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.
Table 1: Reconstruction comparison Loaded file: None |
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FB | s4 | s5 | s6 | s7 | ||||
FBPGHI | fGLA | FBPGHI | fGLA | FBPGHI | fGLA | FBPGHI | fGLA | |
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 |