Mathematical Summary for Digital Signal Processing Applications with Matlab by E. S. Gopi

Author:E. S. Gopi
Language: eng
Format: epub, pdf
Publisher: Springer Netherlands, Dordrecht

Weeker convergence limn → ∞fn(t) = f(t) for all t except at certain discrete time instants t1t2t3…tn

Mean square convergence

The sequence of functions converges to the function f(t) if it satisfies the following condition

This can be interpreted as the sequence of numbers and they converge to the constant 0.

Example: The Fourier series representation of the periodic signal converges in mean square sense.

(i.e.) The function fn(t) = ∑k = − nk = ncke − j ∗ 2 ∗ pi ∗ k ∗ f0 ∗ t converges to the function f(t) in mean square sense.

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