Fourier Series of Finite Power Periodic Signals

Pierre Brémaud ()
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Pierre Brémaud: École Polytechnique Fédérale de Lausanne

Chapter C4 in Mathematical Principles of Signal Processing, 2002, pp 161-166 from Springer

Abstract: Abstract Let us consider the Hilbert space ℓ ℂ 2 of complex sequences a = {a n }, n ∈ ℤ, such that $${\sum\nolimits_{n \in \mathbb{Z}} {|{a_n}|} ^2} \prec \infty $$ with the Hermitian product (43) $${\left\langle {a,b} \right\rangle _{l_\mathbb{C}^2}} = \sum\limits_{n \in \mathbb{Z}} {{a_n}b_n^*} $$ and the Hilbert space L ℂ 2 ([0, T], dt/T) of complex signals x = {x(t)}, t ∈ ℝ, such that $$\int_0^T {{{\left| {x(t)} \right|}^2}dt}

Date: 2002
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DOI: 10.1007/978-1-4757-3669-4_11

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