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    "# Fourier decomposition\n",
    "\n",
    "This example uses the `show()`, `morph()`, `translate()` and `hide()` animations to animate `plot` plot objects to show how we can reconstruct a signal with a Fourier Transform."
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b8ecc773",
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   "source": [
    "import diplotocus as dpl\n",
    "import numpy as np\n",
    "\n",
    "#We create our timeline and define a global easing\n",
    "tl = dpl.Timeline(xlim=(-5,5),ylim=(-0.25,1.5),easing=dpl.easeInCubic())\n",
    "\n",
    "#We create the signal we want to Fourier decompose\n",
    "x = np.linspace(-5,5,100)\n",
    "y = np.exp(-x**2)\n",
    "\n",
    "#Plot the real signal\n",
    "tl.ax.plot(x, y, c='k', ls='--', alpha=0.5)\n",
    "\n",
    "#Get its Fourier power spectrum\n",
    "freq = np.fft.fftfreq(len(x),x[1]-x[0])\n",
    "sp = np.fft.fft(y)\n",
    "\n",
    "#Add a plot object for our reconstructed signal\n",
    "p_total = dpl.plot(x,np.zeros_like(x),c='green',lw=3)\n",
    "p_total.plot(duration=30)\n",
    "\n",
    "#We create a list to store all the plotObjects we will animate\n",
    "plot_objects = [p_total]\n",
    "\n",
    "#Loop over the first 8 frequencies\n",
    "for i in range(8):\n",
    "    amp = np.abs(sp[i])/len(x)\n",
    "    phase = np.angle(sp[i])\n",
    "    if i > 0:\n",
    "        amp *= 2#We need to double the amplitude of doubled modes\n",
    "\n",
    "    x0 = np.linspace(-5,5,500,endpoint=False)\n",
    "    y0 = 0.25*np.cos(x0*2*np.pi*freq[i]) + 1.25\n",
    "    y1 = amp*np.cos((x0-x[0])*2*np.pi*freq[i] + phase) + 1.25\n",
    "\n",
    "    #We first create a cosine wave of the current frequency\n",
    "    p = dpl.plot(x0,y0)\n",
    "\n",
    "    #We delay each mode so they appear sequentially\n",
    "    base_delay = 50*i\n",
    "    #We fade the plot in\n",
    "    p.show(duration=10,delay=base_delay)\n",
    "    #Morph it into the right cosine wave given the power spectrum\n",
    "    p.morph(new_x=x0,new_y=y1,duration=20,delay=base_delay + 10)\n",
    "    #Move it down\n",
    "    p.translate(start_pos=(0,0),end_pos=(0,-1.25),duration=20,delay=base_delay + 30)\n",
    "    #Hide it\n",
    "    p.hide(duration=10,delay=base_delay + 40)\n",
    "    plot_objects.append(p)\n",
    "\n",
    "    #We compute the reconstructed signal from modes <= i\n",
    "    sp_total = np.where(np.abs(freq) > freq[i],0,sp)\n",
    "    y_total = np.fft.ifft(sp_total,n=len(x))\n",
    "    #We update our reconstructed signal\n",
    "    p_total.morph(new_x=x,new_y=y_total,duration=20,delay=base_delay + 30)\n",
    "\n",
    "tl.animate(plot_objects)\n",
    "tl.save_video('../../_static/examples/fourier.mp4')"
   ]
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       "\n",
       "    <video width=\"640\" height=\"460\" autoplay loop muted playsinline>\n",
       "    <source src=\"../../_static/examples/fourier.mp4?randId={}\" type=\"video/mp4\">\n",
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       "<IPython.core.display.HTML object>"
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    "from IPython.display import HTML, display\n",
    "display(HTML(\"\"\"\n",
    "    <video width=\"640\" height=\"460\" autoplay loop muted playsinline>\n",
    "    <source src=\"../../_static/examples/fourier.mp4?randId={}\" type=\"video/mp4\">\n",
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