diff --git a/fft.py b/fft.py
new file mode 100644
index 0000000..58d05e3
--- /dev/null
+++ b/fft.py
@@ -0,0 +1,29 @@
+from dataclasses import dataclass
+import numbers
+import operator
+from typing import Callable, Protocol, Self, cast
+
+
+@dataclass(frozen=True)
+class FFTData:
+    data: dict[float, float]
+
+
+    @classmethod
+    def num_operation(cls, op: Callable[[float, float], float], a: Self | float, b: Self | float):
+        results = {}
+        keyset: set[float] = set.intersection(*(set(x.data.keys()) for x in (a, b) if not isinstance(x, (float, int))))
+
+        for k in keyset:
+            val_a: float = a if isinstance(a, (float, int)) else a.data[k]
+            val_b: float = b if isinstance(b, (float, int)) else b.data[k]
+            results[k] = op(val_a, val_b)
+        return cls(results)
+
+    def __add__(self, other: Self):
+        return self.num_operation(operator.add, self, other)
+
+    def __mul__(self, other: float):
+        return self.num_operation(operator.mul, self, other)
+
+
diff --git a/interpolation.py b/interpolation.py
new file mode 100644
index 0000000..f3f8cae
--- /dev/null
+++ b/interpolation.py
@@ -0,0 +1,41 @@
+from typing import Callable, Protocol, Self, Sequence
+
+
+class Interpolable(Protocol):
+    def __add__(self: Self, other: Self, /) -> Self: ...
+    def __mul__(self: Self, other: float, /) -> Self: ...
+
+def lin_interpolate[T: Interpolable](arg: float, arg_l: float, arg_h: float, val_l: T, val_h: T) -> T:
+    if arg_l == arg_h:
+        return val_l
+
+    w_l = (arg_h - arg) / (arg_h - arg_l)
+    w_h = (arg - arg_l) / (arg_h - arg_l)
+
+    return val_l * w_l + val_h * w_h
+
+# sequence assumed to be in order
+def find_args_binary[T](seq: Sequence[T], key: Callable[[T], float], val: float) -> tuple[T, T]:
+    # print(seq)
+    if len(seq) < 2:
+        raise ValueError()
+    if val < key(seq[0]):
+        raise ValueError()
+    if val > key(seq[-1]):
+        raise ValueError()
+    if len(seq) == 2:
+        return (seq[0], seq[1])
+
+    index_mid = len(seq)//2
+    val_mid = key(seq[index_mid])
+    # print(f'{index_mid}: {val_mid}')
+    if val > val_mid:
+        return find_args_binary(seq[index_mid:], key, val)
+    else:
+        return find_args_binary(seq[:index_mid+1], key, val)
+
+def interp_keyed[T, U: Interpolable](seq: Sequence[T], key_key: Callable[[T], float], key_val: Callable[[T], U], x: float) -> U:
+    args = find_args_binary(seq, key_key, x)
+    karg_l, karg_h = map(key_key, args)
+    val_l, val_h = map(key_val, args)
+    return lin_interpolate(x, karg_l, karg_h, val_l, val_h)