A Framework for Invertible, Real-Time Constant-Q Transforms

Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency bands is preferable. This paper introduces a framework for efficient implementation of invertible signal transforms allowing for non-uniform frequency resolution. No...

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Bibliographic Details
Published inIEEE transactions on audio, speech, and language processing Vol. 21; no. 4; pp. 775 - 785
Main Authors Holighaus, Nicki, Dorfler, M., Velasco, G. A., Grill, T.
Format Journal Article
LanguageEnglish
Published Piscataway, NJ IEEE 01.04.2013
Institute of Electrical and Electronics Engineers
Subjects
Algorithm design and analysis
Applied sciences
Audio signals
constant-Q
Exact sciences and technology
Fourier transforms
Gabor frames
Indexes
Information, signal and communications theory
Miscellaneous
real-time
Real-time systems
Signal processing
Signal resolution
Telecommunications and information theory
Time frequency analysis
time-frequency dictionary
Performance evaluation
Time-frequency analysis
Dictionaries
Audio signal processing
Acoustic signal
Input signal
Fast Fourier transformation
Frequency domain method
Acoustic signal processing
Algorithm
Non uniform distribution
Implementation
time-frequency dictionary
Audio signal
Frequency band
real-time
Audio signals
constant-Q
Numerical simulation
Real time processing
Gabor frames
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Summary:Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency bands is preferable. This paper introduces a framework for efficient implementation of invertible signal transforms allowing for non-uniform frequency resolution. Non-uniformity in frequency is realized by applying nonstationary Gabor frames with adaptivity in the frequency domain. The realization of a perfectly invertible constant-Q transform is described in detail. To achieve real-time processing, independent of signal length, slice-wise processing of the full input signal is proposed and referred to as sliCQ transform. By applying frame theory and FFT-based processing, the presented approach overcomes computational inefficiency and lack of invertibility of classical constant-Q transform implementations. Numerical simulations evaluate the efficiency of the proposed algorithm and the method's applicability is illustrated by experiments on real-life audio signals .
ISSN:1558-7916
1558-7924
DOI:10.1109/TASL.2012.2234114