One way to obtain the Discrete Fourier Series coefficients from a set of data points in Python is to use the numpy.fft
module, which provides a fast and efficient implementation of the Discrete Fourier Transform.
First, we need to obtain the data points and define the sampling rate:
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Next, we can use the numpy.fft.fft
function to obtain the Discrete Fourier Transform of the data points:
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The resulting X
array contains the complex Fourier coefficients, where the k
-th element of X
represents the coefficient X[k]
for the k
-th frequency component. The frequencies are given by the following formula:
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To obtain the magnitude of the coefficients, we can take the absolute value:
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Finally, we can plot the magnitude of the coefficients versus the frequency:
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This will give us a plot of the frequency spectrum of the data points.
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