2c:null 2d:["$","title",null,{"children":"Apple II NTSC Emulation: OpenEmulator explainer | Zellyn Hunter | Observable"}] 32:T79d,C = (() => { const HORIZ_START = 16; const HORIZ_BLANK = (9 + HORIZ_START) // 25; const HORIZ_DISPLAY = 40; const HORIZ_TOTAL = (HORIZ_BLANK + HORIZ_DISPLAY) // 65; const CELL_WIDTH = 14; const VERT_NTSC_START = 38; const VERT_DISPLAY = 192; // From CanvasInterface.h // See https://en.wikipedia.org/wiki/Colorburst const NTSC_FSC = 315 / 88 * 1e6; // 3579545 = 3.5 Mhz: Color Subcarrier const NTSC_4FSC = 4 * NTSC_FSC; // 14318180 = 14.3 Mhz const NTSC_HLENGTH = (52 + 8 / 9) * 1e-6; const NTSC_HHALF = (35 + 2 / 3) * 1e-6; const NTSC_HSTART = NTSC_HHALF - NTSC_HLENGTH / 2; const NTSC_VLENGTH = 240; const NTSC_VSTART = 19; const ntscClockFrequency = NTSC_4FSC * HORIZ_TOTAL / 912; const ntscVisibleRect = {x: ntscClockFrequency * NTSC_HSTART, y: NTSC_VSTART, width: ntscClockFrequency * NTSC_HLENGTH, height: NTSC_VLENGTH}; const ntscDisplayRect = {x: HORIZ_START, y: VERT_NTSC_START, width: HORIZ_DISPLAY, height: VERT_DISPLAY}; const vertStart = ntscDisplayRect.y; // first displayed column. const horizStart = Math.floor(ntscDisplayRect.x); // imageSize is [14 * visible rect width in cells, visible lines] const imageSize = {width: Math.floor(CELL_WIDTH * ntscVisibleRect.width), height: Math.floor(ntscVisibleRect.height)}; // imageLeft is # of pixels from first visible point to first displayed point. const imageLeft = Math.floor((horizStart - ntscVisibleRect.x) * CELL_WIDTH); const colorBurst = 2 * Math.PI * (-33 / 360 + (imageLeft % 4) / 4); // First pixel that OpenEmulator draws when painting normally. const topLeft = {x: imageLeft, y: vertStart - ntscVisibleRect.y}; // First pixel that OpenEmulator draws when painting 80-column mode. const topLeft80Col = {x: imageLeft - CELL_WIDTH / 2, y: vertStart - ntscVisibleRect.y}; return { imageSize, colorBurst, topLeft, NTSC_FSC, NTSC_4FSC, } })()33:T46d,class Matrix3 { constructor(c00, c01, c02, c10, c11, c12, c20, c21, c22) { this.data = [ c00 || 0, c01 || 0, c02 || 0, c10 || 0, c11 || 0, c12 || 0, c20 || 0, c21 || 0, c22 || 0 ]; } static identity() { return new Matrix3(1, 0, 0, 0, 1, 0, 0, 0, 1); } mul(val) { if (typeof val == "number") { return new Matrix3(...this.data.map((x) => x * val)); } if (val instanceof Array) { // vector let v = Array(3).fill(0); for (let i = 0; i < 3; i++) { for (let j = 0; j < 3; j++) { v[i] += this.data[i * 3 + j] * val[j]; } } return v; } let m = new Matrix3(); for (let i = 0; i < 3; i++) { for (let j = 0; j < 3; j++) { for (let k = 0; k < 3; k++) { m.data[i * 3 + j] += val.data[i * 3 + k] * this.data[k * 3 + j]; } } } return m; } transpose() { let m = new Matrix3(); for (let i = 0; i < 3; i++) { for (let j = 0; j < 3; j++) { m.data[j * 3 + i] = this.data[i * 3 + j]; } } return m; } }34:[{"id":"5387cd38c0fb82e696dbd03ec03efe758ba671083d5cbd42cc30e7f5c3d55463ca8fd17c68f7922fd9f9801dca7e59e1c8fb2d029a9e9347f877fb8b61ac6912","href":"https://static.observableusercontent.com/files/5387cd38c0fb82e696dbd03ec03efe758ba671083d5cbd42cc30e7f5c3d55463ca8fd17c68f7922fd9f9801dca7e59e1c8fb2d029a9e9347f877fb8b61ac6912","name":"rescue-raiders-words.png","type":"image/png","lastModified":1619441015874.754,"size":4320}] 30:{"id":"105001bf8df09892","slug":"apple-ii-ntsc-emulation-openemulator-explainer","title":"Apple II NTSC Emulation: OpenEmulator explainer","thumbnail":"49e3b8e7b5c25c76853ac31b4ed41e895e2facb91573182f4e68e995d0ccb899","access_level":"public","create_time":"$D2021-04-26T12:43:26.083Z","update_time":"$D2025-05-12T15:49:46.969Z","view_time":null,"first_public_time":"$D2021-05-06T12:34:40.533Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"d796a03c5877d3c8","login":"zellyn","name":"Zellyn Hunter","avatar_url":"https://avatars-next.observableusercontent.com/350abf8f2766fa17f37644f22ed99fb3aa7c6c5fd47a606cf3678752e007124a","tier":"starter_2024","bio":"Programmer at Square. Mostly (currently) Go."},"version":1254,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"12133cdd10fe21a6","login":"zellyn","name":"Zellyn Hunter","avatar_url":"https://avatars-next.observableusercontent.com/350abf8f2766fa17f37644f22ed99fb3aa7c6c5fd47a606cf3678752e007124a","tier":null,"bio":"Programmer at Square. Mostly (currently) Go."}],"members":[{"type":"individual","id":"12133cdd10fe21a6","login":"zellyn","name":"Zellyn Hunter","avatar_url":"https://avatars-next.observableusercontent.com/350abf8f2766fa17f37644f22ed99fb3aa7c6c5fd47a606cf3678752e007124a","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Apple II NTSC Emulation: OpenEmulator explainer","cells":[{"id":0,"value":"md`# Apple II NTSC Emulation: OpenEmulator explainer\n\nThis is a very stripped-down javascript implementation of Marc S. Ressl's NTSC emulation from OpenEmulator. You can find the full WebGL port [here](https://zellyn.github.io/apple2shader/).`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":102,"value":"md`## Source data\n\nFirst, we load the raw source image. We use 560x192 rather than 280x192 because doubling the horizontal resolution allows us to account for the half-pixel shift resulting from setting the high bit in HGR data.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"image = FileAttachment(\"rescue-raiders-words.png\").image()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":109,"value":"md`Next, we create a display rectangle sized to be accurate to NTSC display, and move the image there.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":629,"value":"width = C.imageSize.width","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":635,"value":"height = C.imageSize.height","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"sourceImage = {\n const canvas = document.createElement('canvas');\n const context = canvas.getContext('2d');\n canvas.width = width;\n canvas.height = height;\n context.fillStyle = 'rgba(0,0,0,1)';\n context.fillRect(0, 0, width, height);\n const topLeft = C.topLeft;\n context.drawImage(image, topLeft.x, topLeft.y);\n return canvas;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":145,"value":"md`### Controls\nWe introduce some controls to change the characteristics of the decoding.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":99,"value":"viewof contrast = Range([0, 2], {value: 1, label: \"Contrast\", step: \"0.01\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":126,"value":"viewof saturation = Range([0, 2], {value: 1, label: \"Saturation\", step: \"0.01\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":127,"value":"viewof Hue = Range([-0.5, 0.5], {value: 0, label: \"Hue\", step: \"0.01\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":129,"value":"viewof luma_bandwidth = Range([0, 7159090], {value: 2000000, label: \"Luma Bandwidth\", step: \"1\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":131,"value":"viewof chroma_bandwidth = Range([0, 7159090], {value: 600000, label: \"Chroma Bandwidth\", step: \"1\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":594,"value":"md`## Calculate pixel weights\n\nWe do some fancy math that ultimately turns into pixel weights for yuv in the source signal for given pixel distances from the current output pixel`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":421,"value":"phaseInfo = {\n const c = C.colorBurst / 2 / Math.PI;\n return c - Math.floor(c)\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":446,"value":"sampleRate = C.NTSC_4FSC","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":443,"value":"subcarrier = C.NTSC_FSC / sampleRate","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":454,"value":"w = normalize(chebyshevWindow(17, 50))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1155,"value":"Plot.plot({\n height: 150,\n marks: [Plot.barY(w.map((d,i) => ({index: i, w: d})), { x: \"index\", y: \"w\" })],\n x: {label: \"chebyshevWindow(17,50)\"},\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":455,"value":"yBandwidth = luma_bandwidth / sampleRate","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":457,"value":"uBandwidth = chroma_bandwidth / sampleRate","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":459,"value":"vBandwidth = uBandwidth","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":461,"value":"wy = normalize(mul(w, lanczosWindow(17, yBandwidth)))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1231,"value":"Plot.plot({\n height: 150,\n marks: [Plot.barY(lanczosWindow(17, yBandwidth).map((d,i) => ({index: i, w: d})), { x: \"index\", y: \"w\" })],\n x: {label: \"lanczosWindow(17, yBandwidth)\"},\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1226,"value":"Plot.plot({\n height: 150,\n marks: [Plot.barY(wy.map((d,i) => ({index: i, w: d})), { x: \"index\", y: \"w\" })],\n x: {label: \"w * lanczosWindow(17, yBandwidth)\"},\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":466,"value":"wu = scale(normalize(mul(w, lanczosWindow(17, uBandwidth))), 2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1237,"value":"Plot.plot({\n height: 150,\n marks: [Plot.barY(lanczosWindow(17, uBandwidth).map((d,i) => ({index: i, w: d})), { x: \"index\", y: \"w\" })],\n x: {label: \"lanczosWindow(17, uBandwidth)\"},\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1241,"value":"Plot.plot({\n height: 150,\n marks: [Plot.barY(wu.map((d,i) => ({index: i, w: d})), { x: \"index\", y: \"w\" })],\n x: {label: \"w * lanczosWindow(17, uBandwidth)\"},\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":468,"value":"wv = scale(normalize(mul(w, lanczosWindow(17, vBandwidth))), 2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":498,"value":"cs = [8, 7, 6, 5, 4, 3, 2, 1, 0].map(i => [wy[i], wu[i], wv[i]])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":588,"value":"md`## Build the decoder matrix\n\nWe take each part of the video decoding process, and multiply it into the decoder matrix`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":528,"value":"matrix0 = Matrix3.identity()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":523,"value":"matrix1 = new Matrix3(1, 0, 0,\n 0, saturation, 0,\n 0, 0, saturation).mul(matrix0)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":525,"value":"matrix2 = {\n const h = 2 * Math.PI * Hue;\n return new Matrix3(1, 0, 0,\n 0, Math.cos(h), -Math.sin(h),\n 0, Math.sin(h), Math.cos(h)).mul(matrix1);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":547,"value":"// Decode Y'UV decoder matrix\nmatrix3 = new Matrix3(1, 1, 1,\n 0, -0.394642, 2.032062,\n 1.139883, -0.580622, 0).mul(matrix2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":552,"value":"matrix4 = matrix3.mul(Math.max(contrast, 0))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":557,"value":"decoderMatrix = matrix4","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1113,"value":"decoderTranspose = decoderMatrix.transpose()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":599,"value":"md`### Helper functions to get source signal data`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":561,"value":"sourceData = sourceImage.getContext('2d').getImageData(0, 0, width, height).data","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":573,"value":"function getRawPixel(x, y) {\n x = Math.min(Math.max(x, 0), width - 1);\n y = Math.min(Math.max(y, 0), height - 1);\n\n let red = (y * width + x) * 4;\n return [sourceData[red], sourceData[red + 1], sourceData[red + 2]];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":609,"value":"function pixel(x, y) {\n let c = scale(getRawPixel(x, y), 1.0 / 255.0);\n let p = phaseInfo;\n let phase = 2.0 * Math.PI * (subcarrier * (x + 0.5) + p);\n return mul(c, [1.0, Math.sin(phase), Math.cos(phase)]);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":615,"value":"pixels = (x, y, i) => add(pixel(x + i, y), pixel(x - i, y))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":659,"value":"function colorAt(x, y) {\n let c = mul(pixel(x, y), cs[0]);\n c = add(c, mul(pixels(x, y, 1), cs[1]));\n c = add(c, mul(pixels(x, y, 2), cs[2]));\n c = add(c, mul(pixels(x, y, 3), cs[3]));\n c = add(c, mul(pixels(x, y, 4), cs[4]));\n c = add(c, mul(pixels(x, y, 5), cs[5]));\n c = add(c, mul(pixels(x, y, 6), cs[6]));\n c = add(c, mul(pixels(x, y, 7), cs[7]));\n c = add(c, mul(pixels(x, y, 8), cs[8]));\n return decoderTranspose.mul(c);\n return c;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1103,"value":"decoderMatrix.mul([0.5, 0.5, 0.5])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":343,"value":"newImage = {\n const canvas = document.createElement(\"canvas\");\n const ctx = canvas.getContext(\"2d\");\n const width = sourceImage.width;\n const height = sourceImage.height;\n canvas.width = width;\n canvas.height = height * 2;\n ctx.fillStyle = \"rgba(0,0,0,1)\";\n ctx.fillRect(0, 0, width, height * 2);\n let imageData = ctx.getImageData(0, 0, width, height * 2);\n const data = imageData.data;\n const setPixel = (x, y, r, g, b) => {\n let red = (y * width + x) * 4;\n data[red] = r;\n data[red + 1] = g;\n data[red + 2] = b;\n };\n for (let x = 84; x < 660; x++) {\n for (let y = 19; y < 211; y++) {\n const sourceColor = scale(colorAt(x, y), 255.0);\n setPixel(x, y * 2, sourceColor[0], sourceColor[1], sourceColor[2]);\n setPixel(x, y * 2 + 1, sourceColor[0], sourceColor[1], sourceColor[2]);\n }\n }\n ctx.putImageData(imageData, 0, 0);\n return canvas;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":213,"value":"md`## Fancy math`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":214,"value":"function realIDFT(ary) {\n const size = ary.length;\n const w = Array(size).fill(0);\n \n for (let i = 0; i < size; i++) {\n const omega = 2 * Math.PI * i / size;\n for (let j = 0; j < size; j++) {\n w[i] += ary[j] * Math.cos(j * omega);\n }\n }\n\n return scale(w, 1/size);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":224,"value":"// Chebyshev Window\n// Based on ideas at http://www.dsprelated.com/showarticle/42.php\nfunction chebyshevWindow(n, sidelobeDb) {\n const m = n - 1;\n let w = Array(m).fill(0);\n const alpha = Math.cosh(Math.acosh(Math.pow(10, sidelobeDb / 20)) / m);\n \n for (let i = 0; i < m; i++) {\n const a = Math.abs(alpha * Math.cos(Math.PI * i / m));\n if (a > 1)\n w[i] = Math.pow(-1, i) * Math.cosh(m * Math.acosh(a));\n else\n w[i] = Math.pow(-1, i) * Math.cos(m * Math.acos(a));\n }\n\n w = realIDFT(w);\n \n w = resize(w, n);\n w[0] /= 2;\n w[n - 1] = w[0];\n \n const max = w.reduce((prev, cur) => Math.max(prev, Math.abs(cur)));\n return scale(w, 1/max);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":283,"value":"// Lanczos Window\nfunction lanczosWindow(n, fc) {\n let v = Array(n).fill(0);\n fc = Math.min(fc, 0.5);\n const halfN = Math.floor(n / 2);\n \n for (let i = 0; i < n; i++) {\n const x = 2 * Math.PI * fc * (i - halfN);\n v[i] = (x == 0.0) ? 1.0 : Math.sin(x) / x;\n }\n \n return v;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":153,"value":"md`### Useful NTSC-related constants`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"$32","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":159,"value":"md`### Miscellanea`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":115,"value":"import {Range} from \"@observablehq/inputs\"\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":237,"value":"d3 = require(\"d3@6\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":165,"value":"// Scale elements of an array so they sum to 1.\nfunction normalize(ary) {\n let sum = ary.reduce((a, b) => a + b, 0)\n return scale(ary, 1.0/sum);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":187,"value":"mul = (ary1, ary2) => ary1.map((e, i) => e * ary2[i])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":622,"value":"add = (ary1, ary2) => ary1.map((e, i) => e + ary2[i])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":201,"value":"scale = (ary, factor) => ary.map((x) => x * factor)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":228,"value":"function resize(ary, n) {\n let w = Array(n).fill(0);\n for (let i = 0; i < Math.min(n, ary.length); i++) {\n w[i] = ary[i];\n }\n return 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