Recovering signals from the Short-Time Fourier Transform magnitude
2015
The problem of recovering signals from the Short-Time Fourier Transform (STFT) magnitude is of paramount importance in many areas of engineering and physics. This problem has received a lot of attention over the last few decades, but not much is known about conditions under which the STFT magnitude is a unique signal representation. Also, the recovery techniques proposed by researchers are mostly heuristic in nature. In this work, we first show that almost all signals can be uniquely identified by their STFT magnitude under mild conditions. Then, we consider a semidefinite relaxation-based algorithm and provide the first theoretical guarantees for the same. Numerical simulations complement our theoretical analysis and provide many directions for future work.
Keywords:
- Short-time Fourier transform
- Mathematical optimization
- Constant Q transform
- Multidimensional signal processing
- Fractional Fourier transform
- Fourier transform on finite groups
- Non-uniform discrete Fourier transform
- Fourier inversion theorem
- Discrete Fourier transform (general)
- Mathematics
- Discrete-time Fourier transform
- Harmonic wavelet transform
- Computer science
- Discrete Fourier transform
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