Abstract:

Signal reconstruction from magnitude-only measurements presents a long-standing problem in signal processing. In this contribution, we propose a phase (re)construction method for filter banks with uniform decimation and controlled frequency variation. The suggested procedure extends the recently introduced phase-gradient heap integration and relies on a phase-magnitude relationship for filter bank coefficients obtained from Gaussian filters. Admissible filter banks are modeled as the discretization of certain generalized translation-invariant systems, for which we derive the phase-magnitude relationship explicitly. The implementation for discrete signals is described and the performance of the algorithm is evaluated on a range of real and synthetic signals.

The preprint is available here.

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Table 1: Reconstruction comparison

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FB s4 s5 s6 s7
FBPGHIfGLA FBPGHIfGLA FBPGHIfGLA FBPGHIfGLA
Gauss window
(1) −20.22 −25.36 −26.61 −29.83 −28.42 −29.86 −26.38 −28.57
(2) −23.24 −27.47 −26.96 −31.11 −31.44 −31.43 −28.70 −29.07
(3) −23.96 −27.27 −27.65 −32.45 −30.28 −32.31 −28.49 −29.74
(4) −23.08 −27.93 −25.70 −30.71 −32.59 −30.55 −29.28 −29.31
(5) −23.41 −27.92 −28.03 −30.99 −33.15 −32.95 −29.93 −30.76
Blackman window
(1) −20.45 −26.03 −26.31 −28.78 −27.20 −30.40 −24.52 −28.77
(2) −21.79 −26.99 −26.56 −32.02 −30.93 −31.59 −28.02 −28.75
(3) −21.13 −26.24 −25.99 −32.19 −29.71 −32.44 −28.30 −29.81
(4) −22.75 −28.21 −25.73 −31.21 −32.08 −31.51 −29.56 −29.10
(5) −17.15 −26.86 −26.56 −32.70 −31.43 −32.35 −29.54 −29.76