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.
Fixed-Point Arithmetic: An Introduction
This document presents definitions of signed and unsigned fixed-point binary number representations and develops basic rules and guidelines for the manipulation of these number representations using the common arithmetic and logical operations found in fixed-point DSPs and hardware components.
Orthogonal Adaptive Digital Filters with Applications to Acoustic System Identification
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.
Teaching MODEM Concepts and Design Procedure with MATLAB Simulations
MATLAB simulation is used as the primary tool to illustrate concepts, to validate MODEM designs, and to vent' operation of the subsystems employed in DSP based transmitters and receivers presented in a pair of classes on MODEM Design and Digital Receiver Design. The whole gamut of subsystems found in conventional and experimental modem designs are simulated and assembled to form a full end-to-end simulation of an operating MODEM. This paper describes the philosophy used to guide class involvement and assess the experience and the learning value to student participants.
A New Contender in the Digital Differentiator Race
This blog proposes a novel differentiator worth your consideration. Although simple, the differentiator provides a fairly wide 'frequency range of linear operation' and can be implemented, if need be, without performing numerical multiplications.
Digital Image Processing Using LabView
Digital Image processing is a topic of great relevance for practically any project, either for basic arrays of photodetectors or complex robotic systems using artificial vision. It is an interesting topic that offers to multimodal systems the capacity to see and understand their environment in order to interact in a natural and more efficient way. The development of new equipment for high speed image acquisition and with higher resolutions requires a significant effort to develop techniques that process the images in a more efficient way. Besides, medical applications use new image modalities and need algorithms for the interpretation of these images as well as for the registration and fusion of the different modalities, so that the image processing is a productive area for the development of multidisciplinary applications. The aim of this chapter is to present different digital image processing algorithms using LabView and IMAQ vision toolbox. IMAQ vision toolbox presents a complete set of digital image processing and acquisition functions that improve the efficiency of the projects and reduce the programming effort of the users obtaining better results in shorter time. Therefore, the IMAQ vision toolbox of LabView is an interesting tool to analyze in detail and through this chapter it will be presented different theories about digital image processing and different applications in the field of image acquisition, image transformations. This chapter includes in first place the image acquisition and some of the most common operations that can be locally or globally applied, the statistical information generated by the image in a histogram is commented later. Finally, the use of tools allowing to segment or filtrate the image are described making special emphasis in the algorithms of pattern recognition and matching template.
OPTIMAL DESIGN OF DIGITAL EQUIVALENTS TO ANALOG FILTERS
The proposed optimal algorithm for the digitizing of analog filters is based on two existing filter design methods: the extended window design (EWD) and the matched–pole (MP) frequency sampling design. The latter is closely related to the filter design with iterative weighted least squares (WLS). The optimization is performed with an original MP design that yields an equiripple digitizing error. Then, a drastic reduction of the digitizing error is achieved through the introduction of a fractional time shift that minimizes the magnitude of the equiripple error within a given frequency interval. The optimal parameters thus obtained can be used to generate the EWD equations, together with a variable fractional delay output, as described in an earlier paper. Finally, in contrast to the WLS procedure, which relies on a “good guess” of the weighting function, the MP optimization is straightforward.
A NEW PARALLEL IMPLEMENTATION FOR PARTICLE FILTERS AND ITS APPLICATION TO ADAPTIVE WAVEFORM DESIGN
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.
Design of a Scalable Polyphony-MIDI Synthesizer for a Low Cost DSP
In this thesis, the design of a music synthesizer implementing the Scalable Polyphony-MIDI soundset on a low cost DSP system is presented. First, the SP-MIDI standard and the target DSP platform are presented followed by review of commonly used synthesis techniques and their applicability to systems with limited computational and memory resources. Next, various oscillator and filter algorithms used in digital subtractive synthesis are reviewed in detail. Special attention is given to the aliasing problem caused by discontinuities in classical waveforms, such as sawtooth and pulse waves and existing methods for bandlimited waveform synthesis are presented. This is followed by review of established structures for computationally efficient time-varying filters. A novel digital structure is presented that decouples the cutoff and resonance controls. The new structure is based on the analog Korg MS-20 lowpass filter and is computationally very efficient and well suited for implementation on low bitdepth architectures. Finally, implementation issues are discussed with emphasis on the Differentiated Parabole Wave oscillator and MS-20 filter structures and the effects of limited computational capability and low bitdepth. This is followed by designs for several example instruments.
Real Time Implementation of Multi-Level Perfect Signal Reconstruction Filter Bank
Discrete Wavelet Transform (DWT) is an efficient tool for signal and image processing applications which has been utilized for perfect signal reconstruction. In this paper, twenty seven optimum combinations of three different wavelet filter types, three different filter reconstruction levels and three different kinds of signal for multi-level perfect reconstruction filter bank were implemented in MATLAB/Simulink. All the filters for different wavelet types were designed using Filter Design Analysis (FDA) and Wavelet toolbox. Signal to Noise Ratio (SNR) was calculated for each combination. Combination with best SNR was then implemented on TMS320C6713 DSP kit. Real time testing of perfect reconstruction on DSP kit was then carried out by two different methods. Experimental results accede with theory and simulations.
