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Mirror style (AZ, BY, CX etc) 1 1 plusforparents co uk 1 1 plusforparents co uk 1 1 plusforparents co uk Author Study Created Date 5/10/12 AM. FOURIER BOOKLET2 51 Simple Properties The convolution is a linear operation which is distributative, so that for three functions f(x), g(x) and h(x) we have that f(x) (g(x) h(x))=(f(x) g(x)) h(x) (3) and commutative, so that f(x) h(x)=h(x) f(x) (4) If the two functions f(x) and h(x) are of nite extent, (are zero outwith a nite range of x), then the extent (or width) of the convolution g(x. _ X C x g E 쎖 _ X X N t y p ҏW E s GRANDSOUL DANCE TV v f X _ T h _ X f U C _ X ֘A O b c E ̔ Ȏ p C I j A } h X ː 򊔎. Q1() ( )x,t =g x−ct (1a) or q2 ( )x,t = f xct, (1b) where c is some positive constant1 The constant c is the speed of propagation of the wave The wave in Eq (1a) propagates in the positive xdirection, while the wave in Eq (1b) propagates in the negative xdirection Now the functions g and f in Eq.