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What are the conditions called which are required for a signal to fulfil to be represented as Fourier series?
- a)Dirichlet’s conditions
- b)Gibbs phenomenon
- c)Fourier conditions
- d)Fourier phenomenon
Correct answer is option 'A'. Can you explain this answer?
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What are the conditions called which are required for a signal to fulf...
When the Dirichlet’s conditions are satisfied, then only for a signal, the fourier series exist. Fourier series is of two types- trigonometric series and exponential series.
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What are the conditions called which are required for a signal to fulf...
Dirichlet's Conditions for Fourier Series Representation
The conditions required for a signal to be represented as a Fourier series are known as Dirichlet's conditions. These conditions ensure that the Fourier series representation is valid and accurate.
Key Points:
- Dirichlet's conditions state that for a periodic signal to be represented as a Fourier series, it must satisfy the following criteria:
- The signal must be absolutely integrable over one period.
- The signal must have a finite number of maxima and minima within one period.
- The signal must have a finite number of discontinuities within one period, and these discontinuities must be of bounded variation.
- The signal must be of bounded variation over one period.
- If a signal meets all these conditions, it can be accurately represented as a Fourier series.
By ensuring that these conditions are met, the Fourier series representation of a signal will be valid and provide an accurate representation of the original signal. Failure to meet these conditions can result in inaccuracies, such as the Gibbs phenomenon, where oscillations occur near discontinuities in the signal.
The conditions required for a signal to be represented as a Fourier series are known as Dirichlet's conditions. These conditions ensure that the Fourier series representation is valid and accurate.
Key Points:
- Dirichlet's conditions state that for a periodic signal to be represented as a Fourier series, it must satisfy the following criteria:
- The signal must be absolutely integrable over one period.
- The signal must have a finite number of maxima and minima within one period.
- The signal must have a finite number of discontinuities within one period, and these discontinuities must be of bounded variation.
- The signal must be of bounded variation over one period.
- If a signal meets all these conditions, it can be accurately represented as a Fourier series.
By ensuring that these conditions are met, the Fourier series representation of a signal will be valid and provide an accurate representation of the original signal. Failure to meet these conditions can result in inaccuracies, such as the Gibbs phenomenon, where oscillations occur near discontinuities in the signal.
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