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Rsw
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what is the difference between Fourier series and Fourier transforms ?
A Fourier Series is a mathematical representation of a periodic function as a sum of sinusoidal functions. It is used to analyze and approximate the behavior of a periodic signal. On the other hand, a Fourier Transform is used to analyze a non-periodic signal and decompose it into its constituent frequencies. Unlike a Fourier Series, a Fourier Transform does not assume periodicity in the signal.
The mathematical equation for a Fourier Series is where and are coefficients that represent the amplitudes of the cosine and sine functions, respectively. The mathematical equation for a Fourier Transform is where represents the frequency.
A Fourier Series is used to analyze periodic signals, which are signals that repeat themselves after a certain interval of time. On the other hand, a Fourier Transform is used to analyze non-periodic signals, which do not repeat themselves.
Fourier Series and Fourier Transform have various applications in science, including signal processing, image and sound analysis, data compression, and solving differential equations. They are also widely used in fields such as physics, engineering, and mathematics.
No, a Fourier Series is only applicable to periodic signals and a Fourier Transform is only applicable to non-periodic signals. However, a Fourier Transform can be used to analyze a periodic signal by assuming it is a non-periodic signal with a very long period.