Updated Project DFT and Original Dataset Model Evaluation

Project_DFT.ipynb

@@ -488,7 +488,33 @@
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-    "# Discrete Fourier Transform (DFT)"
+    "# Discrete Fourier Transform (DFT)\n",
+    "\n",
+    "The `perform_dft` function performs a Discrete Fourier Transform (DFT) on the Channel Impulse Response (CIR) values. The DFT is a mathematical technique used to transform a sequence of complex numbers into another sequence of complex numbers with the same length. It is widely used in signal processing to analyze the frequency components of a time-domain signal.\n",
+    "\n",
+    "Here's a step-by-step breakdown of the function:\n",
+    "\n",
+    "1. **Extract the CIR values**: The function takes a DataFrame and the column names of the CIR values as input, and extracts the CIR values.\n",
+    "\n",
+    "2. **Perform DFT on the CIR values**: The function uses the `numpy.fft.fft` function to perform the DFT on the CIR values. The DFT is computed along the second axis of the array (axis=1), which corresponds to the columns of the DataFrame.\n",
+    "\n",
+    "3. **Take the absolute values of the DFT**: The DFT operation returns complex numbers, which can be difficult to interpret and visualize. Therefore, the function takes the absolute values of the DFT, which gives the magnitude of the frequency components.\n",
+    "\n",
+    "4. **Return the absolute values**: The function returns the absolute values of the DFT.\n",
+    "\n",
+    "The mathematical representation of the DFT is:\n",
+    "\n",
+    "$$\n",
+    "X[k] = \\sum_{n=0}^{N-1} x[n] \\cdot e^{-j(2\\pi/N)kn}\n",
+    "$$\n",
+    "\n",
+    "where:\n",
+    "- $X[k]$ is the $k$-th element of the DFT.\n",
+    "- $x[n]$ is the $n$-th element of the input sequence.\n",
+    "- $N$ is the total number of elements in the input sequence.\n",
+    "- $j$ is the imaginary unit.\n",
+    "\n",
+    "The reason for using the DFT in this context is to analyze the frequency components of the CIR values. This can provide valuable insights into the characteristics of the wireless channel, such as the presence of multipath propagation."
    ],
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