## A Quadrature Signals Tutorial: Complex, But Not Complicated

●3 commentsQuadrature signals are based on the notion of complex numbers and perhaps no other topic causes more heartache for newcomers to DSP than these numbers and their strange terminology of j operator, complex, imaginary, real, and orthogonal. If you're a little unsure of the physical meaning of complex numbers and the j = √-1 operator, don't feel bad because you're in good company. Why even Karl Gauss, one the world's greatest mathematicians, called the j operator the "shadow of shadows". Here we'll shine some light on that shadow so you'll never have to call the Quadrature Signal Psychic Hotline for help. Quadrature signal processing is used in many fields of science and engineering, and quadrature signals are necessary to describe the processing and implementation that takes place in modern digital communications systems. In this tutorial we'll review the fundamentals of complex numbers and get comfortable with how they're used to represent quadrature signals. Next we examine the notion of negative frequency as it relates to quadrature signal algebraic notation, and learn to speak the language of quadrature processing. In addition, we'll use three-dimensional time and frequency-domain plots to give some physical meaning to quadrature signals. This tutorial concludes with a brief look at how a quadrature signal can be generated by means of quadrature-sampling.

## Computing Translated Frequencies in Digitizing and Downsampling Analog Bandpass Signals

In digital signal processing (DSP) we're all familiar with the processes of bandpass sampling an analog bandpass signal and downsampling a digital bandpass signal. The overall spectral behavior of those operations are well-documented. However, mathematical expressions for computing the translated frequency of individual spectral components, after bandpass sampling or downsampling, are not available in the standard DSP textbooks. This document explains how to compute the frequencies of translated spectral components and provide the desired equations in the hope that they are of use to you.

## Hilbert Transform and Applications

●1 commentSection 1: reviews the mathematical deﬁnition of Hilbert transform and various ways to calculate it.

Sections 2 and 3: review applications of Hilbert transform in two major areas: Signal processing and system identiﬁcation.

Section 4: concludes with remarks on the historical development of Hilbert transform

## Voice Activity Detection. Fundamentals and Speech Recognition System Robustness

An important drawback affecting most of the speech processing systems is the environmental noise and its harmful effect on the system performance. Examples of such systems are the new wireless communications voice services or digital hearing aid devices. In speech recognition, there are still technical barriers inhibiting such systems from meeting the demands of modern applications. Numerous noise reduction techniques have been developed to palliate the effect of the noise on the system performance and often require an estimate of the noise statistics obtained by means of a precise voice activity detector (VAD). Speech/non-speech detection is an unsolved problem in speech processing and affects numerous applications including robust speech recognition, discontinuous transmission, real-time speech transmission on the Internet or combined noise reduction and echo cancellation schemes in the context of telephony. The speech/non-speech classification task is not as trivial as it appears, and most of the VAD algorithms fail when the level of background noise increases. During the last decade, numerous researchers have developed different strategies for detecting speech on a noisy signal and have evaluated the influence of the VAD effectiveness on the performance of speech processing systems. Most of the approaches have focussed on the development of robust algorithms with special attention being paid to the derivation and study of noise robust features and decision rules. The different VAD methods include those based on energy thresholds, pitch detection, spectrum analysis, zero-crossing rate, periodicity measure, higher order statistics in the LPC residual domain or combinations of different features. This chapter shows a comprehensive approximation to the main challenges in voice activity detection, the different solutions that have been reported in a complete review of the state of the art and the evaluation frameworks that are normally used. The application of VADs for speech coding, speech enhancement and robust speech recognition systems is shown and discussed. Three different VAD methods are described and compared to standardized and recently reported strategies by assessing the speech/non-speech discrimination accuracy and the robustness of speech recognition systems.

## 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.

## De-Noising Audio Signals Using MATLAB Wavelets Toolbox

Based on the fact that noise and distortion are the main factors that limit the capacity of data transmission in telecommunications and that they also affect the accuracy of the results in the signal measurement systems, whereas, modeling and removing noise and distortions are at the core of theoretical and practical considerations in communications and signal processing. Another important issue here is that, noise reduction and distortion removal are major problems in applications such as; cellular mobile communication, speech recognition, image processing, medical signal processing, radar, sonar, and any other application where the desired signals cannot be isolated from noise and distortion. The use of wavelets in the field of de-noising audio signals is relatively new, the use of this technique has been increasing over the past 20 years. One way to think about wavelets matches the way how our eyes perceive the world when they are faced to different distances. In the real world, a forest can be seen from many different perspectives; they are, in fact, different scales of resolution. From the window of an airplane, for instance, the forest cover appears as a solid green roof. From the window of a car, the green roof gets transformed into individual trees, and if we leave the car and approach to the forest, we can gradually see details such as the trees branches and leaves. If we had a magnifying glass, we could see a dew drop on the tip of a leaf. As we get closer to even smaller scales, we can discover details that we had not seen before. On the other hand, if we tried to do the same thing with a photograph, we would be completely frustrated. If we enlarged the picture "closer" to a tree, we would only be able to see a blurred tree image; we would not be able to spot neither the branch, nor the leaf, and it would be impossible to spot the dew drop. Although our eyes can see on many scales of resolution, the camera can only display one at a time. In this chapter, we introduce the reader to a way to reduce noise in an audio signal by using wavelet transforms. We developed this technique by using the wavelet tool in MATLAB. A Simulink is used to acquire an audio signal and we use it to convert the signal to a digital format so it can be processed. Finally, a Graphical User Interface Development Environment (GUIDE) is used to create a graphical user interface. The reader can go through this chapter systematically, from the theory to the implementation of the noise reduction technique. We will introduce in the first place the basic theory of an audio signal, the noise treatment fundamentals and principles of the wavelets theory. Then, we will present the development of noise reduction when using wavelet functions in MATLAB. In the foreground, we will demonstrate the usefulness of wavelets to reduce noise in a model system where Gaussian noise is inserted to an audio signal. In the following sections, we will present a practical example of noise reduction in a sinusoidal signal that has been generated in the MATLAB, which it is followed by an example with a real audio signal captured via Simulink. Finally, the graphic noise reduction model using GUIDE will be shown.

## Complex Digital Signal Processing in Telecommunications

●2 commentsDigital Signal Processing (DSP) is a vital tool for scientists and engineers, as it is of fundamental importance in many areas of engineering practice and scientific research. The "alphabet" of DSP is mathematics and although most practical DSP problems can be solved by using real number mathematics, there are many others which can only be satisfactorily resolved or adequately described by means of complex numbers. If real number mathematics is the language of real DSP, then complex number mathematics is the language of complex DSP. In the same way that real numbers are a part of complex numbers in mathematics, real DSP can be regarded as a part of complex DSP (Smith, 1999). Complex mathematics manipulates complex numbers - the representation of two variables as a single number - and it may appear that complex DSP has no obvious connection with our everyday experience, especially since many DSP problems are explained mainly by means of real number mathematics. Nonetheless, some DSP techniques are based on complex mathematics, such as Fast Fourier Transform (FFT), z-transform, representation of periodical signals and linear systems, etc. However, the imaginary part of complex transformations is usually ignored or regarded as zero due to the inability to provide a readily comprehensible physical explanation. One well-known practical approach to the representation of an engineering problem by means of complex numbers can be referred to as the assembling approach: the real and imaginary parts of a complex number are real variables and individually can represent two real physical parameters. Complex math techniques are used to process this complex entity once it is assembled. The real and imaginary parts of the resulting complex variable preserve the same real physical parameters. This approach is not universally-applicable and can only be used with problems and applications which conform to the requirements of complex math techniques. Making a complex number entirely mathematically equivalent to a substantial physical problem is the real essence of complex DSP. Like complex Fourier transforms, complex DSP transforms show the fundamental nature of complex DSP and such complex techniques often increase the power of basic DSP methods. The development and application of complex DSP are only just beginning to increase and for this reason some researchers have named it theoretical DSP. It is evident that complex DSP is more complicated than real DSP. Complex DSP transforms are highly theoretical and mathematical; to use them efficiently and professionally requires a large amount of mathematics study and practical experience. Complex math makes the mathematical expressions used in DSP more compact and solves the problems which real math cannot deal with. Complex DSP techniques can complement our understanding of how physical systems perform but to achieve this, we are faced with the necessity of dealing with extensive sophisticated mathematics. For DSP professionals there comes a point at which they have no real choice since the study of complex number mathematics is the foundation of DSP.

## Algorithms for Efficient Computation of Convolution

●4 commentsConvolution is an important mathematical tool in both ﬁelds of signal and image processing. It is employed in ﬁltering, denoising, edge detection, correlation, compression, deconvolution, simulation, and in many other applications. Although the concept of convolution is not new, the efﬁcient computation of convolution is still an open topic. As the amount of processed data is constantly increasing, there is considerable request for fast manipulation with huge data. Moreover, there is demand for fast algorithms which can exploit computational power of modern parallel architectures.

## Digital Signal Processor Fundamentals and System Design

●8 commentsDigital Signal Processors (DSPs) have been used in accelerator systems for more than fifteen years and have largely contributed to the evolution towards digital technology of many accelerator systems, such as machine protection, diagnostics and control of beams, power supply and motors. This paper aims at familiarising the reader with DSP fundamentals, namely DSP characteristics and processing development. Several DSP examples are given, in particular on Texas Instruments DSPs, as they are used in the DSP laboratory companion of the lectures this paper is based upon. The typical system design flow is described; common difficulties, problems and choices faced by DSP developers are outlined; and hints are given on the best solution.

## Novel Method of Showing Frequency Transients in the Fourier Transform and it’s Application in Time-Frequency Analysis

Fourier Transform in the frequency domain is modified to also analyse frequency transients i.e. changes in the frequency spectrum with time variable of any order. This is analytically, a very useful tool as there are many problems where frequency variation with time has to be analyzed e.g. Doppler shift, Light through different mediums in time and space. Numerical calculations are usually done for such problems when needed. Here, Fourier transform is analyzed to incorporate more variables that simultaneously do the Time lag-Frequency Analysis (TLFA) from Fourier Transform by changing the Fourier Operator. Also, the Frequency Derivative Analysis (FDA) of any order can be analyzed from Fourier Transform. Validity of the operator is examined using Eigen value analysis and operator algebra.

## Correcting an Important Goertzel Filter Misconception

Correcting an Important Goertzel Filter Misconception

## Introduction to Signal Processing

This book provides an applications-oriented introduction to digital signal processing written primarily for electrical engineering undergraduates. Practicing engineers and graduate students may also ﬁnd it useful as a ﬁrst text on the subject.

## Region based Active Contour Segmentation

In this paper, we propose a natural framework that allows any region-based segmentation energy to be re-formulated in a local way. We consider local rather than global image statistics and evolve a contour based on local information. Localized contours are capable of segmenting objects with heterogeneous feature profiles that would be difficult to capture correctly using a standard global method. The presented technique is versatile enough to be used with any global region-based active contour energy and instill in it the benefits of localization. We describe this framework and demonstrate the localization of three well-known energies in order to illustrate how our framework can be applied to any energy. We then compare each localized energy to its global counterpart to show the improvements that can be achieved. Next, an in-depth study of the behaviors of these energies in response to the degree of localization is given. Finally, we show results on challenging images to illustrate the robust and accurate segmentations that are possible with this new class of active contour models.

## Evaluation of a Floating Point Acoustic Echo Canceller Implementation

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.

## Using the DFT as a Filter: Correcting a Misconception

●2 commentsI have read, in some of the literature of DSP, that when the discrete Fourier transform (DFT) is used as a filter the process of performing a DFT causes an input signal's spectrum to be frequency translated down to zero Hz (DC). I can understand why someone might say that, but I challenge that statement as being incorrect. Here are my thoughts.

## Computing Translated Frequencies in Digitizing and Downsampling Analog Bandpass Signals

In digital signal processing (DSP) we're all familiar with the processes of bandpass sampling an analog bandpass signal and downsampling a digital bandpass signal. The overall spectral behavior of those operations are well-documented. However, mathematical expressions for computing the translated frequency of individual spectral components, after bandpass sampling or downsampling, are not available in the standard DSP textbooks. This document explains how to compute the frequencies of translated spectral components and provide the desired equations in the hope that they are of use to you.

## Fully Programmable LDPC Decoder Hardware Architectures

●1 commentIn 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.

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

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.

## Blind Adaptive Dereverberation of Speech Signals Using a Microphone Array

In this thesis, we present a blind adaptive speech dereverberation method based on the use of a reduced mutually referenced equalizers (RMRE) criterion. The method is based on the idea of the inversion of single-input multiple-output FIR linear systems, and as such requires the use of multiple microphones. However, unlike many traditional microphone array methods, there is no need for a specific array configuration or geometry. The RMRE method finds a subset of equalizers for a given delay in a single step, without the need for the typical channel estimation step. This makes the method practical in terms of implementation and avoids the pitfalls of the more complicated two step dereverberation approach, typical in many inversion methods. Additionally, only the second-order statistics of the signals recorded by the microphones are used, without the need for utilizing higher-order statistics information typically needed when the channsls have a nonminimum phase response, as is the case with room impulse responses. We present simulations and experimental results that demonstrate the applicability of the method when the input is speech, and show that in the noiseless case, perfect dereverberation can be achieved. We also evaluate its performance in the presence of noise, and we present a possible way to modify the proposed RMRE to work for very low SNR values. We also explore the problems when model-order mismatches are present, and demonstrate that the under-modeling of the channel impulse responses order can be combated by increasing the number of microphones. For order over-estimation, we will show that RMRE can handle such errors with no modification.

## Decimator Image Response

This article presents a way to compute and plot the image response of a decimator. I'm defining the image response as the unwanted spectrum of the impulse response after downsampling, relative to the desired passband response.