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I am new to FFT and currently studying it for harmonic analysis. I have a set of data of inrush currents from the results of simulation involving equipment energization. The data has $N = 40,001$ sample points evenly spaced at $t = 50 \mu_s$. I generated the FFT spectrum through a python code below.

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from numpy.fft import fft, ifft, fftfreq, rfftfreq, rfft

df = pd.read_csv('inrush2.csv', delimiter = ',')

plt.plot(df['Time'], df['Phase A'])
plt.plot(df['Time'], df['Phase B'])
plt.plot(df['Time'], df['Phase C'])
plt.xlabel('Time (s)')
plt.ylabel('Current (kA)')
plt.show()

# Sampling rate
sr = np.size(df['Phase A'])
N = len(df['Phase A'])

frequency = rfftfreq(N, d=1.0/sr)
plt.plot(frequency, np.abs(rfft(df['Phase A'])))
plt.xlim(0.0, 480)
plt.show()

FFT

I have the following questions: What is the unit of the amplitude in the FFT spectrum if the input signal is in Amperes? I know the THD is $$100\frac{\sqrt{\sum_{k=2}^{\infty}V_k^2}}{V_1}$$ where $V_k$ are the harmonics and $V_1$ is the fundamental, but this formula doesn't seem to be applicable here. How do I calculate the THD from the FFT spectrum?

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1 Answer 1

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The output of a single-sided DFT such as this is scaled by the number of samples. Therefore, for an input time history that is $N$ samples in length, the DFT at each frequency point returns the product $N\cdot A$ where $A$ is the complex amplitude of the signal component at that frequency.

So to answer your question directly, the units are indeed still Amperes, but probably need re-scaling to make sense.

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