From bde048062854006edd16da5d64ba151497f5afaa Mon Sep 17 00:00:00 2001
From: Nimitt Sharma <84977996+Nimittxo@users.noreply.github.com>
Date: Sat, 12 Oct 2024 00:54:04 +0530
Subject: [PATCH] Fourier_Transform.py

Creation of another folder and creating the first Algorithm for Fourier_Transform
---
 maths/Transforms/Fourier_Transform.py | 34 +++++++++++++++++++++++++++
 1 file changed, 34 insertions(+)
 create mode 100644 maths/Transforms/Fourier_Transform.py

diff --git a/maths/Transforms/Fourier_Transform.py b/maths/Transforms/Fourier_Transform.py
new file mode 100644
index 000000000000..4a5b677ea4a3
--- /dev/null
+++ b/maths/Transforms/Fourier_Transform.py
@@ -0,0 +1,34 @@
+import numpy as np
+from typing import List, Union
+
+def fourier_transform(signal: List[Union[int, float]]) -> List[complex]:
+    """
+    Compute the discrete Fourier transform (DFT) of a signal.
+
+    Args:
+    signal (List[Union[int, float]]): A list of numerical values representing the input signal.
+
+    Returns:
+    List[complex]: The Fourier transform of the input signal as a list of complex numbers.
+
+    Example:
+    >>> fourier_transform([1, 2, 3, 4])
+    [(10+0j), (-2+2j), (-2+0j), (-2-2j)]
+
+    Note:
+    This is a basic implementation of the DFT and can be optimized using FFT for larger datasets.
+    """
+    n = len(signal)
+    result = []
+    for k in range(n):  
+        summation = 0 + 0j 
+        for t in range(n):  
+            angle = -2j * np.pi * t * k / n
+            summation += signal[t] * np.exp(angle)
+        result.append(summation)
+    return result
+
+if __name__ == "__main__":
+    sample_signal = [1, 2, 3, 4]
+    result = fourier_transform(sample_signal)
+    print("Fourier Transform of the signal:", result)