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. Author manuscript; available in PMC: 2008 Aug 18.
Published in final edited form as: J Acoust Soc Am. 2006 Nov;120(5 Pt 1):2450–2459. doi: 10.1121/1.2356839

TABLE I.

Basis functions for time-space decomposition with a Hanning-weighted pulse.

Temporal basis functions gn(t) Spatial basis functions fn(τ)
g1(t)= 1/2 sin(2πf0t) f1(τ)=cos(2πf0τ)
g2(t)=−1/2 cos(2πf0t) f2(τ)=sin(2πf0τ)
g3(t)=−1/2 cos(2πt/W)sin(2πf0t) f3(τ)=cos(2πτ/W)cos(2πf0τ)
g4(t)= 1/2 cos(2πt/W)cos(2πf0t) f4(τ)=cos(2πτ/W)sin(2πf0τ)
g5(t)= - 1/2 sin(2πt/W)sin(2πf0t) f5(τ)=sin(2πτ/W)cos(2πf0τ)
g6(t)= 1/2 sin(2πt/W)cos(2πf0t) f6(τ)=sin(2πτ/W)sin(2πf0τ)