FFTLibraryLibrary "FFTLibrary" contains a function for performing Fast Fourier Transform (FFT) along with a few helper functions. In general, FFT is defined for complex inputs and outputs. The real and imaginary parts of formally complex data are treated as separate arrays (denoted as x and y). For real-valued data, the array of imaginary parts should be filled with zeros.
FFT function
fft(x, y, dir) : Computes the one-dimensional discrete Fourier transform using an in-place complex-to-complex FFT algorithm . Note: The transform also produces a mirror copy of the frequency components, which correspond to the signal's negative frequencies.
Parameters:
x : float array, real part of the data, array size must be a power of 2
y : float array, imaginary part of the data, array size must be the same as x ; for real-valued input, y must be an array of zeros
dir : string, options = , defines the direction of the transform: forward" (time-to-frequency) or inverse (frequency-to-time)
Returns: x, y : tuple (float array, float array), real and imaginary parts of the transformed data (original x and y are changed on output)
Helper functions
fftPower(x, y) : Helper function that computes the power of each frequency component (in other words, Fourier amplitudes squared).
Parameters:
x : float array, real part of the Fourier amplitudes
y : float array, imaginary part of the Fourier amplitudes
Returns: power : float array of the same length as x and y , Fourier amplitudes squared
fftFreq(N) : Helper function that returns the FFT sample frequencies defined in cycles per timeframe unit. For example, if the timeframe is 5m, the frequencies are in cycles/(5 minutes).
Parameters:
N : int, window length (number of points in the transformed dataset)
Returns: freq : float array of N, contains the sample frequencies (with zero at the start).
Signalprocessing
SignalProcessingClusteringKMeansLibrary "SignalProcessingClusteringKMeans"
K-Means Clustering Method.
nearest(point_x, point_y, centers_x, centers_y) finds the nearest center to a point and returns its distance and center index.
Parameters:
point_x : float, x coordinate of point.
point_y : float, y coordinate of point.
centers_x : float array, x coordinates of cluster centers.
centers_y : float array, y coordinates of cluster centers.
@ returns tuple of int, float.
bisection_search(samples, value) Bissection Search
Parameters:
samples : float array, weights to compare.
value : float array, weights to compare.
Returns: int.
label_points(points_x, points_y, centers_x, centers_y) labels each point index with cluster index and distance.
Parameters:
points_x : float array, x coordinates of points.
points_y : float array, y coordinates of points.
centers_x : float array, x coordinates of points.
centers_y : float array, y coordinates of points.
Returns: tuple with int array, float array.
kpp(points_x, points_y, n_clusters) K-Means++ Clustering adapted from Andy Allinger.
Parameters:
points_x : float array, x coordinates of the points.
points_y : float array, y coordinates of the points.
n_clusters : int, number of clusters.
Returns: tuple with 2 arrays, float array, int array.
