Source Code for Calculating Time Series Average Period Using FFT Method

The following source code demonstrates how to calculate the average period of a time series using the Fast Fourier Transform (FFT) method:

```python

import numpy as np

def calculate_average_period(time_series):

# Transform time domain signal to frequency domain using FFT

# The FFT algorithm efficiently computes the Discrete Fourier Transform (DFT)

freq_domain_signal = np.fft.fft(time_series)

# Identify the dominant frequency by finding the peak magnitude

# np.abs() computes magnitude spectrum, argmax() returns index of maximum value

peak_frequency = np.argmax(np.abs(freq_domain_signal))

# Calculate average period as inverse of peak frequency

# This transforms frequency (cycles per sample) to period (samples per cycle)

average_period = 1 / peak_frequency

return average_period

# Example implementation with synthetic data

time_series = [1, 2, 3, 4, 5, 4, 3, 2, 1]

result = calculate_average_period(time_series)

print("The average period of the time series is:", result)

```

This basic example illustrates the fundamental FFT approach for period calculation in time series analysis. The method works by converting the signal to frequency domain and extracting the dominant frequency component. Note that real-world applications may require additional preprocessing steps like windowing or zero-padding for improved accuracy.