All-Pole Recursive Digital Filters Design Based on Ultraspherical Polynomials

A simple method for approximation of all-pole recursive digital filters, directly in digital domain, is described. Transfer function of these filters, referred to as Ultraspherical filters, is controlled by order of the Ultraspherical polynomial, nu. Parameter nu, restricted to be a nonnegative real number (nu ≥ 0), controls ripple peaks in the passband of the magnitude response and enables a trade-off between the passband loss and the group delay response of the resulting filter. Chebyshev filters of the first and of the second kind, and also Legendre and Butterworth filters are shown to be special cases of these allpole recursive digital filters. Closed form equations for the computation of the filter coefficients are provided. The design technique is illustrated with examples

Study of Microstrip filters

Volume 2 Issue 1 (January 2014

Analyzing and clustering neural data

This thesis aims to analyze neural data in an overall effort by the Charles Stark Draper Laboratory to determine an underlying pattern in brain activity in healthy individuals versus patients with a brain degenerative disorder. The neural data comes from ECoG (electrocorticography) applied to either humans or primates. Each ECoG array has electrodes that measure voltage variations which neuroscientists claim correlates to neurons transmitting signals to one another. ECoG differs from the less invasive technique of EEG (electroencephalography) in that EEG electrodes are placed above a patients scalp while ECoG involves drilling small holes in the skull to allow electrodes to be closer to the brain. Because of this ECoG boasts an exceptionally high signal-to-noise ratio and less susceptibility to artifacts than EEG [6]. While wearing the ECoG caps, the patients are asked to perform a range of different tasks. The tasks performed by patients are partitioned into different levels of mental stress i.e. how much concentration is presumably required. The specific dataset used in this thesis is derived from cognitive behavior experiments performed on primates at MGH (Massachusetts General Hospital). The content of this thesis can be thought of as a pipelined process. First the data is collected from the ECoG electrodes, then the data is pre-processed via signal processing techniques and finally the data is clustered via unsupervised learning techniques. For both the pre-processing and the clustering steps, different techniques are applied and then compared against one another. The focus of this thesis is to evaluate clustering techniques when applied to neural data. For the pre-processing step, two types of bandpass filters, a Butterworth Filter and a Chebyshev Filter were applied. For the clustering step three techniques were applied to the data, K-means Clustering, Spectral Clustering and Self-Tuning Spectral Clustering. We conclude that for pre-processing the results from both filters are very similar and thus either filter is sufficient. For clustering we conclude that K- means has the lowest amount of overlap between clusters. K-means is also the most time-efficient of the three techniques and is thus the ideal choice for this application.2016-10-27T00:00:00

ShearLab 3D: Faithful Digital Shearlet Transforms based on Compactly Supported Shearlets

Wavelets and their associated transforms are highly efficient when approximating and analyzing one-dimensional signals. However, multivariate signals such as images or videos typically exhibit curvilinear singularities, which wavelets are provably deficient of sparsely approximating and also of analyzing in the sense of, for instance, detecting their direction. Shearlets are a directional representation system extending the wavelet framework, which overcomes those deficiencies. Similar to wavelets, shearlets allow a faithful implementation and fast associated transforms. In this paper, we will introduce a comprehensive carefully documented software package coined ShearLab 3D (www.ShearLab.org) and discuss its algorithmic details. This package provides MATLAB code for a novel faithful algorithmic realization of the 2D and 3D shearlet transform (and their inverses) associated with compactly supported universal shearlet systems incorporating the option of using CUDA. We will present extensive numerical experiments in 2D and 3D concerning denoising, inpainting, and feature extraction, comparing the performance of ShearLab 3D with similar transform-based algorithms such as curvelets, contourlets, or surfacelets. In the spirit of reproducible reseaerch, all scripts are accessible on www.ShearLab.org.Comment: There is another shearlet software package (http://www.mathematik.uni-kl.de/imagepro/members/haeuser/ffst/) by S. H\"auser and G. Steidl. We will include this in a revisio

A Signal Conditioner for Speech Processing

This thesis describes the design, implementation and testing of an analog signal conditioner for use in processing of speech signals. The signal conditioner provides gain and bandwidth control for the speech signal and also indicates the signal level. It is designed to be used in conjunction with a digital speech processor and has ports for a microphone or other signal source, an input signal monitoring device such as an oscilloscope, and interfaces to the digital speech processor. Signal bandwidth control is provided by a variable cutoff frequency lowpass switched capacitor filter, which is driven by a clock. In this thesis, the speech signal is examined and is related to the problem at hand. An overall description of the signal conditioner is then presented, emphasizing each of the signal conditioner is then presented, emphasizing each of the individual building blocks in the system. A description of switched capacitor filter theory and application follows, and signal conditioner system test results and conclusions are given. It was found that the system performance satisfied the desired specifications that were laid out when the system was first conceived

Oversampled Filter Banks

Perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in t(2)(Z), These frames are the subject of this paper. First, necessary and sufficient conditions on a filter bank for implementing a frame or a tight frame expansion are established, as well as a. necessary and sufficient condition for perfect reconstruction using FIR filters after an FIR analysis. Complete parameterizations of oversampled filter banks satisfying these conditions are given, Further, we study the condition under which the frame dual to the frame associated with an FIR filter bank is also FIE and give a parameterization of a class of filter banks satisfying this property, Then, we focus on nonsubsampled filter banks. Nonsubsampled filter banks implement transforms similar to continuous-time transforms and allow for very flexible design. We investigate relations of these filter banks to continuous-time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two-channel filter banks that yield highly regular wavelets with a given number of vanishing moments

Design of Generalized Chebyshev Microwave Filter with Prescribed Transmission Zeroes

This paper presents a better prototype approximation which is generalized Chebyshev where its transmission zeroes can be located arbitrarily and have high selectivity. The purpose of selecting generalized Chebyshev is because it can be designed in low loss and small size for prototype which such requirements are hardly achieved by other filter prototype. The scope of this project include microwave low pass generalized Chebyshev filter design using distributed elements particularly microstrip. Methodology of carrying out practical design work will be presented through different stages from design to fabrication. Results will be recorded and observed. In conclusion, generalized Chebyshev filter gives customer advantages for their requirement of filter devices due to its low impedance variance and flexibility locating zeroes