Yes, you are correct. The Fourier series and the Fourier transform are based on the same mathematical ideas, but they serve different purposes. The Fourier series is used to analyze periodic functions by representing them as a sum of sine and cosine functions with different frequencies. The Fourier transform, on the other hand, is used to analyze non-periodic functions by representing them as a sum of sine and cosine functions with different frequencies over an infinite interval. In summary, while both the Fourier series and the Fourier transform are based on the same mathematical concepts, they are used for different types of functions and serve different purposes.
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