Lecture 14 : Convergence of Fourier Series and Gibb's Phenomenon
Conclusion:
In
this lecture you have learnt:
We have discussed the convergence of the Fourier series representation of a periodic signal in two contexts, namely Pointwise convergence and Convergence in squared norm .
Dirichlet Conditions For Pointwise Convergence are:
(a)absolute integrabilty (b) finite number of discontinuities over one period (c) finite number of extremas over one period
If a signal is a finite power signal then it is convergent in squared norm
The partial sum oscillates near the point of discontinuity. These oscillations do not decrease as the number of terms taken is increased. But in reality, as the number of terms taken is increased, although these oscillations get closer and closer to the point of discontinuity, their amplitude does not decrease to zero, but tends to a non zero limit. This phenomenon is known as the Gibb's Phenomenon ,
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