From 835603223fff4ed651fc8e2343b2eaadb8ece0aa Mon Sep 17 00:00:00 2001
From: Nimitt Sharma <84977996+Nimittxo@users.noreply.github.com>
Date: Sat, 12 Oct 2024 00:59:11 +0530
Subject: [PATCH 1/3] fourier_transform.py

create a new directory called ``` transforms ``` for transforms in calculus added first transform named 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..bec7212e60a6
--- /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)

From 45b18a8669656ebc317b76a39b438d575012d16c Mon Sep 17 00:00:00 2001
From: Nimitt Sharma <84977996+Nimittxo@users.noreply.github.com>
Date: Sat, 12 Oct 2024 01:06:50 +0530
Subject: [PATCH 2/3] Update fourier_transform.py

---
 maths/transforms/fourier_transform.py | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/maths/transforms/fourier_transform.py b/maths/transforms/fourier_transform.py
index bec7212e60a6..c50bbdd7378a 100644
--- a/maths/transforms/fourier_transform.py
+++ b/maths/transforms/fourier_transform.py
@@ -1,28 +1,28 @@
-import numpy as np
 from typing import List, Union
+import numpy as np
 
-def fourier_transform(signal: List[Union[int, float]]) -> List[complex]:
+def fourier_transform(signal: list[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.
+        signal (list[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.
+        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)]
+        >>> 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.
+        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):  
+    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)

From cf00b93ad6c1056dc3461c4e70f8e53fa5b2ab23 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Fri, 11 Oct 2024 19:43:07 +0000
Subject: [PATCH 3/3] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/transforms/fourier_transform.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/maths/transforms/fourier_transform.py b/maths/transforms/fourier_transform.py
index c50bbdd7378a..e0d6bc65bf3a 100644
--- a/maths/transforms/fourier_transform.py
+++ b/maths/transforms/fourier_transform.py
@@ -1,6 +1,7 @@
 from typing import List, Union
 import numpy as np
 
+
 def fourier_transform(signal: list[int | float]) -> list[complex]:
     """
     Compute the discrete Fourier transform (DFT) of a signal.
@@ -28,6 +29,7 @@ def fourier_transform(signal: list[int | float]) -> list[complex]:
         result.append(summation)
     return result
 
+
 if __name__ == "__main__":
     sample_signal = [1, 2, 3, 4]
     result = fourier_transform(sample_signal)