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What is exponential form of Fourier series?
As for the trigonometric Fourier series, the exponential form allows us to approximate a periodic signal to any degree of accuracy by adding a sufficient number of complex exponential functions. A distinct advantage of the exponential Fourier series, however, is that it requires only a single integral (Eq.
What is the disadvantage of exponential Fourier series?
Explanation: The major disadvantage of exponential Fourier series is that it cannot be easily visualized as sinusoids. Moreover, it is easier to calculate and easy for manipulation leave aside the disadvantage. Explanation: Fourier series uses frequency domain representation of signals.
What is the difference between Fourier transform?
5 Answers. The Fourier series is used to represent a periodic function by a discrete sum of complex exponentials, while the Fourier transform is then used to represent a general, nonperiodic function by a continuous superposition or integral of complex exponentials.
What are the disadvantages of Fourier tranform?
The major disadvantage of the Fourier transformation is the inherent compromise that exists between frequency and time resolution. The length of Fourier transformation used can be critical in ensuring that subtle changes in frequency over time, which are very important in bat echolocation calls, are seen.
Why do Fourier transforms use complex numbers?
Fourier Transforms are performed using complex numbers. Since Fourier Transforms are used to analyze real-world signals , why is it useful to have complex (or imaginary) numbers involved at all? It turns out the complex form of the equations makes things a lot simpler and more elegant.
Why there is a need of Fourier transform?
Fourier Transform is used in spectroscopy, to analyze peaks, and troughs. Also it can mimic diffraction patterns in images of periodic structures, to analyze structural parameters. Similar principles apply to other ‘transforms’ such as Laplace transforms, Hartley transforms.
What are the different types of the Fourier transform?
aperiodic spectrum This is the most general form of continuous time Fourier transform.