LibDSP: Add windowing functions

Windows are used in many DSP related applications. A prominent use case
is spectral analysis, where windowing the signal before doing spectral
analysis mitigates spectral leakage.

Userland/Libraries/LibDSP/Window.h

@@ -0,0 +1,70 @@
+/*
+ * Copyright (c) 2021, Arne Elster (arne@elster.li)
+ *
+ * SPDX-License-Identifier: BSD-2-Clause
+ */
+
+#pragma once
+
+#include <AK/FixedArray.h>
+#include <AK/Math.h>
+
+namespace LibDSP {
+
+template<typename T>
+class Window final {
+public:
+    template<size_t size>
+    constexpr static Array<T, size> hamming() { return make_window<size>(calculate_hamming); }
+    constexpr static FixedArray<T> hamming(size_t size) { return make_window(size, calculate_hamming); }
+
+    template<size_t size>
+    constexpr static Array<T, size> hann() { return make_window<size>(calculate_hann); }
+    constexpr static FixedArray<T> hann(size_t size) { return make_window(size, calculate_hann); }
+
+    template<size_t size>
+    constexpr static Array<T, size> blackman_harris() { return make_window<size>(calculate_blackman_harris); }
+    constexpr static FixedArray<T> blackman_harris(size_t size) { return make_window(size, calculate_blackman_harris); }
+
+private:
+    constexpr static double calculate_hann(size_t index, size_t size)
+    {
+        return 0.5 * (1 - AK::cos((2 * AK::Pi<T> * index) / (size - 1)));
+    }
+
+    constexpr static double calculate_hamming(size_t index, size_t size)
+    {
+        return 0.54 - 0.46 * AK::cos((2 * AK::Pi<T> * index) / (size - 1));
+    }
+
+    constexpr static double calculate_blackman_harris(size_t index, size_t size)
+    {
+        T const a0 = 0.35875;
+        T const a1 = 0.48829;
+        T const a2 = 0.14128;
+        T const a3 = 0.01168;
+        return a0 - a1 * AK::cos(2 * AK::Pi<T> * index / size) + a2 * AK::cos(4 * AK::Pi<T> * index / size) - a3 * AK::cos(6 * AK::Pi<T> * index / size);
+    }
+
+    template<size_t size>
+    constexpr static Array<T, size> make_window(auto window_function)
+    {
+        Array<T, size> result;
+        for (size_t i = 0; i < size; i++) {
+            result[i] = window_function(i, size);
+        }
+        return result;
+    }
+
+    constexpr static FixedArray<T> make_window(size_t size, auto window_function)
+    {
+        FixedArray<T> result;
+        result.resize(size);
+        for (size_t i = 0; i < size; i++) {
+            result[i] = window_function(i, size);
+        }
+        return result;
+    }
+};
+
+}