29:null 2a:["$","title",null,{"children":"05. PN & black box DSP algorithm | Andrzej Kubaszek | Observable"}] 2f:T471,x_b_xy__y_xy = { let [h__, b_] = h_b_; let p_ = new PN('c_P_TRAP', 1/h__); let p_to2 = new PN("c_P_TRAP_PWR_2", 1/h__); let x_b = p_.mul(b_).exp() .mul( p_.mul('c_05111') ); //p · {1} · exp(-(-b) p) } let blackBox2; if (blackBox2_hist.lastPN && blackBox2_hist.h === h__) blackBox2 = blackBox2_hist.lastPN; else { blackBox2 = ( // ( 1 / (p² + p + 4) ) exp( -(0.5)√(p² +1) ) p_to2.add(1).pow(0.5).mul(-0.5).exp() .div(p_.mul(p_).add(p_).add(4)) );/*/console.log(blackBox2.toString())/**/ blackBox2_hist.h = h__; blackBox2_hist.lastPN = blackBox2; } let y_ = x_b.mul(blackBox2); let x_b_xy__y_xy = []; //graphs let x_b__y_ = [y_, x_b]; for (let k = x_b__y_.length; k--; ) { x_b_xy__y_xy[k] = //data for d3chartPN(); [ //only 1 line on figure {xy:x_b__y_[k].asPointsList(h__) ,nmHtml:' ‒○‒ '+['y(t)|_h,b', 'x_b(t)|_h,b'][k] ,color:colors_[k] ,symbAttrs:{symb: "circle", r:3}} ] } /*/console.log(x_a_xy__y_xy)/**/ return (x_b_xy__y_xy);//[x_a, y_] graphs }30:[] 2d:{"id":"6c1ab6d0847f7a7e","slug":"05-pn-black-box-dsp-algorithm","title":"05. PN & black box DSP algorithm","thumbnail":"964dc471747f9c8b30d7a0fa96e0969a71a4623e9723c53969e7ccbd1f91208a","access_level":"public","create_time":"$D2019-03-04T07:56:43.986Z","update_time":"$D2019-03-15T13:10:06.298Z","view_time":null,"first_public_time":"$D2019-03-04T09:18:12.724Z","has_unpublished_edits":null,"fork":{"id":"889dce8edb64fe79","slug":"discrete-representations-of-generalized-time-domain-func","title":"04. Discrete representations of generalized time domain functions","owner":{"id":"12ed84ab2a5fb1d1","login":"andrzejq","name":"Andrzej Kubaszek"}},"stars":0,"starred":false,"owner":{"type":"team","id":"12ed84ab2a5fb1d1","login":"andrzejq","name":"Andrzej Kubaszek","avatar_url":"https://avatars-next.observableusercontent.com/d5544e4f3e218de6ac8d753ce4dc79d57d9e2452dd35a57847ea297f0ad39698","tier":"starter_2024"},"version":1787,"publish_version":1787,"role":null,"authored":false,"authors":[{"type":"individual","id":"a26fa75e78b968fe","login":"andrzejq","name":"Andrzej Kubaszek","avatar_url":"https://avatars-next.observableusercontent.com/d5544e4f3e218de6ac8d753ce4dc79d57d9e2452dd35a57847ea297f0ad39698","tier":null}],"members":[{"type":"individual","id":"a26fa75e78b968fe","login":"andrzejq","name":"Andrzej Kubaszek","avatar_url":"https://avatars-next.observableusercontent.com/d5544e4f3e218de6ac8d753ce4dc79d57d9e2452dd35a57847ea297f0ad39698","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":{"id":"40fb5921db7af181","slug":"polynomial-numbers-pn","title":"Polynomial Numbers (PN)","owner":{"id":"12ed84ab2a5fb1d1","login":"andrzejq","name":"Andrzej Kubaszek"}},"type":"notebook","body":{"title":"05. PN & black box DSP algorithm","cells":[{"id":861,"value":"md`\n# 05. PN & black box DSP algorithm\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":0,"value":"md`\n\nThe properties of [**dynamic graphs of abstract functions**](https://observablehq.com/@andrzejq/discrete-representations-of-generalized-time-domain-func) based on [**expression for approximate sequence of samples**](https://observablehq.com/@andrzejq/02-laplace-transform-and-z-transform) of function ${tex`\\{ x(t) \\}`}:\n\n\n ${tex.block`\n\\underline{x} = {\\color{magenta}X (\\underline{p})} {\\color{brown} \\ \\cdot \\ \\underline{p} \\cdot (^\\sim0.5^\\sim, 1^\\sim1^\\sim1^\\sim \\dots ^\\sim) }\n `}\n\ncan be used to test the parameters of DSP algorithms.\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1209,"value":"html`

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