Fundamentals of the DFT (fft) Algorithms
In this article, a physical explanation of the fundamentals of the DFT (fft) algorithms is presented in terms of waveform decomposition. After reading the article and trying the examples, the reader is expected to gain a clear understanding of the basics of the mysterious DFT (fft) algorithms.
Optimization of Synthesis Oversampled Complex Filter Banks
An important issue with oversampled FIR analysis filter banks (FBs) is to determine inverse synthesis FBs, when they exist. Given any complex oversampled FIR analysis FB, we first provide an algorithm to determine whether there exists an inverse FIR synthesis system. We also provide a method to ensure the Hermitian symmetry property on the synthesis side, which is serviceable to processing real-valued signals. As an invertible analysis scheme corresponds to a redundant decomposition, there is no unique inverse FB. Given a particular solution, we parameterize the whole family of inverses through a null space projection. The resulting reduced parameter set simplifies design procedures, since the perfect reconstruction constrained optimization problem is recast as an unconstrained optimization problem. The design of optimized synthesis FBs based on time or frequency localization criteria is then investigated, using a simple yet efficient gradient algorithm.
Hybrid Floating Point Technique Yields 1.2 Gigasample Per Second 32 to 2048 point Floating Point FFT in a single FPGA
Hardware Digital Signal Processing, especially hardware targeted to FPGAs, has traditionally been done using fixed point arithmetic, mainly due to the high cost associated with implementing floating point arithmetic. That cost comes in the form of increased circuit complexity. The increase circuit complexity usually also degrades maximum clock performance. Certain applications demand the dynamic range offered by floating point hardware, and yet require the speeds and circuit density usually associated with fixed point hardware. The Fourier transform is one DSP building block that frequently requires floating point dynamic range. Textbook construction of a pipelined floating point FFT engine capable of continuous input entails dozens of floating point adders and multipliers. The complexity of those circuits quickly exceeds the resources available on a single FPGA. This paper describes a technique that is a hybrid of fixed point and floating point operations designed to significantly reduce the overhead for floating point. The results are illustrated with an FFT processor that performs 32, 64, 128, 256, 512, 1024 and 2048 point Fourier transforms with IEEE single precision floating point inputs and outputs. The design achieves sufficient density to realize a continuous complex data rate of 1.2 Gigasamples per second data throughput using a single Virtex4-SX55-10 device.
Audio Time-Scale Modification
Audio time-scale modification is an audio effect that alters the duration of an audio signal without affecting its perceived local pitch and timbral characteristics. There are two broad categories of time-scale modification algorithms, time-domain and frequency-domain. The computationally efficient time-domain techniques produce high quality results for single pitched signals such as speech, but do not cope well with more complex signals such as polyphonic music. The less efficient frequencydomain techniques have proven to be more robust and produce high quality results for a variety of signals; however they introduce a reverberant artefact into the output. This dissertation focuses on incorporating aspects of time-domain techniques into frequency-domain techniques in an attempt to reduce the presence of the reverberant artefact and improve upon computational demands. From a review of prior work it was found that there are a number of time-domain algorithms available and that the choice of algorithm parameters varies considerably in the literature. This finding prompted an investigation into the effects of the choice of parameters and a comparison of the various techniques employed in terms of computational requirements and output quality. The investigation resulted in the derivation of an efficient and flexible parameter set for use within time-domain implementations. Of the available frequency-domain approaches the phase vocoder and timedomain/ subband techniques offer an efficiency and robustness advantage over sinusoidal modelling and iterative phase update techniques, and as such were identified as suitable candidates for the provision of a framework for further investigation. Following from this observation, improvements in the quality produced by time-domain/subband techniques are realised through the use of a bark based subband partitioning approach and effective subband synchronisation techniques. In addition, computational and output quality improvements within a phase vocoder implementation are achieved by taking advantage of a certain level of flexibility in the choice of phase within such an implementation. The phase flexibility established is used to push or pull phase values into a phase coherent state. Further improvements are realised by incorporating features of time-domain algorithms into the system in order to provide a ‘good’ initial set of phase estimates; the transition to ‘perfect’ phase coherence is significantly reduced through this scheme, thereby improving the overall output quality produced. The result is a robust and efficient time-scale modification algorithm which draws upon various aspects of a number of general approaches to time-scale modification.
Signal Processing Requirements for WiMAX (802.16e) Base Station
802.16e provides specifications for non line of sight, mobile wireless communications in the frequency range of 2-6 GHz. It is well implemented by using OFDMA as its physical layer scheme. The OFDM symbol time (sT) is to be selected depending on the channel conditions, available bandwidth and, simulations provide a means of selecting right values of sTin different channel conditions. Additionally it has been shown that certain values of sT outperform others in all conditions, thus invalidating their use. Moreover, a solution proposed by INTEL is also analyzed. One of the major requirements of OFDM is high synchronization. Detecting the timing offset of a new mobile user, entering the network, which is not time aligned using cross-correlation and ‘auto-correlation’ in time domain and cross-correlation in frequency domain at the base station has been simulated. Results point that the processing load can be significantly reduced by using frequency domain correlation of the received data or by using ‘auto-correlation’ followed by cross-correlation on localized data. The use of adaptive antenna system in 802.16e improves the system performance, where beamforming is implemented in the direction of desired user. Capon’s method and MUSIC method have been simulated to compute the direction of arrival for OFDMA uplink. A new user, while in the ranging process, transmits data with unknown time offset and unknown direction. The thesis describes the procedure to find the two unknown one after another.
Acoustic Echo Cancellation using Digital Signal Processing
Acoustic echo cancellation is a common occurrence in todays telecommunication systems. It occurs when an audio source and sink operate in full duplex mode, an example of this is a hands-free loudspeaker telephone. In this situation the received signal is output through the telephone loudspeaker (audio source), this audio signal is then reverberated through the physical environment and picked up by the systems microphone (audio sink). The effect is the return to the distant user of time delayed and attenuated images of their original speech signal. The signal interference caused by acoustic echo is distracting to both users and causes a reduction in the quality of the communication. This thesis focuses on the use of adaptive filtering techniques to reduce this unwanted echo, thus increasing communication quality. Adaptive filters are a class of filters that iteratively alter their parameters in order to minimise a function of the difference between a desired target output and their output. In the case of acoustic echo in telecommunications, the optimal output is an echoed signal that accurately emulates the unwanted echo signal. This is then used to negate the echo in the return signal. The better the adaptive filter emulates this echo, the more successful the cancellation will be. This thesis examines various techniques and algorithms of adaptive filtering, employing discrete signal processing in MATLAB. Also a real-time implementation of an adaptive echo cancellation system has been developed using the Texas Instruments TMS320C6711 DSP development kit.
A Prototype Laboratory Environment for Digital Signal Processing Using Simulink and a Texas Instrument DSP Device
Normally, when a model is designed from building blocks in Simulink, the simulation is performed within the Simulink environment. A test of the design in a real-time environment requires that source code is generated, compiled and downloaded to the target hardware. As a first attempt to bridge this software gap, this thesis describes and evaluates a prototype laboratory environment, which directly links Simulink to a Texas Instrument DSP device. The prototype system converts graphical models and makes available various real-time signal processing algorithms, such as adders, delays, FFTs, IIR filters and multipliers. Future work is to consider modification of the prototype to allow for feedback in the graphical models and to find an efficient way of handling signal processing algorithms where variable buffer lengths are required.
Efficient Digital Fiilters
What would you do in the following situation? Let ’ s say you are diagnosing a DSP system problem in the field. You have your trusty laptop with your development system and an emulator. You figure out that there was a problem with the system specifications and a symmetric FIR filter in the software won ’ t do the job; it needs reduced passband ripple, or maybe more stopband attenuation. You then realize you don ’ t have any filter design software on the laptop, and the customer is getting angry. The answer is easy: You can take the existing filter and sharpen it. Simply stated, filter sharpening is a technique for creating a new filter from an old one [1] – [3] . While the technique is almost 30 years old, it is not generally known by DSP engineers nor is it mentioned in most DSP textbooks.
Interaction with Sound and Pre-Recorded Music: Novel Interfaces and Use Patterns
Computers are changing the way sound and recorded music are listened to and used. The use of computers to playback music makes it possible to change and adapt music to different usage situations in ways that were not possible with analog sound equipment. In this thesis, interaction with pre-recorded music is investigated using prototypes and user studies. First, different interfaces for browsing music on consumer or mobile devices were compared. It was found that the choice of input controller, mapping and auditory feedback influences how the music was searched and how the interfaces were perceived. Search performance was not affected by the tested interfaces. Based on this study, several ideas for the future design of music browsing interfaces were proposed. Indications that search time depends linearly on distance to target were observed and examined in a related study where a movement time model for searching in a text document using scrolling was developed. Second, work practices of professional disc jockeys (DJs) were studied and a new design for digital DJing was proposed and tested. Strong indications were found that the use of beat information could reduce the DJ’s cognitive workload while maintaining flexibility during the musical performance. A system for automatic beat extraction was designed based on an evaluation of a number of perceptually important parameters extracted from audio signals. Finally, auditory feedback in pen-gesture interfaces was investigated through a series of informal and formal experiments. The experiments point to several general rules of auditory feedback in pen-gesture interfaces: a few simple functions are easy to achieve, gaining further performance and learning advantage is difficult, the gesture set and its computerized recognizer can be designed to minimize visual dependence, and positive emotional or aesthetic response can be achieved using musical auditory feedback.
Hidden Markov Model based recognition of musical pattern in South Indian Classical Music
Automatic recognition of musical patterns plays a crucial part in Musicological and Ethno musicological research and can become an indispensable tool for the search and comparison of music extracts within a large multimedia database. This paper finds an efficient method for recognizing isolated musical patterns in a monophonic environment, using Hidden Markov Model. Each pattern, to be recognized, is converted into a sequence of frequency jumps by means of a fundamental frequency tracking algorithm, followed by a quantizer. The resulting sequence of frequency jumps is presented to the input of the recognizer which use Hidden Markov Model. The main characteristic of Hidden Markov Model is that it utilizes the stochastic information from the musical frame to recognize the pattern. The methodology is tested in the context of South Indian Classical Music, which exhibits certain characteristics that make the classification task harder, when compared with Western musical tradition. Recognition of 100% has been obtained for the six typical music pattern used in practise. South Indian classical instrument, flute is used for the whole experiment.
Design and implementation of odd-order wave digital lattice lowpass filters, from specifications to Motorol DSP56307EVM module
This thesis is dedicated to applying and developing explicit formulas for the design and implementation of odd-order lattice Lowpass wave digital filters (WDFs) on a Digital Signal Processor (DSP), such as a Motorola DSP56307EVM (Evaluation Module). The direct design method of Gazsi for filter types such as Butterworfh, Chebyshev, inverse Chebyshev, and Cauer (Elliptic) provides a straightforward method for calculating the coefficients without an extensive knowledge of digital signal processing. A program package to design and implement odd-order WDFs, including detailed procedures and examples, is presented in this thesis and includes not only the calculations of the coefficients, but also the simulation on a MATLAB platform and an implementation on a Motorola DSP56307EVM board. It is very quick, effective and convenient to obtain the coefficients when the user enters a few parameters according to the general specifications; to verify the characteristics of the designed filter; to simulate the filter on the MATLAB platform; to implement the filter on the DSP board; and to compare the results between the simulation and the implementation.
Towards a Real-Time Implementation of Loudness Enhancement Algorithms on a Motorola DSP 56600
Most of the cellular phone companies with audio speaker capabilities focus on reducing the current drain to extend battery life. None of these companies concentrate on modifying the speech signal itself to make it sound louder in noisy listener environments without adding additional energy. Such algorithms have been described in literature by Boillot and form the backbone of this thesis. The current project focusses on taking a step towards running these algorithms in real-time on a 16-bit fixed point Motorola DSP 56600. Implementation of the autocorrelation, Levinson- Durbin, FIR, and IIR filters in assembly for the Motorola DSP 56600 has been investigated in the thesis. The challenges and alternate solutions to circumvent the challenges have been described, and experimental results have been presented. Results indicate that the modified signed LMS algorithm, which can be considered to be a blend between the LMS and signed LMS algorithms, turns out to be an elegant solution to circumvent the challenges in implementing the Levinson-Durbin recursion.
An Advanced Signal Processing Toolkit for Java applications
The aim of this study is to examine the capability, performance, and relevance of a signal processing toolkit in Java, a programming language for Web-based applications. Due to the simplicity, ease and application use of the toolkit and with the advanced Internet technologies such as Remote Method Invocation (RMI), a spectral estimation applet has been created in the Java environment. This toolkit also provides an interactive and visual approach in understanding the various theoretical concepts of spectral estimation and shows the need to create more application applets to better understand the various concepts of signal and image processing. This study also focuses on creating a Java toolkit for embedded systems, such as Personal Digital Assistants (PDAs), embedded Java board, and supporting integer precision, and utilizing COordinate Rotation DIgital Computer (CORDIC) algorithm, both aimed to provide good performance in resource-limited environments. The results show a feasibility and necessity of developing a standardized Application Programming Interface (API) for the fixed-point signal processing library.
Automated Accident Detection in Intersections Via Digital Audio Signal Processing
The aim of this thesis is to design a system for automated accident detection in intersections. The input to the system is a three-second audio signal. The system can be operated in two modes: two-class and multi-class. The output of the two-class system is a label of “crash” or “non-crash”. In the multi-class system, the output is the label of “crash” or various non-crash incidents including “pile drive”, “brake”, and “normal-traffic” sounds. The system designed has three main steps in processing the input audio signal. They are: feature extraction, feature optimization and classification. Five different methods of feature extraction are investigated and compared; they are based on the discrete wavelet transform, fast Fourier transform, discrete cosine transform, real cepstrum transform and Mel frequency cepstral transform. Linear discriminant analysis (LDA) is used to optimize the features obtained in the feature extraction stage by linearly combining the features using different weights. Three types of statistical classifiers are investigated and compared: the nearest neighbor, nearest mean, and maximum likelihood methods. Data collected from Jackson, MS and Starkville, MS and the crash signals obtained from Texas Transportation Institute crash test facility are used to train and test the designed system. The results showed that the wavelet based feature extraction method with LDA and maximum likelihood classifier is the optimum design. This wavelet-based system is computationally inexpensive compared to other methods. The system produced classification accuracies of 95% to 100% when the input signal has a signal-to-noise-ratio of at least 0 decibels. These results show that the system is capable of effectively classifying “crash” or “non-crash” on a given input audio signal.
Ignal Enhancement Using Time-Frequency Based Denoising
This thesis investigates and compares time and wavelet-domain denoising techniques where received signals contain broadband noise. We consider how time and wavelet-domain denoising schemes and their combinations compare in the mean squared error sense. This work applies Wiener prediction and Median filtering as they do not require any prior signal knowledge. In the wavelet-domain we use soft or hard thresholding on the detail coefficients. In addition, we explore the effect of these wavelet-domain thresholding techniques on the coefficients associated with cycle-spinning and the newly proposed recursive cycle-spinning scheme. Finally, we note that thresholding does not make an attempt to de-noise coefficients that remain after thresholding; therefore we apply time domain techniques to the remaining detail coefficients from the first level of decomposition in an attempt to de-noise them further prior to reconstruction. This thesis applies and compares these techniques using a mean squared error criterion to identify the best performing in a robust test signal environment. We find that soft thresholding with Stein’s Unbiased Risk Estimate (SURE) thresholding produces the best mean squared error results in each test case and that the addition of Wiener prediction to the first level of decomposition coefficients leads to a slightly enhanced performance. Finally, we illustrate the effects of denoising algorithms on longer data segments.
Efficient Signal Processing Techniques for Future Wireless Communications Systems
Wireless communications systems are evolving to be more diverse in use and more ubiquitous in nature. It is of fundamental importance that we consume the resources available in such systems, i.e., bandwidth and energy, to preserve room for more users and to preserve longevity. Signal processing can greatly help us achieve this. In this thesis we consider improving the utility of resources available in wireless communications systems. The basic obstacle for most wireless communications systems is the multipath channel that causes intersymbol interference. Channel estimation is a crucial step for recovering the transmitted symbols. Moreover, as more devices are equipped with wireless capabilities, the bandwidth becomes scarce and it is important to allow more than one device or more than one user to use the same frequency range or the same channel. However, this introduces multiuser interference, which is again eliminated only if the channel is known. Furthermore, most wireless systems are battery powered, at least at the transmitter end. Hence it is crucial that energy consumption is minimized to preserve the longevity of the system. The contribution of this thesis is three fold: (i) We propose novel bandwidth efficient blind channel estimation algorithms for single input multiple output systems, and for multiuser OFDM systems. The former exploits cyclostationarity inherent in communications signals. The latter exploits the structure introduced to the transmitted signal via precoding. We consider design of such precoders by optimizing performance metrics such as the bit error rate and signal to interference plus noise ratio. (ii) In the multiuser systems case, we propose a novel cooperative OFDM system and show that, when users face significantly different channel conditions, cooperation can improve the performance of all the cooperating users. (iii) We consider energy efficient training based system estimation in large MIMO systems. The goal there is to minimize energy consumption both in transmission of training symbols and in performing computations. We show that by using a divide and conquer strategy in selecting the active set of transmitters and receivers, it is possible to minimize energy consumption without degrading the accuracy of the channel estimate.
Image Analysis Using a Dual-Tree M-Band Wavelet Transform
We propose a 2D generalization to the M-band case of the dual-tree decomposition structure (initially proposed by N. Kingsbury and further investigated by I. Selesnick) based on a Hilbert pair of wavelets. We particularly address (i) the construction of the dual basis and (ii) the resulting directional analysis. We also revisit the necessary pre-processing stage in the M-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed M- band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various M-band wavelets and thresholding strategies. Signicant improvements in terms of both overall noise reduction and direction preservation are observed.
A Nonlinear Stein Based Estimator for Multichannel Image Denoising
The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this paper, we are interested in multichannel image denoising based on a multiscale representation of the images. A multivariate statistical approach is adopted to take into account both the spatial and the inter-component correlations existing between the different wavelet subbands. More precisely, we propose a new parametric nonlinear estimator which generalizes many reported denoising methods. The derivation of the optimal parameters is achieved by applying Stein’s principle in the multivariate case. Experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising techniques.
Code Acquisition using Smart Antennas with Adaptive Filtering Scheme for DS-CDMA Systems
Pseudo-noise (PN) code synchronizer is an essential element of direct-sequence code division multiple access (DS-CDMA) system because data transmission is possible only after the receiver accurately synchronizes the locally generated PN code with the incoming PN code. The code synchronization is processed in two steps, acquisition and tracking, to estimate the delay offset between the two codes. Recently, the adaptive LMS filtering scheme has been proposed for performing both code acquisition and tracking with the identical structure, where the LMS algorithm is used to adjust the FIR filter taps to search for the value of delay-offset adaptively. A decision device is employed in the adaptive LMS filtering scheme as a decision variable to indicate code synchronization, hence it plays an important role for the performance of mean acquisition time (MAT). In this thesis, only code acquisition is considered. In this thesis, a new decision device, referred to as the weight vector square norm (WVSN) test method, is devised associated with the adaptive LMS filtering scheme for code acquisition in DS-CDMA system. The system probabilities of the proposed scheme are derived for evaluating MAT. Numerical analyses and simulation results verify that the performance of the proposed scheme, in terms of detection probability and MAT, is superior to the conventional scheme with mean-squared error (MSE) test method, especially when the signal-to-interference-plus-noise ratio (SINR) is relatively low. Furthermore, an efficient and joint-adaptation code acquisition scheme, i.e., a smart antenna coupled with the proposed adaptive LMS filtering scheme with the WVSN test method, is devised for applying to a base station, where all antenna elements are employed during PN code acquisition. This new scheme is a process of PN code acquisition and the weight coefficients of smart antenna jointly and adaptively. Numerical analyses and simulation results demonstrate that the performance of the proposed scheme with five antenna elements, in terms of the output SINR, the detection probability and the MAT, can be improved by around 7 dB, compared to the one with single antenna case.
