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.
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 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.
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 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.
Nice slides introducing Digital Signal Processing.
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  –  . While the technique is almost 30 years old, it is not generally known by DSP engineers nor is it mentioned in most DSP textbooks.
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.
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.
Dual-tree wavelet decompositions have recently gained much popularity, mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy. When the decomposition of a random process is performed – which occurs in particular when an additive noise is corrupting the signal to be analyzed – it is useful to characterize the statistical properties of the dual-tree wavelet coefficients of this process. As dual-tree decompositions constitute overcomplete frame expansions, correlation structures are introduced among the coefficients, even when a white noise is analyzed. In this paper, we show that it is possible to provide an accurate description of the covariance properties of the dual-tree coefficients of a wide-sense stationary process. The expressions of the (cross-) covariance sequences of the coefficients are derived in the one and two-dimensional cases. Asymptotic results are also provided, allowing to predict the behaviour of the second-order moments for large lag values or at coarse resolution. In addition, the crosscorrelations between the primal and dual wavelets, which play a primary role in our theoretical analysis, are calculated for a number of classical wavelet families. Simulation results are finally provided to validate these results.
This thesis studies the application of the wavelet filter bank (WFB) in perceptual audio coding by providing brief overviews of perceptual coding, psychoacoustics, wavelet theory, and existing wavelet coding algorithms. Furthermore, it describes the poor frequency localization property of the WFB and explores one filter design method, in particular, for improving channel separation between the wavelet bands. A wavelet audio coder has also been developed by the author to test the new filters. Preliminary tests indicate that the new filters provide some improvement over other wavelet filters when coding audio signals that are stationary-like and contain only a few harmonic components, and similar results for other types of audio signals that contain many spectral and temporal components. It has been found that the WFB provides a flexible decomposition scheme through the choice of the tree structure and basis filter, but at the cost of poor localization properties. This flexibility can be a benefit in the context of audio coding but the poor localization properties represent a drawback. Determining ways to fully utilize this flexibility, while minimizing the effects of poor time-frequency localization, is an area that is still very much open for research.
The fields of neurobiology and electrical engineering have come together to pursue an integrated Brain-Machine Interface (BMI). Signal processing methods are used to find mapping algorithms between motor cortex neural firing rate and hand position. This cognitive extension could help patients with quadriplegia regain some independence using a thought-controlled robot arm. Current signal processing methods to achieve realtime neural-to-motor translation involve large, multi-processor systems to produce motor control parameters. Eventually, software running in a portable signal processing system is needed to allow for the patient to have the BMI in a backpack or attached to a wheelchair. This thesis presents a DSP-Based Computational Engine for a Brain-Machine Interface. The development of a DSP Board based on the Texas Instruments TMS320VC33 DSP will be presented, along with implementations of two digital filters and their training methods: 1) FIR trained with Normalized Least Mean Square Adaptive Filter (NLMS) and 2) Recurrent Multi-Layer Perceptron (RMLP) trained with Real-Time Recurrent Learning (RTRL). The requirements of the DSP Board, component selection and integration, and control software are discussed. The DSP implementations of the digital filters are presented, along with performance and timing analysis in real data collected from an Owl Monkey at Duke University. The weights of the FIR-NLMS filter converged similarly on the DSP as they did in MATLAB. Likewise, the weights of the RMLP-RTRL filter converged similarly on the DSP as they did using the Backpropagation Through Time method in NeuroSolutions. The custom DSP Board and two digital algorithms implemented in this thesis create a starting point for an integrated, portable, real-time signal processing solution for a Brain-Machine Interface.
The success of multicarrier modulation in the form of OFDM in radio channels illuminates a path one could take towards high-rate underwater acoustic communications, and recently there are intensive investigations on underwater OFDM. In this paper, we implement the acoustic OFDM transmitter and receiver design of [4, 5] on a TMS320C6713 DSP board. We analyze the workload and identify the most time-consuming operations. Based on the workload analysis, we tune the algorithms and optimize the code to substantially reduce the synchronization time to 0.2 seconds and the processing time of one OFDM block to 1.7 seconds on a DSP processor at 225 MHz. This experimentation provides guidelines on our future work to reduce the per-block processing time to be less than the block duration of 0.23 seconds for real time operations.
The Transform-Domain LMS Algorithm (Narayan, 1983) is studied in the context of an acoustic system identification problem. The power estimator in this two-stage digital filter is shown to affect the achievable rates and depths of convergence significantly. Preferred values for the two tracking parameters, $\beta$ and $\mu,$ are determined. Dynamic Step-size Initialization is proposed to improve early convergence by accelerating the rate at which true power measurements replace (arbitrary) initial values. Later, linear estimators are shown to be sub-optimal, particularly where the spectral distribution of the reference changes rapidly. A simple non-linear Peak Window Power Estimator which eliminates these problems is described. It will be shown to improve the tracking rates and misadjustment simultaneously. The benefits of these methods are demonstrated using FIR sequences representative of typical acoustic environments and using recordings from a commercial telephone set. The proposed structures surpass theexisting algorithms consistently under all circumstances tested.
Modulation is the process of facilitating the transfer of information over a medium. Typically the objective of a digital communication system is to transport digital data between two or more nodes. In radio communications this is usually achieved by adjusting a physical characteristic of a sinusoidal carrier, either the frequency, phase, amplitude or a combination thereof . This is performed in real systems with a modulator at the transmitting end to impose the physical change to the carrier and a demodulator at the receiving end to detect the resultant modulation on reception. Hence, modulation can be objectively defined as the process of converting information so that it can be successfully sent through a medium. This thesis deals with the current digital modulation techniques used in industry. Also, the thesis examines the qualitative and quantitative criteria used in selection of one modulation technique over the other. All the experiments, and realted data collected were obtained using MATLAB and SIMULINK
A delayless structure targeted for low-resource implementation is proposed to eliminate filterbank processing delays in subband adaptive filters (SAFs). Rather than using direct IFFT or polyphase filterbanks to transform the SAFs back into the time-domain, the proposed method utilizes a weighted overlap-add (WOLA) synthesis. Low-resource real-time implementations are targeted and as such do not involve long (as long as the echo plant) FFT or IFFT operations. Also, the proposed approach facilitates time distribution of the adaptive filter reconstruction calculations crucial for efficient real-time and hardware implementation. The method is implemented on an oversampled WOLA filterbank employed as part of an echo cancellation application. Evaluation results demonstrate that the proposed implementation outperforms conventional SAF systems since the signals used in actual adaptive filtering are not distorted by filterbank aliasing. The method is a good match for partial update adaptive algorithms since segments of the time-domain adaptive filter are sequentially reconstructed and updated.
Sequential Monte Carlo particle ﬁlters (PFs) are useful for estimating nonlinear non-Gaussian dynamic system parameters. As these algorithms are recursive, their real-time implementation can be computationally complex. In this paper, we analyze the bottlenecks in existing parallel PF algorithms, and we propose a new approach that integrates parallel PFs with independent Metropolis-Hastings (PPF-IMH) algorithms to improve root mean-squared estimation error performance. We implement the new PPF-IMH algorithm on a Xilinx Virtex-5 ﬁeld programmable gate array (FPGA) platform. For a onedimensional problem and using 1,000 particles, the PPF-IMH architecture with four processing elements utilizes less than 5% Virtex-5 FPGA resources and takes 5.85 μs for one iteration. The algorithm performance is also demonstrated when designing the waveform for an agile sensing application.
An adaptive distributed noise reduction algorithm for speech enhancement is considered, which operates in a wireless acoustic sensor network where each node collects multiple microphone signals. In previous work, it was shown theoretically that for a stationary scenario, the algorithm provides the same signal estimators as the centralized multi-channel Wiener filter, while significantly compressing the data that is transmitted between the nodes. Here, we present simulation results of a fully adaptive implementation of the algorithm, in a non-stationary acoustic scenario with a moving speaker and two babble noise sources. The algorithm is implemented using a weighted overlap-add technique to reduce the overall input-output delay. It is demonstrated that good results can be obtained by estimating the required signal statistics with a long-term forgetting factor without downdating, even though the signal statistics change along with the iterative filter updates. It is also demonstrated that simultaneous node updating provides a significantly smoother and faster tracking performance compared to sequential node updating.