Fourier Coefficient Amplitude: Is Infinity Possible?

In summary, a Fourier coefficient amplitude is a measure of the strength or magnitude of a specific frequency component in a Fourier series. It is calculated by taking the square root of the sum of the squares of the real and imaginary parts of a complex Fourier coefficient. It cannot be negative and can approach infinity in certain cases. Fourier coefficient amplitude is commonly used in signal processing, image and sound compression, and data analysis to identify important frequency components and determine the overall characteristics of a signal or function.
  • #1
magnifik
360
0
Is it possible to have an infinite value for the amplitude of a Fourier coefficient?

The signal is sin(w0t) from 0 to T/2. My resulting coefficient formula was
Fn = 2/[4pi(1-n)] + 2/[4pi(1+n)]
so for F1 i got infinity ... is this possible?
or is coefficient just wrong?
 
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  • #2
This solution cannot be correct, because if you add the Fourier components up, you will get infinity multiplied by a sinusoid. Does that reconstruct the original signal in the designated range? No, and it must for such a well-behaved original signal.
 

FAQ: Fourier Coefficient Amplitude: Is Infinity Possible?

What is a Fourier coefficient amplitude?

A Fourier coefficient amplitude is a measure of the strength or magnitude of a specific frequency component in a Fourier series. It represents the contribution of that frequency to the overall signal or function being analyzed.

How is Fourier coefficient amplitude calculated?

Fourier coefficient amplitude is calculated by taking the square root of the sum of the squares of the real and imaginary parts of a complex Fourier coefficient. This calculation is typically done using mathematical software or programming languages.

Can Fourier coefficient amplitude be negative?

No, Fourier coefficient amplitude cannot be negative. It represents the magnitude of a specific frequency component, so it is always a positive value.

Is infinity possible for Fourier coefficient amplitude?

Yes, it is possible for Fourier coefficient amplitude to approach infinity. This occurs when there is a dominant frequency component in the signal or function being analyzed, and the contribution of that component becomes increasingly large.

How is Fourier coefficient amplitude used in practical applications?

Fourier coefficient amplitude is used in a wide range of applications, including signal processing, image and sound compression, and data analysis. It allows for the identification of important frequency components in a signal and helps to determine the overall characteristics of the signal or function being analyzed.

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