The present invention is embodied in a system and method for performing spectral analysis (1500) of a digital signal having a discrete duration by spectrally decomposing the digital signal at predefined frequencies uniformly distributed over a sampling frequency interval into complex frequency coefficients (220, 222) so that magnitude and phase information at each frequency is immediately available to produce a modulated complex lapped transform (MCLT). The present invention includes a MCLT processor (1510), an acoustic echo cancellation device (1512) and a noise reducer (1514) integrated with an encoder/decoder device (1500).

Modulated complex lapped transform for integrated signal enhancement and coding

The present invention is embodied in a system and method for performing spectral analysis of a digital signal having a discrete duration by spectrally decomposing the digital signal at predefined frequencies uniformly distributed over a sampling frequency interval into complex frequency coefficients so that magnitude and phase information at each frequency is immediately available to produce a modulated complex lapped transform (MCLT). The system includes real and imaginary window processors and real and imaginary transform processors. The real and imaginary window processors receive the input signal and apply and compute butterfly coefficients for the real and imaginary parts of the signal to produce resulting real and imaginary vectors, respectively. The real and imaginary transform processors compute spatial transforms on the real and imaginary vectors to produce real and imaginary transform coefficient of the MCLT, respectively. The MCLT is a biorthogonal spectral transformation system, in the sense that the original time domain signal can be reconstructed exactly by an inverse MCLT operator.

Adaptive filtering system and method for adaptively canceling echoes and reducing noise in digital signals

System and method for producing modulated complex lapped transforms

Multirate filter banks introduce periodic time-varying phenomena into their subband signals. The nature of these effects depends on whether the signals are regarded as deterministic or as random signals. We analyze the behavior of deterministic and wide-sense stationary (WSS) random signals in multirate filter banks in a comparative manner. While aliasing in the decimation stage causes subband energy spectra of deterministic signals to become shift-variant, imaging in the interpolation stage causes WSS random signals to become WS cyclostationary (WSCS). We provide criteria to quantify both shift variance and cyclic nonstationarity. For shift variance, these criteria separately assess the shift dependence of energy and of energy spectra. Similarly for nonstationarity, they separately assess the nonstationary behavior of signal power and of power spectra. We show that, under aliasing cancellation and perfect reconstruction constraints of paraunitary and biorthogonal filter banks, these criteria evaluate the behavior of deterministic and WSS random signals in a consistent, dual way. We apply our criteria to paraunitary and biorthogonal filter banks as well as to orthogonal block transforms, and show that, for critical signals such as lines or edges in image data, the biorthogonal 9/7 filters perform best among these

/pdf/comparative-analysis-of-shift-variance-and-cyclostationarity-3nhrc65ahk.pdf

Comparative Analysis of Shift Variance and Cyclostationarity in Multirate Filter Banks

http://www.lfb.rwth-aachen.de/files/publications/old/AAC00a.pdf

A lapped directional transform for spectral image analysis and its application to restoration and enhancement

We propose a new real-valued lapped transform for 2D-signal and image processing Lapped transforms are particularly useful in block-based processing, since their intrinsically overlapping basis functions reduce or prevent block artifacts Our transform is derived from the modulated lapped transform (MLT), which, as a real-valued and separable transform like the discrete cosine transform, does not allow to unambiguously identify oriented structures from modulus spectra This is in marked contrast to the (complex-valued) discrete Fourier transform (DFT) The new lapped transform is real-valued, and at the same time allows unambiguous detection of spatial orientation Furthermore, a fast algorithm for this transform exists As an application example, we investigate the transform's performance in spectral approaches to image restoration and enhancement in comparison to the DFT

T. Aach

Papers

Lapped directional transform: a new transform for spectral image analysis