Negative Group Delay
Dispersive linear systems with negative group delay have caused much confusion in the past. Some claim that they violate causality, others that they are the cause of superluminal tunneling. Can we really receive messages before they are sent? This article aims at pouring oil in the fire and causing yet more confusion :-).
A Simplified Matlab Function for Power Spectral Density
In an earlier post, I showed how to compute power spectral density (PSD) of a discrete-time signal using the Matlab function pwelch. Pwelch is a useful function because it gives the correct output, and it has the option to average multiple Discrete Fourier Transforms (DFTs). However, a typical function call has five arguments, and it can be hard to remember how to set them all and how they default.
In this post, I create a simplified PSD function by putting a wrapper on pwelch that sets some parameters and converts the output units from W/Hz to dBW/bin. The function is named psd_simple.m, and its code is listed in the appendix.
Adaptive Algorithms in Digital Signal Processing - Overview, Theory and Applications
OPTIMAL DESIGN OF DIGITAL EQUIVALENTS TO ANALOG FILTERS
The proposed optimal algorithm for the digitizing of analog filters is based on two existing filter design methods: the extended window design (EWD) and the matched–pole (MP) frequency sampling design. The latter is closely related to the filter design with iterative weighted least squares (WLS). The optimization is performed with an original MP design that yields an equiripple digitizing error. Then, a drastic reduction of the digitizing error is achieved through the introduction of a fractional time shift that minimizes the magnitude of the equiripple error within a given frequency interval. The optimal parameters thus obtained can be used to generate the EWD equations, together with a variable fractional delay output, as described in an earlier paper. Finally, in contrast to the WLS procedure, which relies on a “good guess” of the weighting function, the MP optimization is straightforward.
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.
Wavelet Denoising for TDR Dynamic Range Improvement
A technique is presented for removing large amounts of noise present in time-domain-reflectometry (TDR) waveforms to increase the dynamic range of TDR waveforms and TDR based s-parameter measurements.
Algorithm Adaptation and Optimization of a Novel DSP Vector Co-processor
The Division of Computer Engineering at Linköping's university is currently researching the possibility to create a highly parallel DSP platform, that can keep up with the computational needs of upcoming standards for various applications, at low cost and low power consumption. The architecture is called ePUMA and it combines a general RISC DSP master processor with eight SIMD co-processors on a single chip. The master processor will act as the main processor for general tasks and execution control, while the co-processors will accelerate computing intensive and parallel DSP kernels.This thesis investigates the performance potential of the co-processors by implementing matrix algebra kernels for QR decomposition, LU decomposition, matrix determinant and matrix inverse, that run on a single co-processor. The kernels will then be evaluated to find possible problems with the co-processors' microarchitecture and suggest solutions to the problems that might exist. The evaluation shows that the performance potential is very good, but a few problems have been identified, that causes significant overhead in the kernels. Pipeline mismatches, that occurs due to different pipeline lengths for different instructions, causes pipeline hazards and the current solution to this, doesn't allow effective use of the pipeline. In some cases, the single port memories will cause bottlenecks, but the thesis suggests that the situation could be greatly improved by using buffered memory write-back. Also, the lack of register forwarding makes kernels with many data dependencies run unnecessarily slow.
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.
A New Contender in the Digital Differentiator Race
This blog proposes a novel differentiator worth your consideration. Although simple, the differentiator provides a fairly wide 'frequency range of linear operation' and can be implemented, if need be, without performing numerical multiplications.
Method to Calculate the Inverse of a Complex Matrix using Real Matrix Inversion
This paper describes a simple method to calculate the invers of a complex matrix. The key element of the method is to use a matrix inversion, which is available and optimised for real numbers. Some actual libraries used for digital signal processing only provide highly optimised methods to calculate the inverse of a real matrix, whereas no solution for complex matrices are available, like in [1]. The presented algorithm is very easy to implement, while still much more efficient than for example the method presented in [2]. [1] Visual DSP++ 4.0 C/C++ Compiler and Library Manual for TigerSHARC Processors; Analog Devices; 2005. [2] W. Press, S.A. Teukolsky, W.T. Vetterling, B.R. Flannery; Numerical Recipes in C++, The art of scientific computing, Second Edition; p52 : “Complex Systems of Equations”;Cambridge University Press 2002.
Wavelet Denoising for TDR Dynamic Range Improvement
A technique is presented for removing large amounts of noise present in time-domain-reflectometry (TDR) waveforms to increase the dynamic range of TDR waveforms and TDR based s-parameter measurements.
Bilinear Transformation Made Easy
A formula is derived and demonstrated that is capable of directly generating digital filter coefficients from an analog filter prototype using the bilinear transformation. This formula obviates the need for any algebraic manipulation of the analog prototype filter and is ideal for use in embedded systems that must take in any general analog filter specification and dynamically generate digital filter coefficients directly usable in difference equations.
FUZZY LOGIC BASED CONVOLUTIONAL DECODER FOR USE IN MOBILE TELEPHONE SYSTEMS
Efficient convolutional coding and decoding algorithms are most crucial to successful operation of wireless communication systems in order to achieve high quality of service by reducing the overall bit error rate performance. A widely applied and well evaluated scheme for error correction purposes is well known as Viterbi algorithm [7]. Although the Viterbi algorithm has very good error correcting characteristics, computational effort required remains high. In this paper a novel approach is discussed introducing a convolutional decoder design based on fuzzy logic. A simplified version of this fuzzy based decoder is examined with respect to bit error rate (BER) performance. It can be shown that the fuzzy based convolutional decoder here proposed considerably reduces computational effort with only minor BER performance degradation when compared to the classical Viterbi approach.
Method to Calculate the Inverse of a Complex Matrix using Real Matrix Inversion
This paper describes a simple method to calculate the invers of a complex matrix. The key element of the method is to use a matrix inversion, which is available and optimised for real numbers. Some actual libraries used for digital signal processing only provide highly optimised methods to calculate the inverse of a real matrix, whereas no solution for complex matrices are available, like in [1]. The presented algorithm is very easy to implement, while still much more efficient than for example the method presented in [2]. [1] Visual DSP++ 4.0 C/C++ Compiler and Library Manual for TigerSHARC Processors; Analog Devices; 2005. [2] W. Press, S.A. Teukolsky, W.T. Vetterling, B.R. Flannery; Numerical Recipes in C++, The art of scientific computing, Second Edition; p52 : “Complex Systems of Equations”;Cambridge University Press 2002.
Real Time Implementation of Multi-Level Perfect Signal Reconstruction Filter Bank
Discrete Wavelet Transform (DWT) is an efficient tool for signal and image processing applications which has been utilized for perfect signal reconstruction. In this paper, twenty seven optimum combinations of three different wavelet filter types, three different filter reconstruction levels and three different kinds of signal for multi-level perfect reconstruction filter bank were implemented in MATLAB/Simulink. All the filters for different wavelet types were designed using Filter Design Analysis (FDA) and Wavelet toolbox. Signal to Noise Ratio (SNR) was calculated for each combination. Combination with best SNR was then implemented on TMS320C6713 DSP kit. Real time testing of perfect reconstruction on DSP kit was then carried out by two different methods. Experimental results accede with theory and simulations.
Algorithm Adaptation and Optimization of a Novel DSP Vector Co-processor
The Division of Computer Engineering at Linköping's university is currently researching the possibility to create a highly parallel DSP platform, that can keep up with the computational needs of upcoming standards for various applications, at low cost and low power consumption. The architecture is called ePUMA and it combines a general RISC DSP master processor with eight SIMD co-processors on a single chip. The master processor will act as the main processor for general tasks and execution control, while the co-processors will accelerate computing intensive and parallel DSP kernels.This thesis investigates the performance potential of the co-processors by implementing matrix algebra kernels for QR decomposition, LU decomposition, matrix determinant and matrix inverse, that run on a single co-processor. The kernels will then be evaluated to find possible problems with the co-processors' microarchitecture and suggest solutions to the problems that might exist. The evaluation shows that the performance potential is very good, but a few problems have been identified, that causes significant overhead in the kernels. Pipeline mismatches, that occurs due to different pipeline lengths for different instructions, causes pipeline hazards and the current solution to this, doesn't allow effective use of the pipeline. In some cases, the single port memories will cause bottlenecks, but the thesis suggests that the situation could be greatly improved by using buffered memory write-back. Also, the lack of register forwarding makes kernels with many data dependencies run unnecessarily slow.
Correlation and Power Spectrum
In the signals and systems course and in the first course in digital signal processing, a signal is, most often, characterized by its amplitude spectrum in the frequency-domain and its amplitude profile in the time-domain. So much a student gets used to this type of characterization, that the student finds it difficult to appreciate, when encountered in the ensuing statistical signal processing course, the fact that a signal can also be characterized by its autocorrelation function in the time-domain and the corresponding power spectrum in the frequency-domain and that the amplitude characterization is not available. In this article, the characterization of a signal by its autocorrelation function in the time-domain and the corresponding power spectrum in the frequency-domain is described. Cross-correlation of two signals is also presented.
Digital Signal Processing Maths
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.
Auditory Component Analysis Using Perceptual Pattern Recognition to Identify and Extract Independent Components From an Auditory Scene
The cocktail party effect, our ability to separate a sound source from a multitude of other sources, has been researched in detail over the past few decades, and many investigators have tried to model this on computers. Two of the major research areas currently being evaluated for the so-called sound source separation problem are Auditory Scene Analysis (Bregman 1990) and a class of statistical analysis techniques known as Independent Component Analysis (Hyvärinen 2001). This paper presents a methodology for combining these two techniques. It suggests a framework that first separates sounds by analyzing the incoming audio for patterns and synthesizing or filtering them accordingly, measures features of the resulting tracks, and finally separates sounds statistically by matching feature sets and making the output streams statistically independent. Artificial and acoustical mixes of sounds are used to evaluate the signal-to-noise ratio where the signal is the desired source and the noise is comprised of all other sources. The proposed system is found to successfully separate audio streams. The amount of separation is inversely proportional to the amount of reverberation present.
Fundamentals of the DFT (fft) Algorithms
In this article, a physical explanation of the fundamentals of the DFT (fft) algorithms is presented in terms of waveform decomposition. After reading the article and trying the examples, the reader is expected to gain a clear understanding of the basics of the mysterious DFT (fft) algorithms.
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.
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.
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.
Bilinear Transformation Made Easy
A formula is derived and demonstrated that is capable of directly generating digital filter coefficients from an analog filter prototype using the bilinear transformation. This formula obviates the need for any algebraic manipulation of the analog prototype filter and is ideal for use in embedded systems that must take in any general analog filter specification and dynamically generate digital filter coefficients directly usable in difference equations.
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.
The DFT of Finite-Length Time-Reversed Sequences
Recently I've been reading papers on underwater acoustic communications systems and this caused me to investigate the frequency-domain effects of time-reversal of time-domain sequences. I created this article because there is so little coverage of this topic in the literature of DSP.
Sum of Two Equal-Frequency Sinusoids
The sum of two equal-frequency real sinusoids is itself a single real sinusoid. However, the exact equations for all the various forms of that single equivalent sinusoid are difficult to find in the signal processing literature. Here we provide those equations.
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.
EFFICIENT MAPPING OF ADVANCED SIGNAL PROCESSING ALGORITHMS ON MULTI-PROCESSOR ARCHITECTURES
Modern microprocessor technology is migrating from simply increasing clock speeds on a single processor to placing multiple processors on a die to increase throughput and power performance in every generation. To utilize the potential of such a system, signal processing algorithms have to be efficiently parallelized so that the load can be distributed evenly among the multiple processing units. In this paper, we study several advanced deterministic and stochastic signal processing algorithms and their computation using multiple processing units. Specifically, we consider two commonly used time-frequency signal representations, the short-time Fourier transform and the Wigner distribution, and we demonstrate their parallelization with low communication overhead. We also consider sequential Monte Carlo estimation techniques such as particle filtering, and we demonstrate that its multiple processor implementation requires large data exchanges and thus a high communication overhead. We propose a modified mapping scheme that reduces this overhead at the expense of a slight loss in accuracy, and we evaluate the performance of the scheme for a state estimation problem with respect to accuracy and scalability.
A Simplified Matlab Function for Power Spectral Density
In an earlier post, I showed how to compute power spectral density (PSD) of a discrete-time signal using the Matlab function pwelch. Pwelch is a useful function because it gives the correct output, and it has the option to average multiple Discrete Fourier Transforms (DFTs). However, a typical function call has five arguments, and it can be hard to remember how to set them all and how they default.
In this post, I create a simplified PSD function by putting a wrapper on pwelch that sets some parameters and converts the output units from W/Hz to dBW/bin. The function is named psd_simple.m, and its code is listed in the appendix.
