Tree-structured complementary filter banks using all-pass sections

Tree-structured complementary filter banks are developed with transfer functions that are simultaneously all-pass complementary and power complementary. Using a formulation based on unitary transforms and all-pass functions, we obtain analysis and synthesis filter banks which are related through a transposition operation, such that the cascade of analysis and synthesis filter banks achieves an all-pass function. The simplest structure is obtained using a Hadamard transform, which is shown to correspond to a binary tree structure. Tree structures can be generated for a variety of other unitary transforms as well. In addition, given a tree-structured filter bank where the number of bands is a power of two, simple methods are developed to generate complementary filter banks with an arbitrary number of channels, which retain the transpose relationship between analysis and synthesis banks, and allow for any combination of bandwidths. The structural properties of the filter banks are illustrated with design examples, and multirate applications are outlined

Adaptive design of delta sigma modulators

In this thesis, a genetic algorithm based on differential evolution (DE) is used to generate delta sigma modulator (DSM) noise transfer functions (NTFs). These NTFs outperform those generated by an iterative approach described by Schreier and implemented in the delsig Matlab toolbox. Several lowpass and bandpass DSMs, as well as DSM\u27s designed specifically for and very low intermediate frequency (VLIF) receivers are designed using the algorithm developed in this thesis and compared to designs made using the delsig toolbox. The NTFs designed using the DE algorithm always have a higher dynamic range and signal to noise ratio than those designed using the delsig toolbox

Modeling a 300 kHz bathymetric sonar system

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1992The Deep Submergence Laboratory has developed a family of calibrated high frequency bathymetric sonar systems for underwater survey. It is useful to have a detailed mathematical description of these systems to assist in data processing. A model of a generalized sonar system is developed first. This model then is made specific to the DSL 300-kHz forward scanning sonar and is implemented using the MATLAB software package. The model consists of a cascaded series of filters representing the electrical and mechanical components of the system. The model is adjusted after comparison to the transmitted pulse. The results are then inverted to demonstrate how the corrupting effects of the system can be reversed. A technique is developed for applying this reverse model to actual data. The results showed that a good representation of the system can be implemented using relatively simple descriptions of each component. The most important components are the band-limiting filter and the transducer. It is possible to reverse model these components with good results

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for constructing 2D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1D counterpart, we relate the real and imaginary components of these complex wavelets using a multi-dimensional extension of the HT--the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor functions proposed by Daugman. Finally, we present an efficient FFT-based filterbank algorithm for implementing the associated complex wavelet transform.Comment: 36 pages, 8 figure

Analysis and design of ΣΔ Modulators for Radio Frequency Switchmode Power Amplifiers

Power amplifiers are an integral part of every basestation, macrocell, microcell and mobile phone, enabling data to be sent over the distances needed to reach the receiver’s antenna. While linear operation is needed for transmitting WCDMA and OFDM signals, linear operation of a power amplifier is characterized by low power efficiency, and contributes to unwanted power dissipation in a transmitter. Recently, a switchmode power amplifier operation was considered for reducing power losses in a RF transmitter. A linear and efficient operation of a PA can be achieved when the transmitted RF signal is ΣΔ modu- lated, and subsequently amplified by a nonlinear device. Although in theory this approach offers linearity and efficiency reaching 100%, the use of ΣΔ modulation for transmitting wideband signals causes problems in practical implementation: it requires high sampling rate by the digital hardware, which is needed for shaping large contents of a quantization noise induced by the modulator but also, the binary output from the modulator needs an RF power amplifier operating over very wide frequency band. This thesis addresses the problem of noise shaping in a ΣΔ modulator and nonlinear distortion caused by broadband operation in switchmode power amplifier driven by a ΣΔ modulated waveform. The problem of sampling rate increase in a ΣΔ modulator is solved by optimizing structure of the modulator, and subsequent processing of an input signal’s samples in parallel. Independent from the above, a novel technique for reducing quan- tization noise in a bandpass ΣΔ modulator using single bit quantizer is presented. The technique combines error pulse shaping and 3-level quantization for improving signal to noise ratio in a 2-level output. The improvement is achieved without the increase of a digital hardware’s sampling rate, which is advantageous also from the perspective of power consumption. The new method is explored in the course of analysis, and verified by simulated and experimental results. The process of RF signal conversion from the Cartesian to polar form is analyzed, and a signal modulator for a polar transmitter with a ΣΔ-digitized envelope signal is designed and implemented. The new modulator takes an advantage of bandpass digital to analog conversion for simplifying the analog part of the modulator. A deformation of the pulsed RF signal in the experimental modulator is demonstrated to have an effect primarily on amplitude of the RF signal, which is correctable with simple predistortion

Multirate Frequency Transformations: Wideband AM-FM Demodulation with Applications to Signal Processing and Communications

The AM-FM (amplitude & frequency modulation) signal model finds numerous applications in image processing, communications, and speech processing. The traditional approaches towards demodulation of signals in this category are the analytic signal approach, frequency tracking, or the energy operator approach. These approaches however, assume that the amplitude and frequency components are slowly time-varying, e.g., narrowband and incur significant demodulation error in the wideband scenarios. In this thesis, we extend a two-stage approach towards wideband AM-FM demodulation that combines multirate frequency transformations (MFT) enacted through a combination of multirate systems with traditional demodulation techniques, e.g., the Teager-Kasiser energy operator demodulation (ESA) approach to large wideband to narrowband conversion factors. The MFT module comprises of multirate interpolation and heterodyning and converts the wideband AM-FM signal into a narrowband signal, while the demodulation module such as ESA demodulates the narrowband signal into constituent amplitude and frequency components that are then transformed back to yield estimates for the wideband signal. This MFT-ESA approach is then applied to the various problems of: (a) wideband image demodulation and fingerprint demodulation, where multidimensional energy separation is employed, (b) wideband first-formant demodulation in vowels, and (c) wideband CPM demodulation with partial response signaling, to demonstrate its validity in both monocomponent and multicomponent scenarios as an effective multicomponent AM-FM signal demodulation and analysis technique for image processing, speech processing, and communications based applications

Novel Bandpass Filter Design based on Synchronous Filtering

The design of high-performance low-noise bandpass filtering systems has been studied from several aspects: (1) applying the synchronous filtering idea to the development of externally linear, time-invariant filters which can be internally nonlinear and/or time-varying, (2) seeking solutions to improve the noise performance of these filters, from parameter configuration to architecture design, and (3) implementing the systems of interest as transistor level circuits and verifying their function.Particularly, the state space representations for a biquad AM mode synchronous bandpass filter and a biquad FM mode synchronous complex filter have been proposed and realized with ideal Gm-C networks and log-domain circuits. Both systems utilize the modulator-core filter-modulator architecture to synchronize the internal signal processing. The core filter in an AM mode synchronous filter has constant center frequency and time-variant bandwidth, and the terminal modulators perform amplitude modulation to maintain the system’s external linearity and input/output characteristics. An FM mode synchronous filter typically has time-invariant bandwidth and performs frequency modulation before and after the signal filtering. Depending on whether the center frequency and terminal modulating frequency vary with time, there are static and dynamic types of FM mode synchronous filters. They both have the advantage of being able to filter the high frequency input signals in a low frequency range, which greatly alleviates the design and integration challenge due to the high frequency limitation of active components. Moreover, some dynamic filters effectively suppress the injected single-tone noise and generate an output with much higher SNR in comparison to the output from a static filter that implements the same transfer function.As a variation of an AM mode synchronous bandpass filter, the system derived by removing its back end modulator has been verified to have impressive noise reduction capability when processing noisy AM signals. Furthermore, it inspired the development of a feedback filtering system, the effective bandwidth of which could be tuned by scaling the feedback signal that time varies the core filter’s instantaneous bandwidth. It further provides an innovative approach to the design of a high-Q filter with superior immunity to internal noise, using a filter with very low Q factor. Finally, a design that combines the feedback architecture and the biquad FM mode synchronous complex filter is proposed and implemented as a log-domain filtering circuit. Appealing features of this system include wide dynamic range, flexible bandwidth and center frequency tunability. Since there is a low requirement for the high-frequency performance of active components, these filters make a good fit for monolithic integration, and greatly improved immunity to in-filter noise in comparison to that of an open loop complex filter with similar external filtering capability

Multifrequency Aperture-Synthesizing Microwave Radiometer System (MFASMR). Volume 1

Background material and a systems analysis of a multifrequency aperture - synthesizing microwave radiometer system is presented. It was found that the system does not exhibit high performance because much of the available thermal power is not used in the construction of the image and because the image that can be formed has a resolution of only ten lines. An analysis of image reconstruction is given. The system is compared with conventional aperture synthesis systems