{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "50e79b11", "metadata": { "ExecuteTime": { "end_time": "2022-01-15T11:17:21.498334Z", "start_time": "2022-01-15T11:17:19.178844Z" } }, "outputs": [ { "data": { "text/plain": [ "'0.0.9.4'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import signal\n", "import time\n", "\n", "import spkit as sp\n", "sp.__version__" ] }, { "cell_type": "markdown", "id": "1148937e", "metadata": {}, "source": [ "## Sinewave with 2 frequencies" ] }, { "cell_type": "code", "execution_count": 2, "id": "eafe0189", "metadata": { "ExecuteTime": { "end_time": "2022-01-15T11:18:31.376701Z", "start_time": "2022-01-15T11:18:31.187210Z" } }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fs=100\n", "t=np.arange(0,10,1/fs)\n", "f0 = 1.5\n", "x = 0.5*np.sin(2*np.pi*10*t)#*np.exp(t)\n", "x += 0.5*np.sin(2*np.pi*20*t)# + 0.5*np.sin(2*np.pi*40*t)\n", "plt.figure(figsize=(8,3))\n", "plt.plot(t,x)" ] }, { "cell_type": "markdown", "id": "0a91e8be", "metadata": {}, "source": [ "## Spectrogram" ] }, { "cell_type": "code", "execution_count": 5, "id": "5045ba33", "metadata": { "ExecuteTime": { "end_time": "2022-01-15T11:19:16.323005Z", "start_time": "2022-01-15T11:19:16.142349Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fx,tx,Sx = signal.spectrogram(x,fs=fs,nperseg=64,nfft=256,return_onesided=False)\n", "Sx = np.abs(Sx)\n", "plt.figure(figsize=(8,4))\n", "plt.imshow(Sx[:129], aspect='auto',origin='lower',cmap='jet', extent=[tx[0],tx[-1],0,fs/2])#, interpolation='bicubic')\n", "plt.xlabel('time (s)')\n", "plt.ylabel('frequency (Hz)')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "6bea307f", "metadata": {}, "source": [ "## Fractional Fourier Transform" ] }, { "cell_type": "code", "execution_count": 6, "id": "b204ed41", "metadata": { "ExecuteTime": { "end_time": "2022-01-15T11:19:21.325102Z", "start_time": "2022-01-15T11:19:21.315130Z" } }, "outputs": [], "source": [ "%matplotlib notebook" ] }, { "cell_type": "code", "execution_count": 7, "id": "a0b40f2a", "metadata": { "ExecuteTime": { "end_time": "2022-01-15T11:20:33.061376Z", "start_time": "2022-01-15T11:19:47.431108Z" }, "scrolled": false }, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "/* global mpl */\n", "window.mpl = {};\n", "\n", "mpl.get_websocket_type = function () {\n", " if (typeof WebSocket !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof MozWebSocket !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert(\n", " 'Your browser does not have WebSocket support. ' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", " 'Firefox 4 and 5 are also supported but you ' +\n", " 'have to enable WebSockets in about:config.'\n", " );\n", " }\n", "};\n", "\n", "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", " this.supports_binary = this.ws.binaryType !== undefined;\n", "\n", " if (!this.supports_binary) {\n", " var warnings = document.getElementById('mpl-warnings');\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", " warnings.textContent =\n", " 'This browser does not support binary websocket messages. ' +\n", " 'Performance may be slow.';\n", " }\n", " }\n", "\n", " this.imageObj = new Image();\n", "\n", " this.context = undefined;\n", " this.message = undefined;\n", " this.canvas = undefined;\n", " this.rubberband_canvas = undefined;\n", " this.rubberband_context = undefined;\n", " this.format_dropdown = undefined;\n", "\n", " this.image_mode = 'full';\n", "\n", " this.root = document.createElement('div');\n", " this.root.setAttribute('style', 'display: inline-block');\n", " this._root_extra_style(this.root);\n", "\n", " parent_element.appendChild(this.root);\n", "\n", " this._init_header(this);\n", " this._init_canvas(this);\n", " this._init_toolbar(this);\n", "\n", " var fig = this;\n", "\n", " this.waiting = false;\n", "\n", " this.ws.onopen = function () {\n", " fig.send_message('supports_binary', { value: fig.supports_binary });\n", " fig.send_message('send_image_mode', {});\n", " if (fig.ratio !== 1) {\n", " fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n", " }\n", " fig.send_message('refresh', {});\n", " };\n", "\n", " this.imageObj.onload = function () {\n", " if (fig.image_mode === 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function () {\n", " fig.ws.close();\n", " };\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "};\n", "\n", "mpl.figure.prototype._init_header = function () {\n", " var titlebar = document.createElement('div');\n", " titlebar.classList =\n", " 'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n", " var titletext = document.createElement('div');\n", " titletext.classList = 'ui-dialog-title';\n", " titletext.setAttribute(\n", " 'style',\n", " 'width: 100%; 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position: absolute; left: 0; top: 0; z-index: 1;'\n", " );\n", "\n", " // Apply a ponyfill if ResizeObserver is not implemented by browser.\n", " if (this.ResizeObserver === undefined) {\n", " if (window.ResizeObserver !== undefined) {\n", " this.ResizeObserver = window.ResizeObserver;\n", " } else {\n", " var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n", " this.ResizeObserver = obs.ResizeObserver;\n", " }\n", " }\n", "\n", " this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n", " var nentries = entries.length;\n", " for (var i = 0; i < nentries; i++) {\n", " var entry = entries[i];\n", " var width, height;\n", " if (entry.contentBoxSize) {\n", " if (entry.contentBoxSize instanceof Array) {\n", " // Chrome 84 implements new version of spec.\n", " width = entry.contentBoxSize[0].inlineSize;\n", " height = entry.contentBoxSize[0].blockSize;\n", " } else {\n", " // Firefox implements old version of spec.\n", " width = entry.contentBoxSize.inlineSize;\n", " height = entry.contentBoxSize.blockSize;\n", " }\n", " } else {\n", " // Chrome <84 implements even older version of spec.\n", " width = entry.contentRect.width;\n", " height = entry.contentRect.height;\n", " }\n", "\n", " // Keep the size of the canvas and rubber band canvas in sync with\n", " // the canvas container.\n", " if (entry.devicePixelContentBoxSize) {\n", " // Chrome 84 implements new version of spec.\n", " canvas.setAttribute(\n", " 'width',\n", " entry.devicePixelContentBoxSize[0].inlineSize\n", " );\n", " canvas.setAttribute(\n", " 'height',\n", " entry.devicePixelContentBoxSize[0].blockSize\n", " );\n", " } else {\n", " canvas.setAttribute('width', width * fig.ratio);\n", " canvas.setAttribute('height', height * fig.ratio);\n", " }\n", " canvas.setAttribute(\n", " 'style',\n", " 'width: ' + width + 'px; height: ' + height + 'px;'\n", " );\n", "\n", " rubberband_canvas.setAttribute('width', width);\n", " rubberband_canvas.setAttribute('height', height);\n", "\n", " // And update the size in Python. 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Matplotlib will then trigger a resize in the client,\n", " // which will in turn request a refresh of the image.\n", " this.send_message('resize', { width: x_pixels, height: y_pixels });\n", "};\n", "\n", "mpl.figure.prototype.send_message = function (type, properties) {\n", " properties['type'] = type;\n", " properties['figure_id'] = this.id;\n", " this.ws.send(JSON.stringify(properties));\n", "};\n", "\n", "mpl.figure.prototype.send_draw_message = function () {\n", " if (!this.waiting) {\n", " this.waiting = true;\n", " this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", " var format_dropdown = fig.format_dropdown;\n", " var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n", " fig.ondownload(fig, format);\n", "};\n", "\n", "mpl.figure.prototype.handle_resize = function (fig, msg) {\n", " var size = msg['size'];\n", " if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n", " fig._resize_canvas(size[0], size[1], msg['forward']);\n", " fig.send_message('refresh', {});\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n", " var x0 = msg['x0'] / fig.ratio;\n", " var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n", " var x1 = msg['x1'] / fig.ratio;\n", " var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n", " x0 = Math.floor(x0) + 0.5;\n", " y0 = Math.floor(y0) + 0.5;\n", " x1 = Math.floor(x1) + 0.5;\n", " y1 = Math.floor(y1) + 0.5;\n", " var min_x = Math.min(x0, x1);\n", " var min_y = Math.min(y0, y1);\n", " var width = Math.abs(x1 - x0);\n", " var height = Math.abs(y1 - y0);\n", "\n", " fig.rubberband_context.clearRect(\n", " 0,\n", " 0,\n", " fig.canvas.width / fig.ratio,\n", " fig.canvas.height / fig.ratio\n", " );\n", "\n", " fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n", "};\n", "\n", "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n", " // Updates the figure title.\n", " fig.header.textContent = msg['label'];\n", "};\n", "\n", "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n", " var cursor = msg['cursor'];\n", " switch (cursor) {\n", " case 0:\n", " cursor = 'pointer';\n", " break;\n", " case 1:\n", " cursor = 'default';\n", " break;\n", " case 2:\n", " cursor = 'crosshair';\n", " break;\n", " case 3:\n", " cursor = 'move';\n", " break;\n", " }\n", " fig.rubberband_canvas.style.cursor = cursor;\n", "};\n", "\n", "mpl.figure.prototype.handle_message = function (fig, msg) {\n", " fig.message.textContent = msg['message'];\n", "};\n", "\n", "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n", " // Request the server to send over a new figure.\n", " fig.send_draw_message();\n", "};\n", "\n", "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n", " fig.image_mode = msg['mode'];\n", "};\n", "\n", "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n", " for (var key in msg) {\n", " if (!(key in fig.buttons)) {\n", " continue;\n", " }\n", " fig.buttons[key].disabled = !msg[key];\n", " fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n", " if (msg['mode'] === 'PAN') {\n", " fig.buttons['Pan'].classList.add('active');\n", " fig.buttons['Zoom'].classList.remove('active');\n", " } else if (msg['mode'] === 'ZOOM') {\n", " fig.buttons['Pan'].classList.remove('active');\n", " fig.buttons['Zoom'].classList.add('active');\n", " } else {\n", " fig.buttons['Pan'].classList.remove('active');\n", " fig.buttons['Zoom'].classList.remove('active');\n", " }\n", "};\n", "\n", "mpl.figure.prototype.updated_canvas_event = function () {\n", " // Called whenever the canvas gets updated.\n", " this.send_message('ack', {});\n", "};\n", "\n", "// A function to construct a web socket function for onmessage handling.\n", "// Called in the figure constructor.\n", "mpl.figure.prototype._make_on_message_function = function (fig) {\n", " return function socket_on_message(evt) {\n", " if (evt.data instanceof Blob) {\n", " /* FIXME: We get \"Resource interpreted as Image but\n", " * transferred with MIME type text/plain:\" errors on\n", " * Chrome. But how to set the MIME type? It doesn't seem\n", " * to be part of the websocket stream */\n", " evt.data.type = 'image/png';\n", "\n", " /* Free the memory for the previous frames */\n", " if (fig.imageObj.src) {\n", " (window.URL || window.webkitURL).revokeObjectURL(\n", " fig.imageObj.src\n", " );\n", " }\n", "\n", " fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n", " evt.data\n", " );\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " } else if (\n", " typeof evt.data === 'string' &&\n", " evt.data.slice(0, 21) === 'data:image/png;base64'\n", " ) {\n", " fig.imageObj.src = evt.data;\n", " fig.updated_canvas_event();\n", " fig.waiting = false;\n", " return;\n", " }\n", "\n", " var msg = JSON.parse(evt.data);\n", " var msg_type = msg['type'];\n", "\n", " // Call the \"handle_{type}\" callback, which takes\n", " // the figure and JSON message as its only arguments.\n", " try {\n", " var callback = fig['handle_' + msg_type];\n", " } catch (e) {\n", " console.log(\n", " \"No handler for the '\" + msg_type + \"' message type: \",\n", " msg\n", " );\n", " return;\n", " }\n", "\n", " if (callback) {\n", " try {\n", " // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n", " callback(fig, msg);\n", " } catch (e) {\n", " console.log(\n", " \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n", " e,\n", " e.stack,\n", " msg\n", " );\n", " }\n", " }\n", " };\n", "};\n", "\n", "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n", "mpl.findpos = function (e) {\n", " //this section is from http://www.quirksmode.org/js/events_properties.html\n", " var targ;\n", " if (!e) {\n", " e = window.event;\n", " }\n", " if (e.target) {\n", " targ = e.target;\n", " } else if (e.srcElement) {\n", " targ = e.srcElement;\n", " }\n", " if (targ.nodeType === 3) {\n", " // defeat Safari bug\n", " targ = targ.parentNode;\n", " }\n", "\n", " // pageX,Y are the mouse positions relative to the document\n", " var boundingRect = targ.getBoundingClientRect();\n", " var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n", " var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n", "\n", " return { x: x, y: y };\n", "};\n", "\n", "/*\n", " * return a copy of an object with only non-object keys\n", " * we need this to avoid circular references\n", " * http://stackoverflow.com/a/24161582/3208463\n", " */\n", "function simpleKeys(original) {\n", " return Object.keys(original).reduce(function (obj, key) {\n", " if (typeof original[key] !== 'object') {\n", " obj[key] = original[key];\n", " }\n", " return obj;\n", " }, {});\n", "}\n", "\n", "mpl.figure.prototype.mouse_event = function (event, name) {\n", " var canvas_pos = mpl.findpos(event);\n", "\n", " if (name === 'button_press') {\n", " this.canvas.focus();\n", " this.canvas_div.focus();\n", " }\n", "\n", " var x = canvas_pos.x * this.ratio;\n", " var y = canvas_pos.y * this.ratio;\n", "\n", " this.send_message(name, {\n", " x: x,\n", " y: y,\n", " button: event.button,\n", " step: event.step,\n", " guiEvent: simpleKeys(event),\n", " });\n", "\n", " /* This prevents the web browser from automatically changing to\n", " * the text insertion cursor when the button is pressed. We want\n", " * to control all of the cursor setting manually through the\n", " * 'cursor' event from matplotlib */\n", " event.preventDefault();\n", " return false;\n", "};\n", "\n", "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n", " // Handle any extra behaviour associated with a key event\n", "};\n", "\n", "mpl.figure.prototype.key_event = function (event, name) {\n", " // Prevent repeat events\n", " if (name === 'key_press') {\n", " if (event.which === this._key) {\n", " return;\n", " } else {\n", " this._key = event.which;\n", " }\n", " }\n", " if (name === 'key_release') {\n", " this._key = null;\n", " }\n", "\n", " var value = '';\n", " if (event.ctrlKey && event.which !== 17) {\n", " value += 'ctrl+';\n", " }\n", " if (event.altKey && event.which !== 18) {\n", " value += 'alt+';\n", " }\n", " if (event.shiftKey && event.which !== 16) {\n", " value += 'shift+';\n", " }\n", "\n", " value += 'k';\n", " value += event.which.toString();\n", "\n", " this._key_event_extra(event, name);\n", "\n", " this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n", " return false;\n", "};\n", "\n", "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n", " if (name === 'download') {\n", " this.handle_save(this, null);\n", " } else {\n", " this.send_message('toolbar_button', { name: name });\n", " }\n", "};\n", "\n", "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n", " this.message.textContent = tooltip;\n", "};\n", "\n", "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n", "// prettier-ignore\n", "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n", "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n", "\n", "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n", "\n", "mpl.default_extension = \"png\";/* global mpl */\n", "\n", "var comm_websocket_adapter = function (comm) {\n", " // Create a \"websocket\"-like object which calls the given IPython comm\n", " // object with the appropriate methods. Currently this is a non binary\n", " // socket, so there is still some room for performance tuning.\n", " var ws = {};\n", "\n", " ws.close = function () {\n", " comm.close();\n", " };\n", " ws.send = function (m) {\n", " //console.log('sending', m);\n", " comm.send(m);\n", " };\n", " // Register the callback with on_msg.\n", " comm.on_msg(function (msg) {\n", " //console.log('receiving', msg['content']['data'], msg);\n", " // Pass the mpl event to the overridden (by mpl) onmessage function.\n", " ws.onmessage(msg['content']['data']);\n", " });\n", " return ws;\n", "};\n", "\n", "mpl.mpl_figure_comm = function (comm, msg) {\n", " // This is the function which gets called when the mpl process\n", " // starts-up an IPython Comm through the \"matplotlib\" channel.\n", "\n", " var id = msg.content.data.id;\n", " // Get hold of the div created by the display call when the Comm\n", " // socket was opened in Python.\n", " var element = document.getElementById(id);\n", " var ws_proxy = comm_websocket_adapter(comm);\n", "\n", " function ondownload(figure, _format) {\n", " window.open(figure.canvas.toDataURL());\n", " }\n", "\n", " var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n", "\n", " // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n", " // web socket which is closed, not our websocket->open comm proxy.\n", " ws_proxy.onopen();\n", "\n", " fig.parent_element = element;\n", " fig.cell_info = mpl.find_output_cell(\"
\");\n", " if (!fig.cell_info) {\n", " console.error('Failed to find cell for figure', id, fig);\n", " return;\n", " }\n", " fig.cell_info[0].output_area.element.on(\n", " 'cleared',\n", " { fig: fig },\n", " fig._remove_fig_handler\n", " );\n", "};\n", "\n", "mpl.figure.prototype.handle_close = function (fig, msg) {\n", " var width = fig.canvas.width / fig.ratio;\n", " fig.cell_info[0].output_area.element.off(\n", " 'cleared',\n", " fig._remove_fig_handler\n", " );\n", " fig.resizeObserverInstance.unobserve(fig.canvas_div);\n", "\n", " // Update the output cell to use the data from the current canvas.\n", " fig.push_to_output();\n", " var dataURL = fig.canvas.toDataURL();\n", " // Re-enable the keyboard manager in IPython - without this line, in FF,\n", " // the notebook keyboard shortcuts fail.\n", " IPython.keyboard_manager.enable();\n", " fig.parent_element.innerHTML =\n", " '';\n", " fig.close_ws(fig, msg);\n", "};\n", "\n", "mpl.figure.prototype.close_ws = function (fig, msg) {\n", " fig.send_message('closing', msg);\n", " // fig.ws.close()\n", "};\n", "\n", "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n", " // Turn the data on the canvas into data in the output cell.\n", " var width = this.canvas.width / this.ratio;\n", " var dataURL = this.canvas.toDataURL();\n", " this.cell_info[1]['text/html'] =\n", " '';\n", "};\n", "\n", "mpl.figure.prototype.updated_canvas_event = function () {\n", " // Tell IPython that the notebook contents must change.\n", " IPython.notebook.set_dirty(true);\n", " this.send_message('ack', {});\n", " var fig = this;\n", " // Wait a second, then push the new image to the DOM so\n", " // that it is saved nicely (might be nice to debounce this).\n", " setTimeout(function () {\n", " fig.push_to_output();\n", " }, 1000);\n", "};\n", "\n", "mpl.figure.prototype._init_toolbar = function () {\n", " var fig = this;\n", "\n", " var toolbar = document.createElement('div');\n", " toolbar.classList = 'btn-toolbar';\n", " this.root.appendChild(toolbar);\n", "\n", " function on_click_closure(name) {\n", " return function (_event) {\n", " return fig.toolbar_button_onclick(name);\n", " };\n", " }\n", "\n", " function on_mouseover_closure(tooltip) {\n", " return function (event) {\n", " if (!event.currentTarget.disabled) {\n", " return fig.toolbar_button_onmouseover(tooltip);\n", " }\n", " };\n", " }\n", "\n", " fig.buttons = {};\n", " var buttonGroup = document.createElement('div');\n", " buttonGroup.classList = 'btn-group';\n", " var button;\n", " for (var toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", " /* Instead of a spacer, we start a new button group. */\n", " if (buttonGroup.hasChildNodes()) {\n", " toolbar.appendChild(buttonGroup);\n", " }\n", " buttonGroup = document.createElement('div');\n", " buttonGroup.classList = 'btn-group';\n", " continue;\n", " }\n", "\n", " button = fig.buttons[name] = document.createElement('button');\n", " button.classList = 'btn btn-default';\n", " button.href = '#';\n", " button.title = name;\n", " button.innerHTML = '';\n", " button.addEventListener('click', on_click_closure(method_name));\n", " button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n", " buttonGroup.appendChild(button);\n", " }\n", "\n", " if (buttonGroup.hasChildNodes()) {\n", " toolbar.appendChild(buttonGroup);\n", " }\n", "\n", " // Add the status bar.\n", " var status_bar = document.createElement('span');\n", " status_bar.classList = 'mpl-message pull-right';\n", " toolbar.appendChild(status_bar);\n", " this.message = status_bar;\n", "\n", " // Add the close button to the window.\n", " var buttongrp = document.createElement('div');\n", " buttongrp.classList = 'btn-group inline pull-right';\n", " button = document.createElement('button');\n", " button.classList = 'btn btn-mini btn-primary';\n", " button.href = '#';\n", " button.title = 'Stop Interaction';\n", " button.innerHTML = '';\n", " button.addEventListener('click', function (_evt) {\n", " fig.handle_close(fig, {});\n", " });\n", " button.addEventListener(\n", " 'mouseover',\n", " on_mouseover_closure('Stop Interaction')\n", " );\n", " buttongrp.appendChild(button);\n", " var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n", " titlebar.insertBefore(buttongrp, titlebar.firstChild);\n", "};\n", "\n", "mpl.figure.prototype._remove_fig_handler = function (event) {\n", " var fig = event.data.fig;\n", " if (event.target !== this) {\n", " // Ignore bubbled events from children.\n", " return;\n", " }\n", " fig.close_ws(fig, {});\n", "};\n", "\n", "mpl.figure.prototype._root_extra_style = function (el) {\n", " el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n", "};\n", "\n", "mpl.figure.prototype._canvas_extra_style = function (el) {\n", " // this is important to make the div 'focusable\n", " el.setAttribute('tabindex', 0);\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", " } else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", "};\n", "\n", "mpl.figure.prototype._key_event_extra = function (event, _name) {\n", " var manager = IPython.notebook.keyboard_manager;\n", " if (!manager) {\n", " manager = IPython.keyboard_manager;\n", " }\n", "\n", " // Check for shift+enter\n", " if (event.shiftKey && event.which === 13) {\n", " this.canvas_div.blur();\n", " // select the cell after this one\n", " var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n", " IPython.notebook.select(index + 1);\n", " }\n", "};\n", "\n", "mpl.figure.prototype.handle_save = function (fig, _msg) {\n", " fig.ondownload(fig, null);\n", "};\n", "\n", "mpl.find_output_cell = function (html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", " for (var i = 0; i < ncells; i++) {\n", " var cell = cells[i];\n", " if (cell.cell_type === 'code') {\n", " for (var j = 0; j < cell.output_area.outputs.length; j++) {\n", " var data = cell.output_area.outputs[j];\n", " if (data.data) {\n", " // IPython >= 3 moved mimebundle to data attribute of output\n", " data = data.data;\n", " }\n", " if (data['text/html'] === html_output) {\n", " return [cell, data, j];\n", " }\n", " }\n", " }\n", " }\n", "};\n", "\n", "// Register the function which deals with the matplotlib target/channel.\n", "// The kernel may be null if the page has been refreshed.\n", "if (IPython.notebook.kernel !== null) {\n", " IPython.notebook.kernel.comm_manager.register_target(\n", " 'matplotlib',\n", " mpl.mpl_figure_comm\n", " );\n", "}\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize=(8,8)\n", "fig,ax = plt.subplots(3,1,figsize =figsize)\n", "#k=1\n", "for alpha in np.arange(0,2.05,0.05).round(2):\n", " #Xa = FRFT(x.copy(), alpha)\n", " Xa = sp.frft(x.copy(),alpha=alpha)\n", " ax[0].clear()\n", " #ax[0].plot(t,x)\n", " ax[0].plot(t,Xa.real)\n", " ax[0].plot(t,Xa.imag)\n", " ax[0].set_xlim([t[0],t[-1]])\n", " ax[0].set_title(r'$F_a(x)$ at a = '+str(alpha))\n", " ax[0].set_ylabel(r'signal $F_a(x)$')\n", " \n", " fx,tx,Sx = signal.spectrogram(Xa,fs=fs,nperseg=64,nfft=256,return_onesided=False)\n", " Sx = np.abs(Sx)\n", " #Sx = np.log(np.abs(Sx))\n", " ax[1].clear()\n", " ax[1].imshow(Sx[:129], aspect='auto',origin='lower',cmap='jet', extent=[tx[0],tx[-1],0,fs/2])\n", " ax[1].set_ylabel('Spectrogram')\n", " #Fx = np.log10(np.abs(np.fft.fftshift(np.fft.fft(x))))\n", " Ff = np.log10(np.abs(np.fft.fftshift(np.fft.fft(Xa))))\n", " N = len(Ff)\n", " fq = fs*(np.arange(N)- (N//2))/N \n", " ax[2].clear()\n", " #ax[2].plot(fq,Fx)\n", " ax[2].plot(fq,Ff)\n", " ax[2].set_xlim([fq[0],fq[-1]])\n", " ax[2].set_ylabel('Spectrum')\n", " #k+=1\n", " fig.canvas.draw()\n", " time.sleep(0.8)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 5 }