FFT Signal Processing

Overview

This project provides a lightweight C++ implementation of the Fast Fourier Transform (FFT) along with Fourier-based signal reconstruction tools. It allows users to:

• Compute Fourier coefficients from real-valued input data
• Filter frequency components by thresholding
• Reconstruct a signal using a Fourier Series
• Generate interpolated output samples for graphing or analysis

The implementation is fully self-contained, written from scratch, and designed for learning, experimentation, and portfolio demonstration.

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Features

• Fast Fourier Transform (FFT) implementation
• Fourier coefficient filtering for noise reduction
• Fourier-series interpolation and reconstruction
• Clean, easy-to-use C++ API
• Works with std::vector<double> input data
• Produces smooth interpolated output for graphing

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Example Usage (from main.cpp)

Step 1: Load Input Data

std::vector<double> data;
LoadData(data);

Step 2: Create the FFT Object

FFT fft;

Step 3: Compute Fourier Coefficients

fft.CalculateFFT(data);

Step 4: Optional – Filter Coefficients

fft.FilterCoefficients(0);  // 0 = no filtering

Higher values remove more frequency components.

Step 5: Generate Interpolated Fourier-Series Output

int num_of_points = data.size();
double delta = 0.5;
double start_point = 0;
double end_point = data.size();

std::vector<double> interpolated_data =
    fft.GraphFourierSeries(num_of_points, delta, start_point, end_point);

Parameter Descriptions

num_of_points  - Number of reconstructed sample points to generate
delta          - Spacing between the generated x-values
start_point    - First x-value of the interpolation interval
end_point      - Last x-value of the interpolation interval
return value   - Vector of interpolated y-values

Step 6: Display or Graph the Output

double x = 0;
for (auto& elm : interpolated_data)
{
    std::cout << "x = " << x << ", y = " << elm << std::endl;
    x += delta;
}

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Building the Project

This project includes a Makefile for compiling all source files and creating the final executable.

To build the program, simply run:

make

This will:

• Compile main.cpp, Complex.cpp, and FFT.cpp
• Produce object files: main.o, Complex.o, FFT.o
• Link them into an executable named program

Makefile

all: main.o Complex.o FFT.o
        g++ -g main.o Complex.o FFT.o -o program

main.o: main.cpp
        g++ -g -c main.cpp

Complex.o: Complex.cpp
        g++ -g -c Complex.cpp

FFT.o: FFT.cpp
        g++ -g -c FFT.cpp

clean:
        rm -f *.o program

Clean the build with:

make clean

Run the executable with:

./program

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File Structure

FFT-Signal-Processing/
    README.md
    FFT.h
    FFT.cpp
    Complex.cpp
    main.cpp

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Intended Use

This project is useful for:

• Learning FFT and Fourier Series reconstruction
• Demonstrating mathematical and algorithmic skills
• Filtering or smoothing discrete signals
• Experimenting with frequency-domain manipulation

It is dependency-free and easy to integrate into other applications.

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License

This project is released under the MIT License, allowing free use, modification, and distribution.

Copyright (c) 2025 Jerome Richards

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Author

Created by Jerome Richards
LinkedIn: https://www.linkedin.com/in/jerome-richards343
GitHub: https://github.com/Mathmatician