = np.array([10.0, 20.0, 30.0, 40.0, 50.0])
+        result = ema(data, period=3)
+
+        assert result[0] == pytest.approx(10.0, rel=1e-12)
+        assert result[1] == pytest.approx(16.666666666666668, rel=1e-10)
+        assert result[2] == pytest.approx(24.285714285714285, rel=1e-10)
+
+    def test_period_5_constant_100(self) -> None:
+        """Constant 100 through EMA(5) → all 100.0."""
+        data = np.full(20, 100.0)
+        result = ema(data, period=5)
+        np.testing.assert_allclose(result, 100.0, rtol=1e-12)
+
+    def test_ema_alpha_direct(self) -> None:
+        """ema(alpha=0.5) on [10,20,30] → same as period=3."""
+        data = np.array([10.0, 20.0, 30.0])
+        r1 = ema(data, period=3)
+        r2 = ema(data, alpha=0.5)
+        np.testing.assert_allclose(r1, r2, rtol=1e-14)
+
+
+# ═════════════════════════════════════════════════════════════════════════
+#  Stability and performance
+# ═════════════════════════════════════════════════════════════════════════
+
+class TestStability:
+    """Long series shouldn't drift or produce non-finite values."""
+
+    def test_10k_bars_all_finite(self) -> None:
+        rng = np.random.default_rng(42)
+        data = rng.normal(100, 10, size=10_000)
+        result = ema(data, period=20)
+        assert np.all(np.isfinite(result))
+
+    def test_large_values_no_overflow(self) -> None:
+        data = np.full(100, 1e300)
+        result = ema(data, period=10)
+        np.testing.assert_allclose(result, 1e300, rtol=1e-10)
+
+    def test_tiny_values_no_underflow(self) -> None:
+        data = np.full(100, 1e-300)
+        result = ema(data, period=10)
+        np.testing.assert_allclose(result, 1e-300, rtol=1e-10)
+
+    def test_alternating_sign(self) -> None:
+        """Alternating +100 / -100 should converge toward 0 for large period."""
+        data = np.array([100.0, -100.0] * 500)
+        result = ema(data, period=100)
+        # Last few values should be near zero
+        assert abs(result[-1]) < 20.0
+
+
+# ═════════════════════════════════════════════════════════════════════════
+#  Cross-validation with C# native (when available)
+# ═════════════════════════════════════════════════════════════════════════
+
+class TestCrossValidation:
+    """Compare pure Python EMA against NativeAOT EMA (skipped if unavailable)."""
+
+    @pytest.fixture
+    def native_ema(self):
+        """Try to import the native EMA wrapper."""
+        try:
+            from quantalib.trends_iir import ema as native_ema_fn
+            return native_ema_fn
+        except (ImportError, OSError):
+            pytest.skip("quantalib native lib not available")
+
+    def test_matches_native_random_data(self, native_ema) -> None:
+        rng = np.random.default_rng(12345)
+        data = rng.normal(100, 10, size=500)
+        py_result = ema(data, period=14)
+        native_result = native_ema(data, period=14)
+
+        # Convert native result to numpy if needed
+        native_arr = np.asarray(native_result, dtype=np.float64)
+        np.testing.assert_allclose(py_result, native_arr, rtol=1e-10,
+                                   err_msg="Python EMA diverges from native")
+
+    def test_matches_native_with_nans(self, native_ema) -> None:
+        data = np.array([10.0, np.nan, 30.0, 40.0, np.nan, 60.0, 70.0])
+        py_result = ema(data, period=3)
+        native_result = native_ema(data, period=3)
+        native_arr = np.asarray(native_result, dtype=np.float64)
+        np.testing.assert_allclose(py_result, native_arr, rtol=1e-10,
+                                   err_msg="NaN handling diverges from native")