What is the fundamental frequency in a Fourier series representation?
1 Answer
In a Fourier series representation, the fundamental frequency is the lowest frequency component of the series and serves as the building block for all other frequencies present in the signal. It is also referred to as the first harmonic or the fundamental harmonic.
A Fourier series represents a periodic function as a sum of sine and cosine functions with different frequencies and amplitudes. The fundamental frequency is the inverse of the period of the periodic function being represented. In other words, it is the frequency at which the function repeats itself over one complete cycle.
Let's use mathematical notation to represent the fundamental frequency. If the periodic function has a period T (the length of one cycle), then the fundamental frequency, denoted as f0, is given by:
f0 = 1 / T
The Fourier series will include terms with frequencies that are integer multiples of the fundamental frequency. These terms are called harmonics, and they determine the shape of the periodic function and its waveform.
For example, if a periodic function has a period of T = 2 seconds, then the fundamental frequency f0 would be:
f0 = 1 / 2 = 0.5 Hz
And the Fourier series would include terms at 0.5 Hz, 1 Hz, 1.5 Hz, 2 Hz, 2.5 Hz, and so on, each with its respective amplitude and phase, to approximate the original function. The fundamental frequency at 0.5 Hz represents the lowest frequency component in this example.
A Fourier series represents a periodic function as a sum of sine and cosine functions with different frequencies and amplitudes. The fundamental frequency is the inverse of the period of the periodic function being represented. In other words, it is the frequency at which the function repeats itself over one complete cycle.
Let's use mathematical notation to represent the fundamental frequency. If the periodic function has a period T (the length of one cycle), then the fundamental frequency, denoted as f0, is given by:
f0 = 1 / T
The Fourier series will include terms with frequencies that are integer multiples of the fundamental frequency. These terms are called harmonics, and they determine the shape of the periodic function and its waveform.
For example, if a periodic function has a period of T = 2 seconds, then the fundamental frequency f0 would be:
f0 = 1 / 2 = 0.5 Hz
And the Fourier series would include terms at 0.5 Hz, 1 Hz, 1.5 Hz, 2 Hz, 2.5 Hz, and so on, each with its respective amplitude and phase, to approximate the original function. The fundamental frequency at 0.5 Hz represents the lowest frequency component in this example.