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Using Multivariate Statistics

The outline of this chapter is as follows. Section 2 reviews various types of existing finite impulse response (FIR) and infinite impulse response (IIR) two-channel filter banks. The basic operations of these filter banks are considered and the requirements are stated for alias-free, perfect-reconstruction (PR), and nearly perfect-reconstruction (NPR) filter banks. Also some efficient synthesis techniques are referred to. Furthermore, examples are included to compare various two-channel filter banks with each other. Section 3 concentrates on the design of multi-channel (M-channel) uniform filter banks. The main emphasis is laid on designing these banks using tree-structured filter banks with the aid of two-channel filter banks and on generating the overall bank with the aid of a single prototype filter and a proper cosine-modulation or MDFT technique. In Section 4, it is shown how octave filter banks can be generated using a single two-channel filter bank as the basic building block. Also, the relations between the frequency-selective octave filter banks and discrete-time wavelet banks are briefly discussed. Finally, concluding remarks are given in Section 5.

/pdf/multirate-systems-and-filter-banks-3w4ni7zeza.pdf

Multirate Systems and Filter Banks

As of today, orthogonal frequency division multiplexing (OFDM) has been the dominant technology for broadband multicarrier communications. However, in certain applications such as cognitive radios and uplink of multiuser multicarrier systems, where a subset of subcarriers is allocated to each user, OFDM may be an undesirable solution. In this article, we address the shortcomings of OFDM in these and other applications and show that filter bank multicarrier (FBMC) could be a more effective solution. Although FBMC methods have been studied by a number of researchers, and some even before the invention of OFDM, only recently has FBMC been seriously considered by a few standard committees.

OFDM Versus Filter Bank Multicarrier

A discrete-time analysis of the orthogonal frequency division multiplex/offset QAM (OFDM/OQAM) multicarrier modulation technique, leading to a modulated transmultiplexer, is presented. The conditions of discrete orthogonality are established with respect to the polyphase components of the OFDM/OQAM prototype filter, which is assumed to be symmetrical and with arbitrary length. Fast implementation schemes of the OFDM/OQAM modulator and demodulator are provided, which are based on the inverse fast Fourier transform. Non-orthogonal prototypes create intersymbol and interchannel interferences (ISI and ICI) that, in the case of a distortion-free transmission, are expressed by a closed-form expression. A large set of design examples is presented for OFDM/OQAM systems with the number of subcarriers going from four up to 2048, which also allows a comparison between different approaches to get well-localized prototypes.

Analysis and design of OFDM/OQAM systems based on filterbank theory

Digital Coding of Waveforms

In this paper, essential features of the recently introduced modified discrete Fourier transform DFT (MDFT) filter bank are presented. First, it is shown that all analysis and synthesis filters-obtained by appropriate complex modulation of a low-pass prototype filter-are linear phase. This is important for subband image coding applications. Another important property is the structure-inherent alias cancellation: all odd alias spectra are automatically compensated in the synthesis filter bank. Further, the MDFT filter bank provides perfect reconstruction for the same prototypes as for cosine-modulated filter banks. Thus, the same design methods can be used. Finally, different mappings of the input signal into the subbands are discussed and a comparison to the well-known cosine-modulated filter banks is given.

Modified DFT filter banks with perfect reconstruction

This paper presents a general framework for maximally decimated modulated filter banks. The theory covers the known classes of cosine modulation and relates them to complex-modulated filter banks. The prototype filters have arbitrary lengths, and the overall delay of the filter bank is arbitrary, within fundamental limits. Necessary and sufficient conditions for perfect reconstruction (PR) are derived using the polyphase representation. It is shown that these PR conditions are identical for all types of modulation-modulation based on the discrete cosine transform (DCT), both DCT-III/DCT-IV and DCT-I/DCT-II, and modulation based on the modified discrete Fourier transform (MDFT). A quadratic-constrained design method for prototype filters yielding PR with arbitrary length and system delay is derived, and design examples are presented to illustrate the tradeoff between overall system delay and stopband attenuation (subchannelization).

A general formulation of modulated filter banks

We present a new method for the design and implementation of modulated filter banks with perfect reconstruction. It is based on the decomposition of the analysis and synthesis polyphase matrices into a product of two different types of simple matrices, replacing the polyphase filtering part in a modulated filter bank. Special consideration is given to cosine-modulated as well as time-varying filter banks. The new structure provides several advantages. First of all, it allows an easy control of the input-output system delay, which can be chosen in single steps of input sampling rate, independent of the filter length. This property can be used in audio coding applications to reduce pre-echoes. Second, it results in a structure that is nearly twice as efficient as performing the polyphase filtering directly. Perfect reconstruction is a structurally inherent feature of the new formulation, even for nonlinear operations or time-varying coefficients. Hence, the structure is especially suited for the design of time-varying filter banks where both the number of bands as well as the prototype filters can be changed while maintaining perfect reconstruction and critical sampling. Further, a proof of effective completeness is given, and the design of equal magnitude-response analysis and synthesis filter banks is described. Filter design can be performed by nonconstrained optimization of the matrix coefficients according to a given cost function. Design and audio-coding application examples are given to show the performance of the new filter bank.

Modulated filter banks with arbitrary system delay: efficient implementations and the time-varying case

This paper describes key success factors for the implementation and development of a LEGO robotics engineering outreach program for elementary school students in West Texas. The outreach program not only aims at getting young students excited about engineering but at the same time aims at improving retention rates among electrical and computer engineering freshman-level college students by involving them as paid mentors. It particularly takes into consideration the rural character of West Texas, which provides hardly any electrical and computer engineering job opportunities, and the fact that a university with a college of engineering serves as academic hub for the area.

Generation NXT: Building Young Engineers With LEGOs

Electroencephalography (EEG) is a useful tool to inspect the brain activity in resting state and allows to characterize spontaneous brain activity that is not detected when a subject is cognitively engaged. Moreover, taking advantage of the high time resolution in EEG, it is possible to perform fast topographical reference-free analysis, since different scalp potential fields correspond to changes in the underlying sources within the brain. In this study, the spontaneous EEG resting state (eyes closed) was compared between 10 young adults ages 18-30 years with autism spectrum disorder (ASD) and 13 neurotypical controls. A microstate analysis was applied, focusing on four temporal parameters: mean duration, the frequency of occurrence, the ratio of time coverage, and the global explained variance (GEV). Using data that were acquired from a 65-channel EEG system, six resting-state topographies that best describe the dataset across all subjects were identified by running a two-step cluster analysis labeled as microstate classes A-F. The results indicated that microstates B and E displayed statistically significant differences between both groups among the temporal parameters evaluated. Classes B, D, E, and F were consistently more present in ASD, and class C in controls. The combination of these findings with the putative functional significance of the different classes suggests that during resting state, the ASD group was more focused on visual scene reconstruction, while the control group was more engaged with self-memory retrieval. Furthermore, from a connectivity perspective, the resting-state networks that have been previously associated with each microstate class overlap the brain regions implicated in impaired social communication and repetitive behaviors that characterize ASD.

/pdf/eeg-microstates-analysis-in-young-adults-with-autism-12gmahcgor.pdf

Tanja Karp

Papers

Modified DFT filter banks with perfect reconstruction

A general formulation of modulated filter banks

Modulated filter banks with arbitrary system delay: efficient implementations and the time-varying case

Generation NXT: Building Young Engineers With LEGOs

EEG Microstates Analysis in Young Adults With Autism Spectrum Disorder During Resting-State