Last Updated：2025/11/30
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When approximating a square wave with its Fourier series, the Gibbs phenomenon produces persistent oscillation peaks near each jump discontinuity that do not disappear as more terms are added.
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When approximating a square wave with its Fourier series, the Gibbs phenomenon produces persistent oscillation peaks near each jump discontinuity that do not disappear as more terms are added.
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Related words
Gibbs phenomenon
Proper noun
(mathematics)
A
behaviour
of
the
Fourier
series
approximation
at
a
jump
discontinuity
of
a
piecewise
continuously
differentiable
periodic
function,
such
that
partial
sums
exhibit
an
oscillation
peak
adjacent
the
discontinuity
that
may
overshoot
the
function
maximum
(or
minimum)
itself
and
does
not
disappear
as
more
terms
are
calculated,
but
rather
approaches
a
finite
limit.
Japanese Meaning
（数学）フーリエ級数による近似において、区分的に連続微分可能な周期関数の跳躍不連続点周辺で、部分和が振動し、跳躍点付近に顕著なピーク（関数の最大値または最小値を超える可能性がある）が現れる現象で、このピークは項数が増加しても解消されず、有限の極限値に収束する挙動を指す
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