diff --git a/scipy-stubs/signal/_waveforms.pyi b/scipy-stubs/signal/_waveforms.pyi
index 11389919..4886184b 100644
--- a/scipy-stubs/signal/_waveforms.pyi
+++ b/scipy-stubs/signal/_waveforms.pyi
@@ -1,26 +1,229 @@
-from scipy._typing import Untyped
+from collections.abc import Iterable
+from typing import Any, Literal, TypeAlias, TypeVar, overload
+
+import numpy as np
+import numpy.typing as npt
+import optype as op
+import optype.numpy as onp
+from numpy._typing import _DTypeLike
+from scipy._typing import AnyShape
 
 __all__ = ["chirp", "gausspulse", "sawtooth", "square", "sweep_poly", "unit_impulse"]
 
-def sawtooth(t: Untyped, width: int = 1) -> Untyped: ...
-def square(t: Untyped, duty: float = 0.5) -> Untyped: ...
-def gausspulse(
-    t: Untyped,
-    fc: int = 1000,
-    bw: float = 0.5,
-    bwr: int = -6,
-    tpr: int = -60,
-    retquad: bool = False,
-    retenv: bool = False,
-) -> Untyped: ...
+_SCT = TypeVar("_SCT", bound=np.generic)
+
+_Truthy: TypeAlias = Literal[1, True]
+_Falsy: TypeAlias = Literal[0, False]
+_ArrayLikeFloat: TypeAlias = onp.ToFloat | onp.ToFloatND
+_Array_f: TypeAlias = onp.ArrayND[np.floating[Any]]
+_Array_f8: TypeAlias = onp.ArrayND[np.float64]
+
+_ChirpMethod: TypeAlias = Literal["linear", "quadratic", "logarithmic", "hyperbolic"]
+
+def sawtooth(t: _ArrayLikeFloat, width: _ArrayLikeFloat = 1) -> _Array_f8: ...
+def square(t: _ArrayLikeFloat, duty: _ArrayLikeFloat = 0.5) -> _Array_f8: ...
+
+#
+@overload  # Arrays
+def chirp(
+    t: onp.ToFloatND,
+    f0: onp.ToFloat,
+    t1: onp.ToFloat,
+    f1: onp.ToFloat,
+    method: _ChirpMethod = "linear",
+    phi: onp.ToFloat = 0,
+    vertex_zero: op.CanBool = True,
+) -> _Array_f: ...
+@overload  # Scalars
 def chirp(
-    t: Untyped,
-    f0: Untyped,
-    t1: Untyped,
-    f1: Untyped,
-    method: str = "linear",
-    phi: int = 0,
-    vertex_zero: bool = True,
-) -> Untyped: ...
-def sweep_poly(t: Untyped, poly: Untyped, phi: int = 0) -> Untyped: ...
-def unit_impulse(shape: Untyped, idx: Untyped | None = None, dtype: Untyped = ...) -> Untyped: ...
+    t: onp.ToFloat,
+    f0: onp.ToFloat,
+    t1: onp.ToFloat,
+    f1: onp.ToFloat,
+    method: _ChirpMethod = "linear",
+    phi: onp.ToFloat = 0,
+    vertex_zero: op.CanBool = True,
+) -> np.floating[Any]: ...
+
+#
+def sweep_poly(
+    t: _ArrayLikeFloat,
+    poly: onp.ToFloatND | np.poly1d,
+    phi: onp.ToFloat = 0,
+) -> _Array_f8: ...
+
+#
+@overload  # dtype is not given
+def unit_impulse(
+    shape: AnyShape,
+    idx: op.CanIndex | Iterable[op.CanIndex] | Literal["mid"] | None = None,
+    dtype: type[float] = ...,
+) -> _Array_f8: ...
+@overload  # dtype is given
+def unit_impulse(
+    shape: AnyShape,
+    idx: op.CanIndex | Iterable[op.CanIndex] | Literal["mid"] | None,
+    dtype: _DTypeLike[_SCT],
+) -> npt.NDArray[_SCT]: ...
+
+# Overloads for gausspulse when `t` is `"cutoff"`
+@overload  # retquad: False = ..., retenv: False = ...
+def gausspulse(
+    t: Literal["cutoff"],
+    fc: onp.ToFloat = 1000,
+    bw: onp.ToFloat = 0.5,
+    bwr: onp.ToFloat = -6,
+    tpr: onp.ToFloat = -60,
+    retquad: op.CanBool = False,
+    retenv: op.CanBool = False,
+) -> np.float64: ...
+
+# Overloads for gausspulse when `t` is scalar
+@overload  # retquad: False = ..., retenv: False = ...
+def gausspulse(
+    t: onp.ToFloat,
+    fc: onp.ToFloat = 1000,
+    bw: onp.ToFloat = 0.5,
+    bwr: onp.ToFloat = -6,
+    tpr: onp.ToFloat = -60,
+    retquad: _Falsy = False,
+    retenv: _Falsy = False,
+) -> np.float64: ...
+@overload  # retquad: False = ..., retenv: True (keyword)
+def gausspulse(
+    t: onp.ToFloat,
+    fc: onp.ToFloat = 1000,
+    bw: onp.ToFloat = 0.5,
+    bwr: onp.ToFloat = -6,
+    tpr: onp.ToFloat = -60,
+    retquad: _Falsy = False,
+    *,
+    retenv: _Truthy,
+) -> tuple[np.float64, np.float64]: ...
+@overload  # retquad: False (positional), retenv: False (positional)
+def gausspulse(
+    t: onp.ToFloat,
+    fc: onp.ToFloat,
+    bw: onp.ToFloat,
+    bwr: onp.ToFloat,
+    tpr: onp.ToFloat,
+    retquad: _Falsy,
+    retenv: _Truthy,
+) -> tuple[np.float64, np.float64]: ...
+@overload  # retquad: True (positional), retenv: False = ...
+def gausspulse(
+    t: onp.ToFloat,
+    fc: onp.ToFloat,
+    bw: onp.ToFloat,
+    bwr: onp.ToFloat,
+    tpr: onp.ToFloat,
+    retquad: _Truthy,
+    retenv: _Falsy = False,
+) -> tuple[np.float64, np.float64]: ...
+@overload  # retquad: True (keyword), retenv: False = ...
+def gausspulse(
+    t: onp.ToFloat,
+    fc: onp.ToFloat = 1000,
+    bw: onp.ToFloat = 0.5,
+    bwr: onp.ToFloat = -6,
+    tpr: onp.ToFloat = -60,
+    *,
+    retquad: _Truthy,
+    retenv: _Falsy = False,
+) -> tuple[np.float64, np.float64]: ...
+@overload  # retquad: True (positional), retenv: True (positional/keyword)
+def gausspulse(
+    t: onp.ToFloat,
+    fc: onp.ToFloat,
+    bw: onp.ToFloat,
+    bwr: onp.ToFloat,
+    tpr: onp.ToFloat,
+    retquad: _Truthy,
+    retenv: _Truthy,
+) -> tuple[np.float64, np.float64, np.float64]: ...
+@overload  # retquad: True (keyword), retenv: True
+def gausspulse(
+    t: onp.ToFloat,
+    fc: onp.ToFloat = 1000,
+    bw: onp.ToFloat = 0.5,
+    bwr: onp.ToFloat = -6,
+    tpr: onp.ToFloat = -60,
+    *,
+    retquad: _Truthy,
+    retenv: _Truthy,
+) -> tuple[np.float64, np.float64, np.float64]: ...
+
+# Overloads for `gausspulse` when `t` is a non-scalar array like
+@overload  # retquad: False = ..., retenv: False = ...
+def gausspulse(
+    t: onp.ToFloatND,
+    fc: onp.ToFloat = 1000,
+    bw: onp.ToFloat = 0.5,
+    bwr: onp.ToFloat = -6,
+    tpr: onp.ToFloat = -60,
+    retquad: _Falsy = False,
+    retenv: _Falsy = False,
+) -> _Array_f8: ...
+@overload  # retquad: False = ..., retenv: True (keyword)
+def gausspulse(
+    t: onp.ToFloatND,
+    fc: onp.ToFloat = 1000,
+    bw: onp.ToFloat = 0.5,
+    bwr: onp.ToFloat = -6,
+    tpr: onp.ToFloat = -60,
+    retquad: _Falsy = False,
+    *,
+    retenv: _Truthy,
+) -> tuple[_Array_f8, _Array_f8]: ...
+@overload  # retquad: False (positional), retenv: False (positional)
+def gausspulse(
+    t: onp.ToFloatND,
+    fc: onp.ToFloat,
+    bw: onp.ToFloat,
+    bwr: onp.ToFloat,
+    tpr: onp.ToFloat,
+    retquad: _Falsy,
+    retenv: _Truthy,
+) -> tuple[_Array_f8, _Array_f8]: ...
+@overload  # retquad: True (positional), retenv: False = ...
+def gausspulse(
+    t: onp.ToFloatND,
+    fc: onp.ToFloat,
+    bw: onp.ToFloat,
+    bwr: onp.ToFloat,
+    tpr: onp.ToFloat,
+    retquad: _Truthy,
+    retenv: _Falsy = False,
+) -> tuple[_Array_f8, _Array_f8]: ...
+@overload  # retquad: True (keyword), retenv: False = ...
+def gausspulse(
+    t: onp.ToFloatND,
+    fc: onp.ToFloat = 1000,
+    bw: onp.ToFloat = 0.5,
+    bwr: onp.ToFloat = -6,
+    tpr: onp.ToFloat = -60,
+    *,
+    retquad: _Truthy,
+    retenv: _Falsy = False,
+) -> tuple[_Array_f8, _Array_f8]: ...
+@overload  # retquad: True (positional), retenv: True (positional/keyword)
+def gausspulse(
+    t: onp.ToFloatND,
+    fc: onp.ToFloat,
+    bw: onp.ToFloat,
+    bwr: onp.ToFloat,
+    tpr: onp.ToFloat,
+    retquad: _Truthy,
+    retenv: _Truthy,
+) -> tuple[_Array_f8, _Array_f8, _Array_f8]: ...
+@overload  # retquad: True (keyword), retenv: True
+def gausspulse(
+    t: onp.ToFloatND,
+    fc: onp.ToFloat = 1000,
+    bw: onp.ToFloat = 0.5,
+    bwr: onp.ToFloat = -6,
+    tpr: onp.ToFloat = -60,
+    *,
+    retquad: _Truthy,
+    retenv: _Truthy,
+) -> tuple[_Array_f8, _Array_f8, _Array_f8]: ...
diff --git a/tests/signal/test_waveforms.pyi b/tests/signal/test_waveforms.pyi
new file mode 100644
index 00000000..94bbf253
--- /dev/null
+++ b/tests/signal/test_waveforms.pyi
@@ -0,0 +1,208 @@
+from typing import Literal, TypeAlias
+from typing_extensions import assert_type
+
+import numpy as np
+import optype.numpy as onp
+from scipy.signal import gausspulse
+
+_Array_f8: TypeAlias = onp.ArrayND[np.float64]
+_Scalar_f8: TypeAlias = np.float64
+_Falsy: TypeAlias = Literal[0, False]
+_Truthy: TypeAlias = Literal[1, True]
+
+_time_scalar: onp.ToFloat
+_time_array: onp.ToFloatND
+_time_cutoff: Literal["cutoff"]
+_float: onp.ToFloat
+_truthy: _Truthy
+_falsy: _Falsy
+
+# test gausspulse function overloads
+# `time` as an array
+assert_type(gausspulse(_time_array), _Array_f8)
+# Full positional arguments
+assert_type(gausspulse(_time_array, _float, _float, _float, _float, _falsy, _falsy), _Array_f8)
+assert_type(
+    gausspulse(_time_array, _float, _float, _float, _float, _truthy, _falsy),
+    tuple[_Array_f8, _Array_f8],
+)
+assert_type(
+    gausspulse(_time_array, _float, _float, _float, _float, _falsy, _truthy),
+    tuple[_Array_f8, _Array_f8],
+)
+assert_type(
+    gausspulse(_time_array, _float, _float, _float, _float, _truthy, _truthy),
+    tuple[_Array_f8, _Array_f8, _Array_f8],
+)
+# Full keyword arguments
+assert_type(gausspulse(t=_time_array), _Array_f8)
+assert_type(
+    gausspulse(
+        t=_time_array,
+        retquad=_falsy,
+        retenv=_falsy,
+    ),
+    _Array_f8,
+)
+assert_type(
+    gausspulse(
+        t=_time_array,
+        retquad=_truthy,
+        retenv=_falsy,
+    ),
+    tuple[_Array_f8, _Array_f8],
+)
+assert_type(
+    gausspulse(
+        t=_time_array,
+        retquad=_falsy,
+        retenv=_truthy,
+    ),
+    tuple[_Array_f8, _Array_f8],
+)
+assert_type(
+    gausspulse(
+        t=_time_array,
+        retquad=_truthy,
+        retenv=_truthy,
+    ),
+    tuple[_Array_f8, _Array_f8, _Array_f8],
+)
+
+# Mixed positional and keyword arguments
+assert_type(
+    gausspulse(_time_array, _float, _float, _float, _float, retquad=_falsy, retenv=_falsy),
+    _Array_f8,
+)
+assert_type(
+    gausspulse(_time_array, _float, _float, _float, _float, retquad=_truthy, retenv=_falsy),
+    tuple[_Array_f8, _Array_f8],
+)
+assert_type(
+    gausspulse(_time_array, _float, _float, _float, _float, retquad=_falsy, retenv=_truthy),
+    tuple[_Array_f8, _Array_f8],
+)
+assert_type(
+    gausspulse(_time_array, _float, _float, _float, _float, retquad=_truthy, retenv=_truthy),
+    tuple[_Array_f8, _Array_f8, _Array_f8],
+)
+
+# `time` as a scalar
+assert_type(gausspulse(_time_scalar), _Scalar_f8)
+# Full positional arguments
+assert_type(gausspulse(_time_scalar, _float, _float, _float, _float, _falsy, _falsy), _Scalar_f8)
+assert_type(
+    gausspulse(_time_scalar, _float, _float, _float, _float, _truthy, _falsy),
+    tuple[_Scalar_f8, _Scalar_f8],
+)
+assert_type(
+    gausspulse(_time_scalar, _float, _float, _float, _float, _falsy, _truthy),
+    tuple[_Scalar_f8, _Scalar_f8],
+)
+assert_type(
+    gausspulse(_time_scalar, _float, _float, _float, _float, _truthy, _truthy),
+    tuple[_Scalar_f8, _Scalar_f8, _Scalar_f8],
+)
+# Full keyword arguments
+assert_type(gausspulse(t=_time_scalar), _Scalar_f8)
+assert_type(
+    gausspulse(
+        t=_time_scalar,
+        retquad=_falsy,
+        retenv=_falsy,
+    ),
+    _Scalar_f8,
+)
+assert_type(
+    gausspulse(
+        t=_time_scalar,
+        retquad=_truthy,
+        retenv=_falsy,
+    ),
+    tuple[_Scalar_f8, _Scalar_f8],
+)
+assert_type(
+    gausspulse(
+        t=_time_scalar,
+        retquad=_falsy,
+        retenv=_truthy,
+    ),
+    tuple[_Scalar_f8, _Scalar_f8],
+)
+assert_type(
+    gausspulse(
+        t=_time_scalar,
+        retquad=_truthy,
+        retenv=_truthy,
+    ),
+    tuple[_Scalar_f8, _Scalar_f8, _Scalar_f8],
+)
+
+# Mixed positional and keyword arguments
+assert_type(
+    gausspulse(_time_scalar, _float, _float, _float, _float, retquad=_falsy, retenv=_falsy),
+    _Scalar_f8,
+)
+assert_type(
+    gausspulse(_time_scalar, _float, _float, _float, _float, retquad=_truthy, retenv=_falsy),
+    tuple[_Scalar_f8, _Scalar_f8],
+)
+assert_type(
+    gausspulse(_time_scalar, _float, _float, _float, _float, retquad=_falsy, retenv=_truthy),
+    tuple[_Scalar_f8, _Scalar_f8],
+)
+assert_type(
+    gausspulse(_time_scalar, _float, _float, _float, _float, retquad=_truthy, retenv=_truthy),
+    tuple[_Scalar_f8, _Scalar_f8, _Scalar_f8],
+)
+
+# `time` as the literal `"cutoff"`
+assert_type(gausspulse(_time_cutoff), _Scalar_f8)
+# Full positional arguments
+assert_type(gausspulse(_time_cutoff, _float, _float, _float, _float, _falsy, _falsy), _Scalar_f8)
+assert_type(gausspulse(_time_cutoff, _float, _float, _float, _float, _truthy, _falsy), _Scalar_f8)
+assert_type(gausspulse(_time_cutoff, _float, _float, _float, _float, _falsy, _truthy), _Scalar_f8)
+assert_type(gausspulse(_time_cutoff, _float, _float, _float, _float, _truthy, _truthy), _Scalar_f8)
+# Full keyword arguments
+assert_type(gausspulse(t=_time_cutoff), _Scalar_f8)
+assert_type(
+    gausspulse(
+        t=_time_cutoff,
+        retquad=_falsy,
+        retenv=_falsy,
+    ),
+    _Scalar_f8,
+)
+assert_type(
+    gausspulse(
+        t=_time_cutoff,
+        retquad=_truthy,
+        retenv=_falsy,
+    ),
+    _Scalar_f8,
+)
+assert_type(
+    gausspulse(
+        t=_time_cutoff,
+        retquad=_falsy,
+        retenv=_truthy,
+    ),
+    _Scalar_f8,
+)
+assert_type(
+    gausspulse(
+        t=_time_cutoff,
+        retquad=_truthy,
+        retenv=_truthy,
+    ),
+    _Scalar_f8,
+)
+
+# Mixed positional and keyword arguments
+assert_type(
+    gausspulse(_time_cutoff, _float, _float, _float, _float, retquad=_falsy, retenv=_falsy),
+    _Scalar_f8,
+)
+assert_type(gausspulse(_time_cutoff, _float, _float, _float, _float, retquad=_truthy, retenv=_falsy), _Scalar_f8)
+assert_type(gausspulse(_time_cutoff, _float, _float, _float, _float, retquad=_falsy, retenv=_truthy), _Scalar_f8)
+assert_type(gausspulse(_time_cutoff, _float, _float, _float, _float, retquad=_truthy, retenv=_truthy), _Scalar_f8)