Algorithms for Efficient Computation of Convolution
Convolution is an important mathematical tool in both ï¬elds of signal and image processing. It is employed in ï¬ltering, denoising, edge detection, correlation, compression, deconvolution, simulation, and in many other applications. Although the concept of convolution is not new, the efï¬cient 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.
Music Signal Processing
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
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
Adaptive distributed noise reduction for speech enhancement in wireless acoustic sensor networks
An adaptive distributed noise reduction algorithm for speech enhancement is considered, which operates in a wireless acoustic sensor network where each node collects multiple microphone signals. In previous work, it was shown theoretically that for a stationary scenario, the algorithm provides the same signal estimators as the centralized multi-channel Wiener filter, while significantly compressing the data that is transmitted between the nodes. Here, we present simulation results of a fully adaptive implementation of the algorithm, in a non-stationary acoustic scenario with a moving speaker and two babble noise sources. The algorithm is implemented using a weighted overlap-add technique to reduce the overall input-output delay. It is demonstrated that good results can be obtained by estimating the required signal statistics with a long-term forgetting factor without downdating, even though the signal statistics change along with the iterative filter updates. It is also demonstrated that simultaneous node updating provides a significantly smoother and faster tracking performance compared to sequential node updating.
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.
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.
Introduction of C Programming for DSP Applications
Appendix C of the book : Real-Time Digital Signal Processing: Implementations, Application and Experiments with the TMS320C55X
Reduced-Delay IIR Filters
This document describes a straightforward method to significantly reduce the number of necessary multiplies per input sample of traditional IIR lowpass and highpass digital filters.
A pole-zero placement technique for designing second-order IIR parametric equalizer filters
A new procedure is presented for designing second-order parametric equalizer filters. In contrast to the traditional approach, in which the design is based on a bilinear transform of an analog filter, the presented procedure allows for designing the filter directly in the digital domain. A rather intuitive technique known as pole-zero placement, is treated here in a quantitative way. It is shown that by making some meaningful approximations, a set of relatively simple design equations can be obtained. Design examples of both notch and resonance filters are included to illustrate the performance of the proposed method, and to compare with state-of-the-art solutions.
Digital PLL's -- Part 1
We will use Matlab to model the DPLL in the time and frequency domains (Simulink is also a good tool for modeling a DPLL in the time domain). Part 1 discusses the time domain model; the frequency domain model will be covered in Part 2. The frequency domain model will allow us to calculate the loop filter parameters to give the desired bandwidth and damping, but it is a linear model and cannot predict acquisition behavior. The time domain model can be made almost identical to the gate-level system, and as such, is able to model acquisition.
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 deï¬nition 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 identiï¬cation.
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.
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.
Implementing IS-95, the CDMA Standard, on TMS320C6201 DSP
IS-95 is the present U.S. 2nd generation CDMA standard. Currently, the 2nd generation CDMA phones are produced by Qualcomm. Texas Instruments (TI) has ASIC design for Viterbi Decoder on C54x. Several of the components in the forward link process are also implemented in hardware. However, having to design a specific hardware for a particular application is expensive and time consuming. Thus, the possibility of the alternative implementations is of great interest to both customers and TI itself. This research has achieved in successful implementation of IS-95 entirely in software on TI fixed-point DSP TMS320C6201, and met the real time constraint. IS-95 system, the industrial standard for CDMA, is a very complicated system and extremely computationally demanding. The transmission rate for an IS-95 system is 1.2288 Mcps. This research project includes all the major components of the demodulation process for the forward link system: PN Descrambling, Walsh Despreading, Phase Correction & Maximal Ratio Combining, Deinterleaver, Digital Automatic Gain Control, and Viterbi Deccc:r. The entire demodulation process is done completely in C. That makes it a very attractive alternative implementation in the future applications. It is well known that ASIC design is not only expensive and but also time consuming, programming in assembly is easier and cheaper, but programming in C is a much easier and efficient way out, in particular, for general computer engineers. During the whole process, efforts have been devoted on developing various specific techniques to optimize the design for all the components involved. These developments are successfully achieved by making the best use of the following techniques: to simplify the algorithms first before programming, to look for regularity in the problem, to work toward the Compiler's full efficiency, and to use C intrinsics whenever possible. All these attributes together make the implementation scheme great for DSP applications. The benchmark results compare very well to the TI-internal hand scheduled assembly performance of the same type of decoders. The estimated percentage usage of all the components (excluding PN) is only 21.18% of the total CPU cycles available (4,000 K), which is very efficient and impressive.
Hilbert Transform and Applications
Section 1: reviews the mathematical deï¬nition 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 identiï¬cation.
Section 4: concludes with remarks on the historical development of Hilbert transform
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 ï¬lter 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 efï¬cient time-varying ï¬lters. 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 ï¬lter and is computationally very efï¬cient 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 ï¬lter structures and the effects of limited computational capability and low bitdepth. This is followed by designs for several example instruments.
Development of a real time test platform for motor drive algorithms
In this thesis a real time test platform for a permanent magnet synchronous motor is developed. The implemented algorithm is Field Oriented Control (FOC) and it is implemented on a Texas Instruments TMS320F2808 Digital Signal Processor (DSP). The platform is developed in a rapid prototyping approach using Matlab/Simulink and the Real Time Workshop (RTW) packages.With this software the control algorithm and its interface to different DSP modules, such as A/D converter and PWM module, is constructed as a Simulink block scheme. The blocks used come from ordinary Simulink libraries and libraries provided by the RTW packages. From the Simulink block scheme Matlab can auto generate embedded C code adapted for different embedded targets, in this case the 2808 DSP.The developed real time test platform is also a Simulink model, though different from the algorithm model. When the start simulation command is given in the platform model a Graphical User Interface is loaded which lets the user specify motor parameters and certain algorithm parameters. Once the parameters are chosen RTW generates code from the algorithm model, loads it into the DSP and runs the generated program. From the platform model it is possible to set the reference speed of the motor in real time and monitor/log motor parameters such as actual speed and stator currents.
Digital Signal Processing Maths
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.
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.
Filter a Rectangular Pulse with no Ringing
To filter a rectangular pulse without any ringing, there is only one requirement on the filter coefficients: they must all be positive. However, if we want the leading and trailing edge of the pulse to be symmetrical, then the coefficients must be symmetrical. What we are describing is basically a window function.
Complex Down-Conversion Amplitude Loss
This article illustrates the signal amplitude loss inherent in a traditional complex down-conversion system. (In the literature of signal processing, complex down-conversion is also called "quadrature demodulation.")
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.
