What is the interpretation of the Fourier transformation?

In summary, the conversation discussed the confusion surrounding the interpretation of the Fourier transformation of a function. In the discrete case, it was understood as a superposition of sinusoidal functions, but in the continuous case, understanding becomes more difficult. The question of how to interpret the Fourier transformation when the function is non-periodic was also raised.
  • #1
zezima1
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We have just begun that subject, and I'm quite confused as to how the Fourier transformation of a function is to be interpreted. In the discrete case it was easy to understand that you just wrote a periodic function as a superposition of sinusoidal functions.
But in the case of T->∞ everything in my head gets messed up. How am I to interpret the Fourier transformation? Is it essentially transforming the function from a time dependence to a dependence of a continuous frequency spectrum? But why does it even make sense to talk about frequencies when the function is non periodic..??
 
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  • #2
This could help:
 

What is Fourier transformation?

Fourier transformation is a mathematical method used to decompose a function into its underlying frequencies. It is commonly used in signal processing, image analysis, and other fields of science.

Why is Fourier transformation important?

Fourier transformation allows us to analyze complex signals and understand their underlying components. It is a powerful tool for studying periodic phenomena and has many applications in science and engineering.

How does Fourier transformation work?

In Fourier transformation, a function is represented as a combination of sine and cosine waves of different frequencies and amplitudes. This allows us to break down a complex function into simpler components.

What is the difference between Fourier transformation and Fourier series?

Fourier transformation is used to analyze continuous signals, while Fourier series is used for periodic signals. Fourier series assumes that the signal repeats itself, while Fourier transformation does not have this limitation.

What are the applications of Fourier transformation?

Fourier transformation has many applications in various fields, including signal processing, image analysis, physics, and engineering. It is used for filtering and noise reduction, compression, and pattern recognition, among others.

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