{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: FFT Analysis of Hot Wire data via Python\n", "\n", "Murat's Data used. \n", "\n", "100 datasets, each has of 131072 reasilation. \n", "Mean velocity is 6.842 m/s.\n", "\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Data loaded on Ipython environment, and it's shape is (131072, 100)\n", "Mean velocity is 6.84244558364\n" ] } ], "source": [ "import numpy as np\n", "#import pandas as pd\n", "from scipy.fftpack import fft, ifft,fftshift,fftfreq\n", "\n", "data = np.loadtxt('velocity_data.out') #too slow, http://akuederle.com/stop-using-numpy-loadtxt/\n", "#data = pd.read_csv('../../lfs/murats_velocity_data.out') #will not work that with bare version\n", "print(\"Data loaded on Ipython environment, and it's shape is\", data.shape)\n", "\n", "mean_data = np.mean(data)\n", "print(\"Mean velocity is\", mean_data)\n", "\n", "fluc_data= data - mean_data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Function to calculate spectrum\n", "\n", "Often magnitude of FT or FFT is not important, **for us it is**!! \n", "So normalization is important, it is not just the shape.\n", "\n", "There are 3 steps to follow;\n", " 1. Take the FFT of the signal \n", " 2. Calculate spectrum\n", " 3. Normalization\n", " \n", "**Without understanding all these 3, it is difficult get correct transform.**\n", "\n", "It is always possible to `check` that if your transform is correct or not. To do so,\n", " 1. Check the integral of the are under the estimation of S(f), that should be equalt to var(signal)\n", " 2. IFFT of spectrum should give the correlation, and correlation can be also calculated with brute force, so two correlation can be compared (tidious FFT has windowing effect **always**, it needs taken out/handled properly)\n", " 3. In case having both time and space resolved data, spectrums of these to can be compared, of course within the limits of Taylor Hypothesis. Moreover, energy levels should reasonably match, it is a good way to double check correctness of wavenumber/wavelenght conversations. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# Calculates the spectrum of a given signal with fft\n", "def calc_spectrum(mysignal, size, fs, typeWindow):\n", " # Window \n", " # Add window or periodization here \n", " if typeWindow == 'Hanning':\n", " mysignal = mysignal[0:size]*np.hanning(size)\n", " integWindow = np.trapz(np.hanning(size),np.linspace(0,1,size))\n", " elif typeWindow == 'None':\n", " mysignal = mysignal[0:size]*1.0\n", " integWindow = 1.0\n", " \n", " # Take the FFT of the signal, -1 important\n", " # Remember you have the -1 here if you periodize your signal outside of this routine\n", " # Multiplying by 2 or not, and having -fs/2:fs/2 frequencies should be compatible\n", " # following FFT double sided no need to multiply by 2\n", " # Skip the division by N-1 as well, for the moment, normalization is done at the end\n", " myfft = fft(mysignal[0:size-1]) #*2.0 #/float(size-1)\n", " \n", " # Calculate spectrum\n", " # (real**2.0+imag**2.0) is kind of variance\n", " # if you take sqrt() that makes it kind of standart deviation, same unit as velocity, \n", " # nice for Fluid Mechanics applications\n", " # But let's keep (standart deviation)**2.0, so no need take sqrt() \n", " myspec = (myfft.real[0:int((size-1)/2)]**2.0+myfft.imag[0:int((size-1)/2)]**2.0) #**0.5\n", " # OR :: Common way, attention it is missing the sqrt() as well, good\n", " #myspec = myfft[0:(size)/2]*np.conj(myfft)[0:(size)/2]\n", " \n", " # Normalization\n", " # EXAMPLE :: if the data collected with 30kHz, and you want to have first 256 points, at every 2 points\n", " # First 256 points that gives the new size\n", " # New fs 30kHz/2 = 15kHz\n", " myspec = myspec/(float(size-1)*fs)/(integWindow)\n", " \n", " return myspec" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "N=256 #Choose record length, maximum is 131072 \n", "#N=2000\n", "\n", "\n", "fs=30000 # Define fs\n", "freq_3 = fftfreq(N, d=1./fs)[0:int((N/2)-1)] # Create frequencies, needed to plot, pick the half of freq. \n", "spec_3 = calc_spectrum(fluc_data[:,0], N, fs, 'None') # Call function \n", "\n", "fs=15000 # Define fs\n", "freq_4 = fftfreq(int(N/2), d=1./fs)[0:int((N/2)/2)-1] # Create frequencies, needed to plot, pick the half of freq.\n", "spec_4 = calc_spectrum(fluc_data[0::2,0], int(N/2), fs,'None') # Call function\n", "\n", "# Loop over the packages (note: this is unefficient) \n", "for i in range(1,100):\n", " fs=30000\n", " spec_3 += calc_spectrum(fluc_data[: ,i], N, fs,'None')\n", " fs=15000\n", " spec_4 += calc_spectrum(fluc_data[0::2,i], int(N/2), fs,'None')\n", "\n", " \n", "# Do not forget the averaging packages \n", "spec_3 = spec_3/100.\n", "spec_4 = spec_4/100." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "#N=256 #Choose record length, maximum is 131072 \n", "N=13072\n", "\n", "fs=30000 # Define fs\n", "freq_1 = fftfreq(N, d=1./fs)[0:int((N/2)-1)] # Create frequencies, needed to plot, pick the half of freq. \n", "spec_1 = calc_spectrum(fluc_data[: ,0], N, fs, 'None') # Call function \n", "\n", "\n", "# Loop over the packages (note: this is unefficient) \n", "for i in range(1,100):\n", " fs=30000\n", " spec_1 += calc_spectrum(fluc_data[: ,i], N, fs,'None')\n", "\n", "\n", " \n", "# Do not forget the averaging packages \n", "spec_1 = spec_1/100.\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\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('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", "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 = $('
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');\n", " titlebar.append(titletext)\n", " this.root.append(titlebar);\n", " this.header = titletext[0];\n", "}\n", "\n", "\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "\n", "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "mpl.figure.prototype._init_canvas = function() {\n", " var fig = this;\n", "\n", " var canvas_div = $('
');\n", "\n", " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", "\n", " function canvas_keyboard_event(event) {\n", " return fig.key_event(event, event['data']);\n", " }\n", "\n", " canvas_div.keydown('key_press', canvas_keyboard_event);\n", " canvas_div.keyup('key_release', canvas_keyboard_event);\n", " this.canvas_div = canvas_div\n", " this._canvas_extra_style(canvas_div)\n", " this.root.append(canvas_div);\n", "\n", " var canvas = $('');\n", " canvas.addClass('mpl-canvas');\n", " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", "\n", " this.canvas = canvas[0];\n", " this.context = canvas[0].getContext(\"2d\");\n", "\n", " var backingStore = this.context.backingStorePixelRatio ||\n", "\tthis.context.webkitBackingStorePixelRatio ||\n", "\tthis.context.mozBackingStorePixelRatio ||\n", "\tthis.context.msBackingStorePixelRatio ||\n", "\tthis.context.oBackingStorePixelRatio ||\n", "\tthis.context.backingStorePixelRatio || 1;\n", "\n", " mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n", "\n", " var rubberband = $('');\n", " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", "\n", " var pass_mouse_events = true;\n", "\n", " canvas_div.resizable({\n", " start: function(event, ui) {\n", " pass_mouse_events = false;\n", " },\n", " resize: function(event, ui) {\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " stop: function(event, ui) {\n", " pass_mouse_events = true;\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " });\n", "\n", " function mouse_event_fn(event) {\n", " if (pass_mouse_events)\n", " return fig.mouse_event(event, event['data']);\n", " }\n", "\n", " rubberband.mousedown('button_press', mouse_event_fn);\n", " rubberband.mouseup('button_release', mouse_event_fn);\n", " // Throttle sequential mouse events to 1 every 20ms.\n", " rubberband.mousemove('motion_notify', mouse_event_fn);\n", "\n", " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", "\n", " canvas_div.on(\"wheel\", function (event) {\n", " event = event.originalEvent;\n", " event['data'] = 'scroll'\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", " mouse_event_fn(event);\n", " });\n", "\n", " canvas_div.append(canvas);\n", " canvas_div.append(rubberband);\n", "\n", " this.rubberband = rubberband;\n", " this.rubberband_canvas = rubberband[0];\n", " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", " this.rubberband_context.strokeStyle = \"#000000\";\n", "\n", " this._resize_canvas = function(width, height) {\n", " // Keep the size of the canvas, canvas container, and rubber band\n", " // canvas in synch.\n", " canvas_div.css('width', width)\n", " canvas_div.css('height', height)\n", "\n", " canvas.attr('width', width * mpl.ratio);\n", " canvas.attr('height', height * mpl.ratio);\n", " canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n", "\n", " rubberband.attr('width', width);\n", " rubberband.attr('height', height);\n", " }\n", "\n", " // Set the figure to an initial 600x600px, this will subsequently be updated\n", " // upon first draw.\n", " this._resize_canvas(600, 600);\n", "\n", " // Disable right mouse context menu.\n", " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", " return false;\n", " });\n", "\n", " function set_focus () {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", "}\n", "\n", "mpl.figure.prototype._init_toolbar = function() {\n", " var fig = this;\n", "\n", " var nav_element = $('
')\n", " nav_element.attr('style', 'width: 100%');\n", " this.root.append(nav_element);\n", "\n", " // Define a callback function for later on.\n", " function toolbar_event(event) {\n", " return fig.toolbar_button_onclick(event['data']);\n", " }\n", " function toolbar_mouse_event(event) {\n", " return fig.toolbar_button_onmouseover(event['data']);\n", " }\n", "\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", " // put a spacer in here.\n", " continue;\n", " }\n", " var button = $('