Fourier series representation for trigonometric and complex form base

In summary, a Fourier Series is a mathematical representation of a periodic function as a sum of simpler trigonometric functions, used to break down any periodic function into its individual frequency components. It has applications in physics, engineering, and mathematics, and is calculated using integration techniques and Fourier coefficients. However, not every function can be accurately represented by a Fourier Series, as it requires the function to be periodic and have a finite number of discontinuities. A Fourier Transform is a more general version of the Fourier Series and is used to represent non-periodic functions over an infinite interval, providing a continuous spectrum of frequencies.
  • #1
onceinalifetim
38
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May i know to obtain Fourier series representation for trigonometric and complex form base on magnitude spectrum and phase spectrum??

what i found is that to get trigonometric form is from phase spectrum, but i don't know how.. can anyone help
 
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  • #2
You need to give some more details about what you are trying to do.
 

1. What is a Fourier Series?

A Fourier Series is a mathematical representation of a periodic function as a sum of simpler trigonometric functions. It allows us to break down any periodic function into its individual frequency components.

2. What are the applications of Fourier Series?

Fourier Series have a wide range of applications in physics, engineering, and mathematics. They are used to analyze and solve problems related to heat transfer, signal processing, and vibration analysis, among others.

3. How is a Fourier Series calculated?

A Fourier Series is calculated using integration techniques and a set of complex mathematical formulas known as the Fourier coefficients. These coefficients represent the amplitudes and frequencies of the individual trigonometric functions in the series.

4. Can any function be represented by a Fourier Series?

No, not every function can be represented by a Fourier Series. The function must be periodic and have a finite number of discontinuities to be represented accurately by a Fourier Series.

5. What is the difference between a Fourier Series and a Fourier Transform?

The Fourier Transform is a more general version of the Fourier Series and is used to represent non-periodic functions. It provides a continuous spectrum of frequencies, while a Fourier Series only represents discrete frequencies. Additionally, a Fourier Series is defined over a finite interval, while a Fourier Transform is defined over an infinite interval.

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