Unified Theory for Biorthogonal Modulated Filter Banks

Modulated filter banks (MFBs) are practical signal decomposition tools for M -channel multirate systems. They combine high subfilter selectivity with efficient realization based on polyphase filters and block transforms. Consequently, the O(M 2 ) burden of computations in a general filter bank (FB) is reduced to O(M log2 M ) - the latter being a complexity order comparable with the FFT-like transforms.Often hiding from the plain sight, these versatile digital signal processing tools have important role in various professional and everyday life applications of information and communications technology, including audiovisual communications and media storage (e.g., audio codecs for low-energy music playback in portable devices, as well as communication waveform processing and channelization). The algorithmic efficiency implies low cost, small size, and extended battery life, bringing the devices close to our skins.The main objective of this thesis is to formulate a generalized and unified approach to the MFBs, which includes, in addition to the deep theoretical background behind these banks, both their design by using appropriate optimization techniques and efficient algorithmic realizations. The FBs discussed in this thesis are discrete-time time-frequency decomposition/reconstruction, or equivalently, analysis-synthesis systems, where the subfilters are generated through modulation from either a single or two prototype filters. The perfect reconstruction (PR) property is a particularly important characteristics of the MFBs and this is the core theme of this thesis. In the presented biorthogonal arbitrary-delay exponentially modulated filter bank (EMFB), the PR property can be maintained also for complex-valued signals.The EMFB concept is quite flexible, since it may respond to the various requirements given to a subband processing system: low-delay PR prototype design, subfilters having symmetric impulse responses, efficient algorithms, and the definition covers odd and even-stacked cosine-modulated FBs as special cases. Oversampling schemes for the subsignals prove out to be advantageous in subband processing problems requiring phase information about the localized frequency components. In addition, the MFBs have strong connections with the lapped transform (LT) theory, especially with the class of LTs grounded in parametric window functions.<br/

Efficient Implementation of Complex Modulated Filter Banks Using Cosine and Sine Modulated Filter Banks

<p/> <p>The recently introduced exponentially modulated filter bank (EMFB) is a <inline-formula><graphic file="1687-6180-2006-058564-i1.gif"/></inline-formula>-channel uniform, orthogonal, critically sampled, and frequency-selective complex modulated filter bank that satisfies the perfect reconstruction (PR) property if the prototype filter of an <inline-formula><graphic file="1687-6180-2006-058564-i2.gif"/></inline-formula>-channel PR cosine modulated filter bank (CMFB) is used. The purpose of this paper is to present various implementation structures for the EMFBs in a unified framework. The key idea is to use cosine and sine modulated filter banks as building blocks and, therefore, polyphase, lattice, and extended lapped transform (ELT) type of implementation solutions are studied. The ELT-based EMFBs are observed to be very competitive with the existing modified discrete Fourier transform filter banks (MDFT-FBs) when comparing the number of multiplications/additions and the structural simplicity. In addition, EMFB provides an alternative channel stacking arrangement that could be more natural in certain subband processing applications and data transmission systems.</p

Multicarrier Waveform Processing for HF Communications

High-frequency (HF) band communications can be flexibly realized using multicarrier modulation (MCM) techniques. HF channels are typically characterized by severe multi-path effects and high Doppler spreads requiring advanced estimation and equalization methods as well as elaborate waveform design for addressing these issues. This paper compares the performance of three widely utilized MCM techniques, namely, cyclic prefix (CP) orthogonal frequency-division multiplexing (OFDM), filter bank multicarrier/offset-QAM (FBMC/OQAM), and filtered multitone (FMT) in HF communications. In addition, the filtered variant of CP-OFDM is included in the comparison. The performance of these systems is simulated using commonly adopted HF-channel models. Channel estimation is carried out using scattered pilots with minimum mean-squared error based interpolation schemes whereas the equalization is realized using frequency-sampling based subcarrier equalizer. It is shown that the simulated uncoded bit-error rate of CP-OFDM is superior when compared with FBMC/OQAM and FMT even in the case when CP-OFDM waveform is filtered for better spectral containment. In addition, the implementation complexity and peak-to-average power ratio performance of (filtered) CP-OFDM compare favourable with FBMC/OQAM and FMT.acceptedVersionPeer reviewe