Digital Signal Processing: Spectral Computation And Filter Design (The Oxford Series In Electrical A
Elis Riebow
This course provides students with an understanding of the theory, interpretation, design and application of DSP techniques. In particular the course covers the theory and practice of digital filters and Fourier transform based spectrum analysis. Spectral descriptions of continuous-time and discrete-time waveforms are reviewed and related, and the FFT algorithm is used as a spectral analysis tool. The behaviour of digital filters is analysed through the use of difference equations and transfer functions via the z-transform. Methods for designing IIR and FIR filters are described, and various issues associated with their practical implementation are discussed.
To complement and aid understanding of the lecture material, students will be required to use Matlab to complete a series of coursework activities. These will provide practical experience of spectral analysis, digital filtering and digital filter design. The coursework will be assessed by means of four Matlab assignments with electronic submission of results.
Digital Signal Processing: Spectral Computation And Filter Design (The Oxford Series In Electrical A
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Signal Processing Toolbox provides functions and apps to manage, analyze, preprocess, and extract features from uniformly and nonuniformly sampled signals. The toolbox includes tools for filter design and analysis, resampling, smoothing, detrending, and power spectrum estimation. You can use the Signal Analyzer app for visualizing and processing signals simultaneously in time, frequency, and time-frequency domains. With the Filter Designer app you can design and analyze FIR and IIR digital filters. Both apps generate MATLAB scripts to reproduce or automate your work.
In 2005, a study was conducted on the issue of an embedded physiological signal processing platform. The entire research project was divided into three phases, the first of which is the development of a biomedical engineering teaching system, the second is that of an embedded mixed signal processing system, and the last is an online database construction. In contrast with such project, the features of our study may be stated as follows: firstly, featuring the EEG, eye sliding diagram, EMG, blood pressure, vascular volume, breath, pulse, etc., a KL-720 system is exploited as a major biomedical sensing system. Although a satisfactory accuracy is demonstrated by the KL-720, a low noise filter and a high performance AD converter are both used in this work to deal with a low detected physiological signal in an effort to increase the system accuracy. Secondly, a real time FPGA based embedded SOC is developed on an ARM10 PXA270 development environment as a signal processing platform. It exhibits a superior performance relative to its predecessors, i.e., ARM 8 and 9, whereby a high computation speed is seen in this study as opposed to conventional embedded physiological systems. Thirdly, this work performs more types of feature extractions out of detected physiological signals, following which various features are presented for comparison purposes. To this end, an FPGA-based SOC is designed and then implemented for physical time EEG signal acquisition, analysis and validation. An accurate feature extraction is made by means of an independent component analysis (ICA) algorithm, that is an issue not well addressed in the literature. Lastly, unlike all the existing platforms, a complete visual integration platform, all the way from a prototype design to a finalized embedded system, is developed with an NI LABVIEW interface for either teaching or R&D purposes.
In digital filters theory, filtering techniques generally deal with pole-zero structures. In this context, filtering schemes, such as infinite impulse response (IIR) filters, are described by linear differential equations or linear transformations, in which the impulse response of each filter provides its complete characterization, under filter design specifications. On the other hand, finite impulse response (FIR) digital filters are more flexible than the analog ones, yielding higher quality factors. Since many approaches to the circuit synthesis using the wavelet transform have been recently proposed, here we present a digital filter design algorithm, based on signal wavelet decomposition, which explores the energy partitioning among frequency sub-bands. Exploring such motivation, the method involves the design of a perfect reconstruction wavelet filter bank, of a suitable choice of roots in the Z-plane, through a spectral factorization, exploring the orthogonality and localization property of the wavelet functions. This approach resulted in an energy partitioning across scales of the wavelet transform that enabled a superior filtering performance, in terms of its behavior on the pass and stop bands. This algorithm presented superior results when compared to windowed FIR digital filter design, in terms of the intended behavior in its transition band. Simulations of the filter impulse response for the proposed method are presented, displaying the good behavior of the method with respect to the transition bandwidth of the involved filters.
Filter design has been extensively explored in circuit synthesis and signal processing, as a part of circuit theory [1,2,3,4,5,6,7]. Within this context, one of the major challenges of the IIR filters is determining its respective coefficients: in a digital form, the IIR filters can be designed from their analog versions, a procedure that is not easily performed [2, 4]. On the other hand, the FIR filters are more powerful than the IIR ones [4], but they also require more processing power. In this scenario of drawbacks, the frequency partitioning into sub-bands, obtained by the wavelet transform, could be useful: in the wavelet decomposition of a given signal, frequency sub-bands are obtained with peculiar amplitude values, which could be explored in selective filtering techniques.
The wavelet filter banks provide the advantage of separating the signal under consideration into two or more signals, in the frequency domain. Since signals can show different amplitude levels in both time and wavelet transform domains, it is interesting to partition the energy into several frequency sub-bands for several applications. This could be achieved using low-pass or high-pass filters, associated with wavelets respectively with few or many vanishing moments [8,9,10]. This apparent duality could be better described using spectral factorization [9,10,11,12], which allows separating polynomial roots into two corresponding sequences of low-pass filters in a wavelet filter bank, according to a criterion of perfect reconstruction [12]. The selective filtering method proposed here designs a wavelet family that decomposes the signal to be filtered into sub-bands fitted in amplitude, obtaining good quantitative results in terms of accuracy of filtering and simultaneously with a low computational cost. Although this technique has been studied in several digital signal processing applications, so far it has not been widely explored in digital circuit theory [13,14,15], which is the main focus of this investigation, primarily the digital filter synthesis, showing the good choice for wavelets in digital filtering applications.
In signal processing, a filter bank is an array of band-pass filters that separates the input signal into multiple components, each one carrying a single frequency sub-band of the original signal. For example, an application of a filter bank lies in designing a graphic equalizer, which can attenuate the components differently and recombine them into a modified version of the original signal [16, 17]. The decomposition process, performed by the filter bank, is labeled analysis (meaning analysis of the signal in terms of its components in each sub-band); the output of the analysis is referred to as a sub-band signal, where each frequency sub-band is related to a specific filter in a bank. The reconstruction process is labeled synthesis, meaning the reconstitution of a complete signal resulting from the filtering process [18]. Particularly in digital signal processing, the term filter bank is also commonly applied to a bank of receivers [19, 20]. The difference is that receivers also down-convert the sub-bands to a low-center frequency that can be resampled at a reduced rate. The same procedure could be sometimes performed by undersampling the band-pass sub-bands.
Digital filters have been widely used in signal processing and communication systems, in applications such as channel equalization, noise reduction, radar, audio and video processing, biomedical signal processing, and analysis of economic data [2, 3, 23,24,25]. In those examples, the roots of the digital filters play a major role in their design. Their location in the Z-plane allows the designer to establish specific applications, mainly to confine a signal in a prescribed frequency band as in low-pass, high-pass, and band-pass filters; to decompose a signal into two or more sub-bands as in filter-banks, graphic equalizers, sub-band coders, and frequency multiplexers; to modify the frequency spectrum of a signal as in telephone channel equalization and audio graphic equalizers; to model the input-output relationship of a system, such as telecommunication channels, human vocal tract, and music synthesizers [26]. Those features could be directly transferred to circuit theory without loss of generality.
Specific Course Information:
2021-2022 Catalog Data: Analysis and design of analog and digital communication systems based on Fourier analysis. Topics include linear systems and filtering, power and energy spectral density, basic analog modulation techniques, quantization of analog signals, line coding, pulse shaping, AM and FM modulation, digital carrier modulation, and transmitter and receiver design concepts. Applications include AM and FM radio, television, digital communications, and frequency-division and time-division multiplexing.
A zero in the frequency response is seen in a Sinc filter at frequency multiples of the output data rate. For instance, the frequency components at 60 Hz can be fully removed for a data rate of 60 Hz. Likewise, frequency components at either 50 or 60 Hz are completely eliminated for a data rate of 10 Hz. As suggested in [65], the effective resolution is found to increase with ENOB, which is directly affected by the ratio between input sampling rate and the output data rate [65]. For the sake of implementing a BEAM analyzer, a simulated analog EEG signal is sampled, quantized, converted into digital form, analyzed, modified, then extracted and finally converted back to analog form. Over recent years, the most popular digital signal processing approaches include Fast Fourier Transfer (FFT), Wavelet Transform (WT), Bispectral, Power Spectral Density (PSD), etc., among which adopted in this work are PSD and FFT, the most common approach seen in conventional brain wave analysis. A time domain signal is transformed into the frequency domain by means of FFT for synthesis of an EEG signal (see Figure 7).
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