DSPRelated.com
Filtered by topic: Statistical Signal Processing [clear filter]
Method to Calculate the Inverse of a Complex Matrix using Real Matrix Inversion

Method to Calculate the Inverse of a Complex Matrix using Real Matrix Inversion

Andreas Falkenberg
Still RelevantAdvanced

This paper describes a simple method to calculate the invers of a complex matrix. The key element of the method is to use a matrix inversion, which is available and optimised for real numbers. Some actual libraries used for digital signal processing only provide highly optimised methods to calculate the inverse of a real matrix, whereas no solution for complex matrices are available, like in [1]. The presented algorithm is very easy to implement, while still much more efficient than for example the method presented in [2]. [1] Visual DSP++ 4.0 C/C++ Compiler and Library Manual for TigerSHARC Processors; Analog Devices; 2005. [2] W. Press, S.A. Teukolsky, W.T. Vetterling, B.R. Flannery; Numerical Recipes in C++, The art of scientific computing, Second Edition; p52 : “Complex Systems of Equations”;Cambridge University Press 2002.


Fully Programmable LDPC Decoder Hardware Architectures

Fully Programmable LDPC Decoder Hardware Architectures

Christiane Maja Beusche
Still RelevantAdvanced

In recent years, the amount of digital data which is stored and transmitted for private and public usage has increased considerably. To allow a save transmission and storage of data despite of error-prone transmission media, error correcting codes are used. A large variety of codes has been developed, and in the past decade low-density parity-check (LDPC) codes which have an excellent error correction performance became more and more popular. Today, low-density parity-check codes have been adopted for several standards, and efficient decoder hardware architectures are known for the chosen structured codes. However, the existing decoder designs lack flexibility as only few structured codes can be decoded with one decoder chip. In consequence, different codes require a redesign of the decoder, and few solutions exist for decoding of codes which are not quasi-cyclic or which are unstructured. In this thesis, three different approaches are presented for the implementation of fully programmable LDPC decoders which can decode arbitrary LDPC codes. As a design study, the first programmable decoder which uses a heuristic mapping algorithm is realized on an field-programmable gate array (FPGA), and error correction curves are measured to verify the correct functionality. The main contribution of this thesis lies in the development of the second and the third architecture and an appropriate mapping algorithm. The proposed fully programmable decoder architectures use one-phase message passing and layered decoding and can decode arbitrary LDPC codes using an optimum mapping and scheduling algorithm. The presented programmable architectures are in fact generalized decoder architectures from which the known decoders architectures for structured LDPC codes can be derived.


Music Signal Processing

Music Signal Processing

Saeed V. Vaseghi
Still RelevantIntermediate

Chapter 12 of the book "Multimedia Signal Processing: Theory and Applications in Speech, Music and Communications" - Musical Instruments - A Review of Basic Physics of Sound - Music Signal Features and Models - Ear: Hearing of Sounds - Psychoacoustics of Hearing - Music Compression - High Quality Music Coding: MPEG - Stereo Music - Music Recognition


High speed data collection with Blackfin DSP

High speed data collection with Blackfin DSP

Axel Alatalo
Still RelevantIntermediate

This report covers a master thesis in embedded systems, the goal of which was to investigate the high speed data collection capabilities with a Blackfin DSP. Basic theory about sampling and noise is covered briefly from a practical point of view. The theory is intended to be useful for those diving into a ADC datasheet for the first time. After an investigation of the delimiting factors, suitable components were selected and a prototype ADC PCB was designed from scratch. The goal is to design a general low noise data collecting unit compatible with the Blackfin DSP. Finally simple DSP software is designed to prove that DSP can handle such a high datastream.Testing the ADC card with the target Blackfin platform indicates thatthe analog parts indeed works. An analog bandwidth of over 10MHz ismeasured at a resolution exceeding 10 bits with respect to noise. The digital parts intended to interleave the two channels digital streams into one Blackfin unit did not work as intended. Only one channel is supported as of now. The report contains suggestions for future work in this area.


Evaluation of a Floating Point Acoustic Echo Canceller Implementation

Evaluation of a Floating Point Acoustic Echo Canceller Implementation

Anders Dahlberg
Still RelevantIntermediate

This master thesis consists of implementation and evaluation of an AEC, Acoustic Echo Canceller, algorithm in a floating-point architecture. The most important question this thesis will try to answer is to determine benefits or drawbacks of using a floating-point architecture, relative a fixed-point architecture, to do AEC. In a telephony system there is two common forms of echo, line echo and acoustic echo. Acoustic echo is introduced by sound emanating from a loudspeaker, e.g. in a handsfree or speakerphone, being picked up by a microphone and then sent back to the source. The problem with this feedback is that the far-end speaker will hear one, or multiple, time-delayed version(s) of her own speech. This time-delayed version of speech is usually perceived as both confusing and annoying unless removed by the use of AEC. In this master thesis the performance of a floating-point version of a normalized least-mean-square AEC algorithm was evaluated in an environment designed and implemented to approximate live telephony calls. An instruction-set simulator and assembler available at the initiation of this master thesis were extended to enable; zero-overhead loops, modular addressing, post-increment of registers and register-write forwarding. With these improvements a bit-true assembly version was implemented capable of real-time AEC requiring 15 million instructions per second. A solution using as few as eight mantissa bits, in an external format used when storing data in memory, was found to have an insignificant effect on the selected AEC implementation’s performance. Due to the relatively low memory requirement of the selected AEC algorithm, the use of a small external format has a minor effect on the required memory size. In total this indicates that the possible reduction of the memory requirement and related energy consumption, does not justify the added complexity and energy consumption of using a floating-point architecture for the selected algorithm. Use of a floating-point format can still be advantageous in speech-related signal processing when the introduced time delay by a subband, or a similar frequency domain, solution is unacceptable. Speech algorithms that have high memory use and small introduced delay requirements are a good candidate for a floating-point digital signal processor architecture.


Correlation and Power Spectrum

Correlation and Power Spectrum

Duraisamy Sundararajan
TimelessIntermediate

In the signals and systems course and in the first course in digital signal processing, a signal is, most often, characterized by its amplitude spectrum in the frequency-domain and its amplitude profile in the time-domain. So much a student gets used to this type of characterization, that the student finds it difficult to appreciate, when encountered in the ensuing statistical signal processing course, the fact that a signal can also be characterized by its autocorrelation function in the time-domain and the corresponding power spectrum in the frequency-domain and that the amplitude characterization is not available. In this article, the characterization of a signal by its autocorrelation function in the time-domain and the corresponding power spectrum in the frequency-domain is described. Cross-correlation of two signals is also presented.


Digital Signal Processing Maths

Digital Signal Processing Maths

Markus Hoffmann
TimelessIntermediate

Modern digital signal processing makes use of a variety of mathematical techniques. These techniques are used to design and understand efficient filters for data processing and control.


EngD thesis: Reduced-Complexity Signal Detection in Digital Communications Receivers

EngD thesis: Reduced-Complexity Signal Detection in Digital Communications Receivers

Julian Penketh
Still RelevantAdvanced

The Author began this Engineering Doctorate (EngD) in Autumn 1999, whilst already in full-time employment as a DSP software engineer at Nortel Networks, Harlow. This EngD comprises a set of three projects. The first project was focused on the development of dual-tone multi-frequency (DTMF) signal detection software. DTMF signals are currently used for operating menu-driven services such as voice-mail, telephone banking and share-dealing. The need for detection software in a packet networking environment exists because such signals become degraded when they travel through speech compression circuits. In addition, if they appear as echoes on a telephone line, they can affect the operation of echo cancellation systems. In this thesis a number of DSP algorithms are discussed where fast detection and minimum complexity are key characteristics. A key contribution here was the development of a novel detection algorithm based on the extraction of parameters that model the DTMF signal. The thesis reports a method combining parameter extraction with the technique of maximum likelihood to perform DTMF detection, resulting in very short time-frames when compared to standard approaches. Reducing the complexity of detection techniques is also important in today’s communication systems. To this end a key contribution here was the development of the ‘split Goertzel algorithm’, which permitted an overlapping of analysis windows without the need for reprocessing input data. Besides being applied to voice-band signals, such as in the case of DTMF, the Author also had the opportunity during the EngD to apply the skills and knowledge acquired in signal processing to higher-rate data-streams. This involved work concerning the equalisation of channel distortion commonly found in wireless communication systems. This covers two projects, with the first being conducted at Verticalband Ltd. (now no longer operational) in the area of digital television receivers. In this part of the thesis a real-time DSP implementation is discussed for enhancing a simulation system developed for wireless channels. A number of channel equalisation approaches are studied. The work concludes that for high-rate signals, non-linear algorithms have the best error rate performance. On the basis of the studies carried out, the thesis considers development and implementation issues of designs based on the decision feedback equaliser. The thesis reports on a software design which applies the method of least squares to carry out filter coefficient adaptation. The Verticalband studies reported lead on to further research within the context of channel equalisation, in the context of the detection of data in multiple-input multiple-output (MIMO) wireless local area network (WLAN) systems. This work was undertaken at Philips Research in Eindhoven, The Netherlands. The thesis discusses implementation scenarios of multi-element antenna arrays that aim to provide bit-rates orders of magnitude higher than today’s WLAN offerings, as those required by emerging standards such as 802.11n. The complexity of optimal detection techniques, such as maximum likelihood, scales exponentially with the number of transmit antennas. This translates to high processing costs and power consumption, rendering such techniques unsuitable for use in battery-powered devices. The initial main contribution here was the analysis of the complexity of algorithms whose performance had already been tested, such as the non-linear maximum likelihood approach and also less complex methods utilising linear filtering. This resulted in the development of new formulae to predict processing costs of algorithms based on the number of transmit and receive antennas. Other key contributions were defining a method to reduce the complexity of matrix inversion when using the Moore-Penrose pseudo-inverse, and the application of matrix decomposition to obviate the need for costly matrix inversion at all. Some on-going research into sub-optimal detection is also discussed, which describes methods to reduce the search-space for the maximum likelihood algorithm.


A Subspace Based Approach to the Design, Implementation and Validation of Algorithms for Active Vibration Isolation Control

A Subspace Based Approach to the Design, Implementation and Validation of Algorithms for Active Vibration Isolation Control

Gerard Nijsse
Still RelevantAdvanced

Vibration isolation endeavors to reduce the transmission of vibration energy from one structure (the source) to another (the receiver), to prevent undesirable phenomena such as sound radiation. A well-known method for achieving this is passive vibration isolation (PVI). In the case of PVI, mounts are used - consisting of springs and dampers - to connect the vibrating source to the receiver. The stiffness of the mount determines the fundamental resonance frequency of the mounted system and vibrations with a frequency higher than the fundamental resonance frequency are attenuated. Unfortunately, however, other design requirements (such as static stability) often impose a minimum allowable stiffness, thus limiting the achievable vibration isolation by passive means. A more promising method for vibration isolation is hybrid vibration isolation control. This entails that, in addition to PVI, an active vibration isolation control (AVIC) system is used with sensors, actuators and a control system that compensates for vibrations in the lower frequency range. Here, the use of a special form of AVIC using statically determinate stiff mounts is proposed. The mounts establish a statically determinate system of high stiffness connections in the actuated directions and of low stiffness connections in the unactuated directions. The latter ensures PVI in the unactuated directions. This approach is called statically determinate AVIC (SD-AVIC). The aim of the control system is to produce antidisturbance forces that counteract the disturbance forces stemming from the source. Using this approach, the vibration energy transfer from the source to the receiver is blocked in the mount due to the anti-forces. This thesis deals with the design of controllers generating the anti-forces by applying techniques that are commonly used in the field of signal processing. The control approaches - that are model-based - are both adaptive and fixed gain and feedforward and feedback oriented. The control approaches are validated using two experimental vibration isolation setups: a single reference single actuator single error sensor (SR-SISO) setup and a single reference input multiple actuator input multiple error sensor output (SR-MIMO) setup. Finding a plant model can be a problem. This is solved by using a black-box modelling strategy. The plants are identified using subspace model identification. It is shown that accurate linear models can be found in a straightforward manner by using small batches of recorded (sampled) time-domain data only. Based on the identified models, controllers are designed, implemented and validated. Due to resonance in mechanical structures, adaptive SD-AVIC systems are often hampered by slow convergence of the controller coefficients. In general, it is desirable that the SD-AVIC system yields fast optimum performance after it is switched on. To achieve this result and speed up the convergence of the adaptive controller coefficients, the so-called inverse outer factor model is included in the adaptive control scheme. The inner/outer factorization, that has to be performed to obtain the inverse outer factor model, is completely determined in state space to enable a numerically robust computation. The inverse outer factor model is also incorporated in the control scheme as a state space model. It is found that fast adaptation of the controller coefficients is possible. Controllers are designed, implemented and validated to suppress both narrowband and broadband disturbances. Scalar regularization is used to prevent actuator saturation and an unstable closed loop. In order to reduce the computational load of the controllers, several steps are taken including controller order reduction and implementation of lower order models. It is found that in all experiments the simulation and real-time results correspond closely for both the fixed gain and adaptive control situation. On the SR-SISO setup, reductions up to 5.0 dB are established in real-time for suppressing a broadband disturbance output (0-2 kHz) using feedback-control. On the SR-MIMO vibration isolation setup, using feedforward-control reductions of broadband disturbances (0-1 kHz) of 9.4 dB are established in real-time. Using feedback-control, reductions are established up to 3.5 dB in real-time (0-1 kHz). In case of the SR-MIMO setup, the values for the reduction are obtained by averaging the reductions obtained in all sensor outputs. The results pave the way for the next generation of algorithms for SD-AVIC.


Auditory System for a Mobile Robot

Auditory System for a Mobile Robot

Jean-Marc Valin
Still RelevantAdvanced

The auditory system of living creatures provides useful information about the world, such as the location and interpretation of sound sources. For humans, it means to be able to focus one's attention on events, such as a phone ringing, a vehicle honking, a person taking, etc. For those who do not suffer from hearing impairments, it is hard to imagine a day without being able to hear, especially in a very dynamic and unpredictable world. Mobile robots would also benefit greatly from having auditory capabilities. In this thesis, we propose an artificial auditory system that gives a robot the ability to locate and track sounds, as well as to separate simultaneous sound sources and recognising simultaneous speech. We demonstrate that it is possible to implement these capabilities using an array of microphones, without trying to imitate the human auditory system. The sound source localisation and tracking algorithm uses a steered beamformer to locate sources, which are then tracked using a multi-source particle filter. Separation of simultaneous sound sources is achieved using a variant of the Geometric Source Separation (GSS) algorithm, combined with a multisource post-filter that further reduces noise, interference and reverberation. Speech recognition is performed on separated sources, either directly or by using Missing Feature Theory (MFT) to estimate the reliability of the speech features. The results obtained show that it is possible to track up to four simultaneous sound sources, even in noisy and reverberant environments. Real-time control of the robot following a sound source is also demonstrated. The sound source separation approach we propose is able to achieve a 13.7 dB improvement in signal-to-noise ratio compared to a single microphone when three speakers are present. In these conditions, the system demonstrates more than 80% accuracy on digit recognition, higher than most human listeners could obtain in our small case study when recognising only one of these sources. All these new capabilities will allow humans to interact more naturally with a mobile robot in real life settings.