 Since a spatially planar signal is also a linear trajectory signal, it maybe written in the form, = 
x(formula_41 - formula_483formula_454, formula_42 - formula_486formula_454,formula_454 ), where formula_483 = formula_453/formula_440 and formula_486 = formula_453/formula_442.Now, using the shift property of 2-D DHT, we get,
formula_478(formula_135,formula_136,formula_454) = formula_478(formula_135,formula_136,0)cosformula_458Wformula_466 + formula_478(N - formula_135, N - formula_136,0)cosformula_458Wformula_466, where W = cosformula_4582(formula_483formula_135 + formula_486formula_136)(formula_454formula_515)/Nformula_466.This equation implies that the passband sequences, formula_478(formula_135,formula_136,formula_481) at each tuple {formula_135,formula_136} are real sampled sinusoids that may be selectively transmitted by employing LDE's that are characterized by narrowband bandpass magnitude frequency respone having Normalized frequencies given by, 
v = 2(formula_483formula_135 + formula_486formula_136)/N.