## How Discrete Signal Interpolation Improves D/A Conversion

Earlier this year, for the Linear Audio magazine, published in the Netherlands whose subscribers are technically-skilled hi-fi audio enthusiasts, I wrote an article on the fundamentals of interpolation as it's used to improve the performance of analog-to-digital conversion. Perhaps that article will be of some value to the subscribers of dsprelated.com. Here's what I wrote: We encounter the process of digital-to-analog conversion every day—in telephone calls (land lines and cell phones), telephone answering machines, CD & DVD players, iPhones, digital television, MP3 players, digital radio, and even talking greeting cards. This material is a brief tutorial on how sample rate conversion improves the quality of digital-to-analog conversion.

## Understanding the 'Phasing Method' of Single Sideband Demodulation

There are four ways to demodulate a transmitted single sideband (SSB) signal. Those four methods are: synchronous detection, phasing method, Weaver method, and filtering method. Here we review synchronous detection in preparation for explaining, in detail, how the phasing method works. This blog contains lots of preliminary information, so if you're already familiar with SSB signals you might want to scroll down to the 'SSB DEMODULATION BY SYNCHRONOUS DETECTION' section.

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

I 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.

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

Quadrature 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

Section 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

Digital 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.

## Implementing Simultaneous Digital Differentiation, Hilbert Transformation, and Half-Band Filtering

Recently I've been thinking about digital differentiator and Hilbert transformer implementations and I've developed a processing scheme that may be of interest to the readers here on dsprelated.com.

## Correcting an Important Goertzel Filter Misconception

Correcting an Important Goertzel Filter Misconception

## Introduction to Compressed Sensing

Chapter 1 of the book: "Compressed Sensing: Theory and Applications".

## 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.

## STUDY OF DIGITAL MODULATION TECHNIQUES

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

## Optimization of Audio Processing algorithms (Reverb) on ARMv6 family of processors

Audio processing algorithms are increasingly used in cell phones and today’s customers are placing more demands on cell phones. Feature phones, once the advent of mobile phone technology, nowadays do more than just providing the user with MP3 play back or advanced audio effects. These features have become an integral part of medium as well as low-end phones. On the other hand, there is also an endeavor to include as improved quality as possible into products to compete in market and satisfy users’ needs. Tackling the above requirements has been partly satisfied by the advance in hardware design and manufacturing technology. However, as new hardware emerges into market the need for competence to write efficient software and exploit the new features thoroughly and effectively arises. Even though compilers are also keeping up with the new tide space for hand optimized code still exist. Wrapped in the above goal, an effort was made in this thesis to partly cover the competence requirement at Multimedia Section (part of Ericsson Mobile Platforms) to develope optimized code for new processors. Forging persistently ahead with new products, EMP has always incorporated the latest technology into its products among which ARMv6 family of processors has the main central processing role in a number of upcoming products. To fully exploit latest features provided by ARMv6, it was required to probe its new instruction set among which new media processing instructions are of outmost importance. In order to execute DSP-intensive algorithms (e.g. Audio Processing algorithms) efficiently, the implementation should be done in low-level code applying available instruction set. Meanwhile, ARMv6 comes with a number of new features in comparison with its predecessors. SIMD (Single Instruction Multiple Data) and VFP (Vector Floating Point) are the most prominent media processing improvements in ARMv6. Aligned with thesis goals and guidelines, Reverb algorithm which is among one of the most complicated audio features on a hand-held devices was probed. Consequently, its kernel parts were identified and implementation was done both in fixed-point and floating-point using the available resources on hardware. Besides execution time and amount of code memory for each part were measured and provided in tables and charts for comparison purposes. Conclusions were finally drawn based on developed code’s efficiency over ARM compiler’s as well as existing code already developed and tailored to ARMv5 processors. The main criteria for optimization was the execution time. Moreover, quantization effect due to limited precision fixed-point arithmetic was formulated and its effect on quality was elaborated. The outcomes, clearly indicate that hand optimization of kernel parts are superior to Compiler optimized alternative both from the point of code memory as well as execution time. The results also confirmed the presumption that hand optimized code using new instruction set can improve efficiency by an average 25%-50% depending on the algorithm structure and its interaction with other parts of audio effect. Despite its many draw backs, fixed-point implementation remains yet to be the dominant implementation for majority of DSP algorithms on low-power devices.

## DSP Memory Management in a Third Generation High Performance Base Station

Most of the tasks in a mobile cellular network base station are performed with programmable digital signal processors. Their memory spaces and management features are very limited. The buffering requirements in the base station can have large instantaneous variations during the simultaneous transmission of burst' data on multiple channels to multiple users. In particular the high bit-rates of the Wideband Code Division Multiple Access data transfer evolution High Speed Downlink Packet Access create very high demands for buffering. The fragmentation of the buffer memory is a threat. It causes a gradual decrease in performance, which is critical in a long running process like the base station. The amount of fragmentation is different with different memory management methods. In this work the features and applicability of different memory management methods for signal processors used in the base stations of third generation cellular networks have been studied. Software based memory management includes a high amount of conditional branches. The signal processor, which is optimized for highly parallel sequential computing, executes conditional branches very badly when compared to microcontrollers and general-purpose processors. The memory management methods are first studied in theory and then experimentally. In the experiments two different memory management methods were analyzed. The memory managers were loaded with a synthetic workload program that simulates multi-user high bit-rate data transmissions in the base station. The performances of the memory managers were measured in terms of fragmentation, execution time and memory utilization. The experiments confirmed the information gained from the theoretical studies that different memory management methods are usually optimized for a certain feature. The experiments showed that a simple method is fast to execute and works well with small and intermediate loads. When the load is increased the performance decreases. The second, more complex, measured method was found to require more computing, but to be capable of using the memory space assigned to it more effectively.

## 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.

## 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.

## HIERARCHICAL MOTION ESTIMATION FOR EMBEDDED OBJECT TRACKING

This paper presents an algorithm developed to provide automatic motion detection and object tracking embedded within intelligent CCTV systems. The algorithm development focuses on techniques which provide an efficient embedded systems implementation with the ability to target both FPGA and DSP devices. During algorithm development constraints on hardware implementation have been fully considered resulting in an algorithm which, when targeted at current FPGA devices, will take full advantage of the DSP resource commonly provided in such devices. The hierarchical structure of the proposed algorithm provides the system with a multi-level motion estimation process allowing low resolution estimation for motion detection and further higher resolution stages for motion estimation. An initial MATLAB prototype has demonstrated this algorithm capable of object motion estimation while compensating for camera motion, allowing a moving object to be tracked by a moving camera.