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Fourier Series & How to get Fourier transform from Fourier Series ? Video Lecture | Crash Course for IIT JAM Physics
FAQs on Fourier Series & How to get Fourier transform from Fourier Series ? Video Lecture - Crash Course for IIT JAM Physics
| 1. What is a Fourier series? |  |
Ans. A Fourier series is a mathematical representation of a periodic function in terms of a sum of sine and cosine functions. It decomposes a periodic function into a series of harmonically related sinusoidal functions.
| 2. How is a Fourier series calculated? | |
Ans. To calculate a Fourier series, we need to find the coefficients of sine and cosine terms. These coefficients can be found by taking the inner product of the function with the corresponding sine and cosine functions and then integrating over one period of the function.
| 3. What is the significance of a Fourier series? | |
Ans. Fourier series are used in various fields of science and engineering to analyze and represent periodic functions. They provide a way to decompose complex waveforms into simpler sinusoidal components, making it easier to understand and manipulate them.
| 4. What is the relationship between Fourier series and Fourier transform? | |
Ans. The Fourier series represents a periodic function in terms of a sum of harmonically related sinusoidal functions, whereas the Fourier transform represents a non-periodic function in terms of a continuous spectrum of sinusoidal functions. The Fourier transform can be obtained by taking the limit of the Fourier series as the period approaches infinity.
| 5. How can we obtain Fourier transform from Fourier series? | |
Ans. To obtain the Fourier transform from a Fourier series, we can take the limit of the Fourier series as the period approaches infinity. This effectively converts the discrete harmonics of the Fourier series into a continuous spectrum, resulting in the Fourier transform of the function.
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Dec 27, 2024 Last updated |
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