If you add a lot of sinusoids together, carefully adjusting the amplitude and frequency (and phase) of each, you can generate any shaped waveform you wish, triangle wave, rectangular wave, square wave with a blip on the rising edge, the waveshape of a heartbeat on an ECG, the electrical interference from a distant lightning bolt, etc., etc., any complex waveform you care to nominate.MartinV05 said:I've just started learning Fourier series and I'm having trouble understanding it. What do they actually do? And what does the amplitude-frequency show me?
NascentOxygen said:you can generate any shaped waveform you wish
A Fourier series is a mathematical representation of a periodic function as a sum of sinusoidal functions. It allows us to break down a complex function into simpler components and understand its behavior.
Fourier series have a wide range of applications in science and engineering. They are used to analyze and model periodic phenomena, such as sound waves, electromagnetic waves, and other physical systems. They also have applications in signal processing, image and sound compression, and data analysis.
A Fourier series is calculated by decomposing a periodic function into its constituent sinusoidal components using the Fourier transform. This involves finding the coefficients for each term in the series, which represent the amplitude and phase of the sinusoidal functions.
The key concepts in understanding Fourier series include periodic functions, complex numbers, trigonometric functions, and the Fourier transform. It is also important to understand how to calculate the coefficients for each term in the series and how to interpret them.
Yes, Fourier series can be extended to represent non-periodic functions by using the Fourier transform. This is known as the Fourier integral and allows us to analyze and model non-periodic phenomena as well.