# Define harmonic frequencies in a Fourier series representation.

Define harmonic frequencies in a Fourier series representation.

In a Fourier series representation, harmonic frequencies refer to the integer multiples of the fundamental frequency present in the periodic waveform being analyzed. When a periodic waveform is decomposed into its constituent sinusoidal components using Fourier series, these sinusoids are characterized by their frequencies, amplitudes, and phase angles.

The fundamental frequency is the lowest frequency in the Fourier series and represents the base frequency of the periodic waveform. Harmonic frequencies are then multiples of this fundamental frequency. The nth harmonic frequency is given by:

Harmonic frequency (f_n) = n * Fundamental frequency (f0)

Where:

f_n is the nth harmonic frequency.
n is a positive integer representing the harmonic number (1, 2, 3, ...).
f0 is the fundamental frequency.

For instance, if the fundamental frequency (f0) of a periodic waveform is 100 Hz, the first three harmonic frequencies would be:

1st harmonic frequency (f_1) = 1 * 100 Hz = 100 Hz
2nd harmonic frequency (f_2) = 2 * 100 Hz = 200 Hz
3rd harmonic frequency (f_3) = 3 * 100 Hz = 300 Hz

In the Fourier series representation, each harmonic frequency is associated with a coefficient (amplitude) and a phase angle. These coefficients determine the contribution of each harmonic to the overall shape of the periodic waveform when added together. The Fourier series is a powerful mathematical tool used in signal processing, communications, and various other fields to analyze and synthesize periodic signals.

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