feat: visualized audio generator

Author: ialex32x

README.md

@@ -41,4 +41,4 @@ This is an example originally from https://godotengine.org/asset-library/asset/5
 
 It utilizes [ZzFXM](https://keithclark.github.io/ZzFXM/) which is written in pure javascript to play a 8bit-ish sound without audio media files.
 
-*No graphics available for this example.*
+[![AudioGenerator](./raw/screenshots/audio_generator.gif)](./jumpybaudio_generatorird/generator_demo.ts)

audio_generator/fft.ts

@@ -0,0 +1,222 @@
+/* 
+ * Free FFT and convolution (TypeScript)
+ * 
+ * Copyright (c) 2022 Project Nayuki. (MIT License)
+ * https://www.nayuki.io/page/free-small-fft-in-multiple-languages
+ * 
+ * Permission is hereby granted, free of charge, to any person obtaining a copy of
+ * this software and associated documentation files (the "Software"), to deal in
+ * the Software without restriction, including without limitation the rights to
+ * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
+ * the Software, and to permit persons to whom the Software is furnished to do so,
+ * subject to the following conditions:
+ * - The above copyright notice and this permission notice shall be included in
+ *   all copies or substantial portions of the Software.
+ * - The Software is provided "as is", without warranty of any kind, express or
+ *   implied, including but not limited to the warranties of merchantability,
+ *   fitness for a particular purpose and noninfringement. In no event shall the
+ *   authors or copyright holders be liable for any claim, damages or other
+ *   liability, whether in an action of contract, tort or otherwise, arising from,
+ *   out of or in connection with the Software or the use or other dealings in the
+ *   Software.
+ */
+
+
+/* 
+ * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
+ * The vector can have any length. This is a wrapper function.
+ */
+export function transform(real: Array<number> | Float64Array, imag: Array<number> | Float64Array): void {
+    const n: number = real.length;
+    // if (n != imag.length)
+    //     throw new RangeError("Mismatched lengths");
+    if (n == 0)
+        return;
+    else if ((n & (n - 1)) == 0)  // Is power of 2
+        transformRadix2(real, imag);
+    else  // More complicated algorithm for arbitrary sizes
+        transformBluestein(real, imag);
+}
+
+
+/* 
+ * Computes the inverse discrete Fourier transform (IDFT) of the given complex vector, storing the result back into the vector.
+ * The vector can have any length. This is a wrapper function. This transform does not perform scaling, so the inverse is not a true inverse.
+ */
+export function inverseTransform(real: Array<number> | Float64Array, imag: Array<number> | Float64Array): void {
+    transform(imag, real);
+}
+
+
+/* 
+ * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
+ * The vector's length must be a power of 2. Uses the Cooley-Tukey decimation-in-time radix-2 algorithm.
+ */
+function transformRadix2(real: Array<number> | Float64Array, imag: Array<number> | Float64Array): void {
+    // Length variables
+    const n: number = real.length;
+    // if (n != imag.length)
+    //     throw new RangeError("Mismatched lengths");
+    if (n == 1)  // Trivial transform
+        return;
+    let levels: number = -1;
+    for (let i = 0; i < 32; i++) {
+        if (1 << i == n)
+            levels = i;  // Equal to log2(n)
+    }
+    if (levels == -1)
+        throw new RangeError("Length is not a power of 2");
+
+    // Trigonometric tables
+    let cosTable = new Array<number>(n / 2);
+    let sinTable = new Array<number>(n / 2);
+    for (let i = 0; i < n / 2; i++) {
+        cosTable[i] = Math.cos(2 * Math.PI * i / n);
+        sinTable[i] = Math.sin(2 * Math.PI * i / n);
+    }
+
+    // Bit-reversed addressing permutation
+    for (let i = 0; i < n; i++) {
+        const j: number = reverseBits(i, levels);
+        if (j > i) {
+            let temp: number = real[i];
+            real[i] = real[j];
+            real[j] = temp;
+            temp = imag[i];
+            imag[i] = imag[j];
+            imag[j] = temp;
+        }
+    }
+
+    // Cooley-Tukey decimation-in-time radix-2 FFT
+    for (let size = 2; size <= n; size *= 2) {
+        const halfsize: number = size / 2;
+        const tablestep: number = n / size;
+        for (let i = 0; i < n; i += size) {
+            for (let j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
+                const l: number = j + halfsize;
+                const tpre: number = real[l] * cosTable[k] + imag[l] * sinTable[k];
+                const tpim: number = -real[l] * sinTable[k] + imag[l] * cosTable[k];
+                real[l] = real[j] - tpre;
+                imag[l] = imag[j] - tpim;
+                real[j] += tpre;
+                imag[j] += tpim;
+            }
+        }
+    }
+
+    // Returns the integer whose value is the reverse of the lowest 'width' bits of the integer 'val'.
+    function reverseBits(val: number, width: number): number {
+        let result: number = 0;
+        for (let i = 0; i < width; i++) {
+            result = (result << 1) | (val & 1);
+            val >>>= 1;
+        }
+        return result;
+    }
+}
+
+
+/* 
+ * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
+ * The vector can have any length. This requires the convolution function, which in turn requires the radix-2 FFT function.
+ * Uses Bluestein's chirp z-transform algorithm.
+ */
+function transformBluestein(real: Array<number> | Float64Array, imag: Array<number> | Float64Array): void {
+    // Find a power-of-2 convolution length m such that m >= n * 2 + 1
+    const n: number = real.length;
+    // if (n != imag.length)
+    //     throw new RangeError("Mismatched lengths");
+    let m: number = 1;
+    while (m < n * 2 + 1)
+        m *= 2;
+
+    // Trigonometric tables
+    let cosTable = new Array<number>(n);
+    let sinTable = new Array<number>(n);
+    for (let i = 0; i < n; i++) {
+        const j: number = i * i % (n * 2);  // This is more accurate than j = i * i
+        cosTable[i] = Math.cos(Math.PI * j / n);
+        sinTable[i] = Math.sin(Math.PI * j / n);
+    }
+
+    // Temporary vectors and preprocessing
+    let areal: Array<number> = newArrayOfZeros(m);
+    let aimag: Array<number> = newArrayOfZeros(m);
+    for (let i = 0; i < n; i++) {
+        areal[i] = real[i] * cosTable[i] + imag[i] * sinTable[i];
+        aimag[i] = -real[i] * sinTable[i] + imag[i] * cosTable[i];
+    }
+    let breal: Array<number> = newArrayOfZeros(m);
+    let bimag: Array<number> = newArrayOfZeros(m);
+    breal[0] = cosTable[0];
+    bimag[0] = sinTable[0];
+    for (let i = 1; i < n; i++) {
+        breal[i] = breal[m - i] = cosTable[i];
+        bimag[i] = bimag[m - i] = sinTable[i];
+    }
+
+    // Convolution
+    let creal = new Array<number>(m);
+    let cimag = new Array<number>(m);
+    convolveComplex(areal, aimag, breal, bimag, creal, cimag);
+
+    // Postprocessing
+    for (let i = 0; i < n; i++) {
+        real[i] = creal[i] * cosTable[i] + cimag[i] * sinTable[i];
+        imag[i] = -creal[i] * sinTable[i] + cimag[i] * cosTable[i];
+    }
+}
+
+
+// /* 
+//  * Computes the circular convolution of the given real vectors. Each vector's length must be the same.
+//  */
+// function convolveReal(xvec: Array<number> | Float64Array, yvec: Array<number> | Float64Array, outvec: Array<number> | Float64Array): void {
+//     const n: number = xvec.length;
+//     if (n != yvec.length || n != outvec.length)
+//         throw new RangeError("Mismatched lengths");
+//     convolveComplex(xvec, newArrayOfZeros(n), yvec, newArrayOfZeros(n), outvec, newArrayOfZeros(n));
+// }
+
+
+/* 
+ * Computes the circular convolution of the given complex vectors. Each vector's length must be the same.
+ */
+function convolveComplex(
+    xreal: Array<number> | Float64Array, ximag: Array<number> | Float64Array,
+    yreal: Array<number> | Float64Array, yimag: Array<number> | Float64Array,
+    outreal: Array<number> | Float64Array, outimag: Array<number> | Float64Array): void {
+
+    const n: number = xreal.length;
+    // if (n != ximag.length || n != yreal.length || n != yimag.length
+    //     || n != outreal.length || n != outimag.length)
+    //     throw new RangeError("Mismatched lengths");
+
+    xreal = xreal.slice();
+    ximag = ximag.slice();
+    yreal = yreal.slice();
+    yimag = yimag.slice();
+    transform(xreal, ximag);
+    transform(yreal, yimag);
+
+    for (let i = 0; i < n; i++) {
+        const temp: number = xreal[i] * yreal[i] - ximag[i] * yimag[i];
+        ximag[i] = ximag[i] * yreal[i] + xreal[i] * yimag[i];
+        xreal[i] = temp;
+    }
+    inverseTransform(xreal, ximag);
+
+    for (let i = 0; i < n; i++) {  // Scaling (because this FFT implementation omits it)
+        outreal[i] = xreal[i] / n;
+        outimag[i] = ximag[i] / n;
+    }
+}
+
+
+function newArrayOfZeros(n: number): Array<number> {
+    let result: Array<number> = [];
+    for (let i = 0; i < n; i++)
+        result.push(0);
+    return result;
+}