Abstract. A necessary and sufficient condition is given to show that the indefinite integral of a vector-valued pseudo-almost periodic function is again pseudo-almost periodic. Then we use this result to answer a question about weakly almost periodic functions.Throughout this paper, X denotes a Banach space and $a stands for [a, oo) when a G R and for R when a = -oo ; W($a, X) denotes the space of all bounded continuous functions from JJa to X. Also, m denotes Lebesgue measure on M.Let / G f (R, X). The translate of / by 5 G R is the function RJ(t) = f(t + s),teR.f is called (weakly) almost periodic if the set {Ruf} = {Rsf : s G R} is (weakly) relatively compact in %?(R, X) [3]. Denote by ( Ws/PÇk, X)) jf&(R,X) all such functions.In case X = C, we will omit X from our notation and write, for example, W{Ja) for &{Ja,X).
In the estimation of time delay, there always would not appear obvious peak with the basic cross-correlation (CC). In order to solve the problem of the basic cross-correlation method, this essay represents an improved time delay estimation method based on the generalized cross-correlation (GCC) and combines with the microphone array structure to achieve sound source localization. Finally, the simulation results show that this method could measure the sound source’s location accurately with noise and reverberation, and the distance positioning error is less than 10cm, the direction angle error is below 3°.
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