Max Born, Emil Wolf's Principles of optics PDF

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Extra resources for Principles of optics

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M − 1 } . 64) l=0 The z-transform leads to L h(l) z −l Φ(i, l) . 65) l=0 Applying Eq. 11 and Eq. 30 with ρ(m) = 1 results in M −1 lM −1 Yi (z) = Y (z) h(λ + m M ) z −(λ+m M ) Φ(i, λ) λ=0 m=0 M −1 z −λ · Hλ (M ) = Y (z) (z M ) · Φ(i, λ) . 66) λ=0 The derived PPN implementation of the direct form FBE according to Eq. 63 and Eq. 66 is illustrated in Fig. 14. In contrast to the FBE realization of Fig. 11, the time-domain filtering and calculation of the subband signals is partly done by the same network.

41]. The choice of the filter-bank has a significant influence on the performance of such systems in terms of signal quality, computational complexity, and signal delay. Accordingly, the filter-bank design has to fulfill different, partly conflicting requirements in dependence of the considered application. One prominent example is speech and audio processing for digital hearing aids. The restricted capacity of the battery and the small size of the chip set limit the available computational power. , [1,75].

18) l=0 = Hi (ej Ω ) ; i ∈ {0, 1, . . 19) due to Eq. 15 and Eq. 17. Hence, the allpass transformed filter-bank is a generalization of the uniform filter-bank, which is included as special case for a = 0. 20) where the course of the phase response ϕa (Ω) is determined by the allpass coefficient a. The effect of this allpass transformation is demonstrated in Fig. 5. For a real and positive allpass coefficient a = α > 0, a higher frequency resolution is achieved for the lower frequency bands and vice versa for the higher frequency bands.

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