The Fourier integral is used when the function being analyzed is not periodic, meaning it does not repeat itself over a certain interval. In contrast, Fourier series expansion is used for periodic functions. Therefore, if the function is not periodic, Fourier integral must be used.
Fourier integral and Fourier series expansion are both methods used to analyze functions in terms of their frequency components. However, Fourier integral is used for non-periodic functions, while Fourier series expansion is used for periodic functions. Fourier integral also takes into account all frequencies, while Fourier series expansion only considers integer multiples of the fundamental frequency.
Fourier integral is more appropriate when dealing with non-periodic functions, such as a square wave or a pulse. Additionally, Fourier integral is better suited for functions with discontinuities or singularities, as it takes into account all frequencies and can accurately represent these features.
No, Fourier series expansion can only be used for periodic functions. If a non-periodic function is attempted to be analyzed with Fourier series expansion, the resulting series will not accurately represent the function.
Yes, there are other methods such as the Laplace transform and the Z-transform. These methods are more general and can be used for both periodic and non-periodic functions. However, they are more complex and require advanced mathematical techniques to be applied.