epic-fourier 0.1.1

A library for computing Fourier Series made for Physics Students!

Hello!

It has become evident to me that Python Scipy lacks a Fourier SERIES function! Unbelievable! I have made this for my peers in the Imperial College London Physics Department, I hope you find it useful :).

This package contains two components under the 'series' directory so far. Firstly, Fourier series computation for a periodic function, 'FSeries'. Secondly, Fourier Series computation for a periodic dataset, 'nFSeries'.

Please direct bug reports, feature requests, or anything else regarding this custom library to my personal email: [e-mail]

For those of you reading on GitHub, running 'pip install FSeries' in Python should import this library!

Happy coding!

'series': 'series.FSeries': Compute the Fourier coefficients (a_n, b_n, a_0) for a periodic function f(x) using numerical integration.

    Parameters:
        x: array type int/float - the 'x' axis column
        f: function - the function to be decomposed
        T: float - period of the function (if periodic), or interval length (if non-periodic)
        n_terms: int - number of Fourier terms (default is 10)

    Returns: 
        series: numpy array - Fourier series approximation along x
        a_n: numpy array - Fourier cosine coefficients
        b_n: numpy array - Fourier sine coefficients
        a_0: float - Fourier a_0 coefficient

    Examples: 
        ... #generate x values
        def f_custom(x):
            return 0.5 * np.sin(3 * x) + 0.25 * np.cos(4 * x)

        T = np.pi
        series, a_n, b_n, a_0 = epic_fourier.series.FSeries(x, f_custom, T=T, n_terms=10)

        #You can also plot the series function:
        plt.plot(x, series, label='Fourier Series Approximation')
    

'series.nFSeries': 
    Compute the Fourier coefficients (a_n, b_n, a_0) for a discrete, periodic dataset using numerical summations for each datapoint.
            
    Parameters: 
        data: pandas DataFrame or 2D array, shape - with columns for 'x' and 'y' axis, the dataset to be numerically analyzed
        T: float - period of the function (if periodic), or interval length (if non-periodic)
        n_terms: int - number of Fourier terms (default is 10)

    Returns: 
        series: numpy array - Fourier series approximation along x
        a_n: numpy array - Fourier cosine coefficients
        b_n: numpy array - Fourier sine coefficients
        a_0: float - Fourier a_0 coefficient

    Examples: 
        data = [[ 0.          0.        ]
                [ 0.1010101   0.10083842]
                [ 0.2020202   0.20064886]
                [ 0.3030303   0.2984138 ]
                [ 0.4040404   0.39313661]]
        #the first column here is x, the second is y
 
        series, a_n, b_n, a_0 = epic_fourier.series.nFSeries(data, 240, 20)
        
    
        data = [[ 0.          0.        ]
                [ 0.1010101   0.10083842]
                [ 0.2020202   0.20064886]
                [ 0.3030303   0.2984138 ]
                [ 0.4040404   0.39313661]]
        df = pd.DataFrame(data, columns=['x', 'y'])

        series, a_n, b_n, a_0 = epic_fourier.series.nFSeries(df, 120, 40)


        #You might even find this useful with the scipy.signal.sawtooth 
        function!

        f_values = signal.sawtooth(2 * np.pi * x / (2 * np.pi))  # Sawtooth wave
        data = np.column_stack((x, f_values))

        T = 2 * np.pi  # Period of the sawtooth wave
        series, a_n, b_n, a_0 = epic_fourier.series.nFSeries(data, T, n_terms=10)