+ spike spectra

Analyzing_Rhythms_Lab_2b.ipynb

@@ -200,7 +200,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.18"
+   "version": "3.12.4"
   }
  },
  "nbformat": 4,

Analyzing_Rhythms_Lab_3.ipynb

@@ -0,0 +1,177 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "title: Analyzing Rhythms Part 3 (Spectra of spike trains)\n",
+    "project:\n",
+    "  type: website\n",
+    "format:\n",
+    "  html:\n",
+    "    code-fold: false\n",
+    "    code-tools: true\n",
+    "jupyter: python 3\n",
+    "number-sections: false\n",
+    "---"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Load modules we'll need.\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Example: a randomly spiking neuron"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "To start, let's create a fake spike train for a randomly spiking neuron, and compute the autocovariance and spectrum."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "N  = 5000;                          # Number of bins.                   \n",
+    "dt = 0.001;                         # Duration of each bin [s].\n",
+    "T  = N*dt;                          # Total time of observation [s].\n",
+    "tm = np.arange(0,N)*dt;             # Time axis for plotting\n",
+    "\n",
+    "lambda0 = 5                         # Average firing rate [Hz]\n",
+    "p0      = lambda0*dt;               # Probability of a spike in a time bin\n",
+    "dn      = np.random.binomial(1,p0,N)# Create the spike train as \"coin flips\"\n",
+    "\n",
+    "plt.plot(tm, dn)                    # Plot it.\n",
+    "plt.xlabel('Time [s]');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Compute the autocovariance."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Compute the spectrum."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Repeat the entire simulation many times, and plot the average spectrum"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Example: a randomly spiking neuron + refractory period"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now, let's create a fake spike train for a randomly spiking neuron with a refractory period, and compute the autocovariance and spectrum."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "N  = 5000;                          # Number of bins.                   \n",
+    "dt = 0.001;                         # Duration of each bin [s].\n",
+    "T  = N*dt;                          # Total time of observation [s].\n",
+    "tm = np.arange(0,N)*dt;             # Time axis for plotting\n",
+    "\n",
+    "lambda0 = 5                         # Average firing rate [Hz]\n",
+    "p0      = lambda0*dt;               # Probability of a spike in a time bin\n",
+    "dn      = np.random.binomial(1,p0,N)# Create the spike train as \"coin flips\"\n",
+    "\n",
+    "???????????????????????????????\n",
+    "??? ADD A REFRACTORY PERIOD ???\n",
+    "???????????????????????????????\n",
+    "\n",
+    "plt.plot(tm, dn)                    # Plot it.\n",
+    "plt.xlabel('Time [s]');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Compute the autocovariance."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Compute the spectrum."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Repeat the entire simulation many times, and plot the average spectrum"
+   ]
+  }
+ ],
+ "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": "3.12.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}

_quarto.yml

@@ -25,8 +25,7 @@ website:
       - href: Regression.html
         text: Regression
       - href: Rhythms_1.html
-        text: Rhythms 1
-
+        text: Rhythms Intro
 
 format:
   html:

docs/Analyzing_Rhythms_Lab_1.html

@@ -152,7 +152,7 @@
   </li>  
   <li class="nav-item">
     <a class="nav-link" href="./Rhythms_1.html"> 
-<span class="menu-text">Rhythms 1</span></a>
+<span class="menu-text">Rhythms Intro</span></a>
   </li>  
 </ul>
           </div> <!-- /navcollapse -->

docs/Analyzing_Rhythms_Lab_2a.html

@@ -152,7 +152,7 @@
   </li>  
   <li class="nav-item">
     <a class="nav-link" href="./Rhythms_1.html"> 
-<span class="menu-text">Rhythms 1</span></a>
+<span class="menu-text">Rhythms Intro</span></a>
   </li>  
 </ul>
           </div> <!-- /navcollapse -->

docs/Analyzing_Rhythms_Lab_2b.html

@@ -152,7 +152,7 @@
   </li>  
   <li class="nav-item">
     <a class="nav-link" href="./Rhythms_1.html"> 
-<span class="menu-text">Rhythms 1</span></a>
+<span class="menu-text">Rhythms Intro</span></a>
   </li>  
 </ul>
           </div> <!-- /navcollapse -->