Chapter 1 : Rabiner & Schafer, Theory and Applications of Digital Speech Processing Pearson Paused You're listening to a sample of the Audible audio edition. Learn more. See all 2 images. Theory And Application Of Digital Signal Processing Paperback - Overview[ edit ] A sound wave, in red, represented digitally, in blue after sampling and 4-bit quantization. Digital audio technologies are used in the recording, manipulation, mass-production, and distribution of sound, including recordings of songs, instrumental pieces, podcasts, sound effects, and other sounds. Modern online music distribution depends on digital recording and data compression. The availability of music as data files, rather than as physical objects, has significantly reduced the costs of distribution. With digital-audio and online distribution systems such as itunes, companies sell digital sound files to consumers, which the consumer receives over the Internet. An analog audio system converts physical waveforms of sound into electrical representations of those waveforms by use of a transducer, such as a microphone. The sounds are then stored on an analog medium such as magnetic tape, or transmitted through an analog medium such as a telephone line or radio. The process is reversed for reproduction: Analog audio retains its fundamental wave-like characteristics throughout its storage, transformation, duplication, and amplification. Analog audio signals are susceptible to noise and distortion, due to the innate characteristics of electronic circuits and associated devices. Disturbances in a digital system do not result in error unless the disturbance is so large as to result in a symbol being misinterpreted as another symbol or disturb the sequence of symbols. It is therefore generally possible to have an entirely error-free digital audio system in which no noise or distortion is introduced between conversion to digital format, and conversion back to analog. A digital audio signal may optionally be encoded for correction of any errors that might occur in the storage or transmission of the signal. This technique, known as channel coding, is essential for broadcast or recorded digital systems to maintain bit accuracy. Eight-to-fourteen modulation is a channel code used in the audio compact disc CD. Conversion process[ edit ] The lifecycle of sound from its source, through an ADC, digital processing, a DAC, and finally as sound again. A digital audio system starts with an ADC that converts an analog signal to a digital signal. CD audio, for example, has a sampling rate of Analog signals that have not already been bandlimited must be passed through an anti-aliasing filter before conversion, to prevent the aliasing distortion that is caused by audio signals with frequencies higher than the Nyquist frequency half the sampling rate. A digital audio signal may be stored or transmitted. Digital audio can be stored on a CD, a digital audio player, a hard drive, a USB flash drive, or any other digital data storage device. The digital signal may be altered through digital signal processing, where it may be filtered or have effects applied. Sample-rate conversion including upsampling and downsampling may be used to conform signals that have been encoded with a different sampling rate to a common sampling rate prior to processing. Digital audio can be carried over a network using audio over Ethernet, audio over IP or other streaming media standards and systems. For playback, digital audio must be converted back to an analog signal with a DAC which may use oversampling. History in recording[ edit ] See also: Digital recording Pulse-code modulation was invented by British scientist Alec Reeves in [2] and was used in telecommunications applications long before its first use in commercial broadcast and recording. The first commercial digital recordings were released in By the early s, it had developed a 2-channel recorder, and in it deployed a digital audio transmission system that linked their broadcast center to their remote transmitters. An improved version of the Soundstream system was used to produce several classical recordings by Telarc in The 3M digital multitrack recorder in development at the time was based on BBC technology. British record label Decca began development of its own 2-track digital audio recorders in and released the first European digital recording in The introduction of the CD popularized digital audio with consumers. Page 1
Chapter 2 : Signal Processing - Journal - Elsevier Theory and Application of Digital Signal Processing [Lawrence R. Rabiner, Bernard Gold] on blog.quintoapp.com *FREE* shipping on qualifying offers. This book is one of the two first classic books in DSP from the mid s. What is Digital Signal Processing? A DSP contains four key components: This can be used for various things, depending on the field DSP is being used for, i. Below is a figure of what the four components of a DSP look like in a general system configuration. The design of the Chebyshev filter was engineered around the matematical technique, known as z-transform. Basically, the z-transform converts a discrete-time signal, made up of a sequence of real or complex numbers into a frequency domain representation. These filters are called type 1 filters, meaning that the ripple in the frequency response is only allowed in the passband. This provides the best approximation to the ideal response of any filter for a specified order and ripple. It was designed to remove certain frequencies and allow others to pass through the filter. The Chebyshev filter is generally linear in its response and a nonlinear filter could result in the output signal containing frequency components that were not present in the input signal. Why Use Digital Signal Processing? To understand how digital signal processing, or DSP, compares with analog circuitry, one would compare the two systems with any filter function. The filter function on a DSP system is software-based, so multiple filters can be chosen from. Also, to create flexible and adjustable filters with high-order responses only requires the DSP software, whereas analog requires additional hardware. If analog methods were being used, second-order filters would require a lot of staggered high-q sections, which ultimately means that it will be extremely hard to tune and adjust. With no feedback, its only response to a given sample ends when the sample reaches the "end of the line". With these design differences in mind, DSP software is chosen for its flexibility and simplicity over analog circuitry filter designs. When creating this bandpass filter, using DSP is not a terrible task to complete. Implementing it and manufacturing the filters is much easier, as you only have to program the filters the same with every DSP chip going into the device. However, using analog components, you have the risk of faulty components, adjusting the circuit and program the filter on each individual analog circuit. DSP creates an affordable and less tedious way of filter design for signal processing and increases accuracy for tuning and adjusting filters in general. Take a microphone for example: On the other hand, DAC will convert the already processed digital signal back into the analog signal that is used by audio output equipment such as monitors. Below is a figure showing how the previous example works and how its audio input signals can be enhanced through reproduction, and then outputted as digital signals through monitors. A type of analog to digital converter, known as the digital ramp ADC, involves a comparator. While the output of the DAC is implemented to the other terminal of the comparator, it will trigger a signal if the voltage exceeds the analog voltage input. The transition of the comparator stops the binary counter, which then holds the digital value corresponding to the analog voltage at that point. Applications of DSP There are numerous variants of a digital signal processor that can execute different things, depending on the application being performed. Some of these variants are audio signal processing, audio and video compression, speech processing and recognition, digital image processing, and radar applications. The difference between each of these applications is how the digital signal processor can filter each input. There are five different aspects that varies from each DSP: All of these components really are just going to affect the arithmetic format, speed, memory organization, and data width of a processor. One well-known architecture layout is the Harvard architecture. This design allows for a processor to simultaneously access two memory banks using two independent sets of buses. This architecture can execute mathematical operations while fetching further instructions. Another is the Von Neumann memory architecture. While there is only one data bus, operations cannot be loaded while instructions are fetched. This causes a jam that ultimately slows down the execution of DSP applications. While these processors are similar to a processor used in a standard computer, these digital signal processors are specialized. That often means that, to perform a task, the DSPs are required to used fixed-point arithmetic. Page 2
Another is sampling, which is the reduction of a continuous signal to a discrete signal. One major application is the conversion of a sound wave. Audio sampling uses digital signals and pulse-code modulation for the reproduction of sound. It is necessary to capture audio between 20-20, Hz for humans to hear. Sample rates higher than that of around 50 khz - 60 khz cannot provide any more information to the human ear. I hope that this article has provided enough information to get a general understanding of what DSPs are, how they work, and what they are specifically used for in a plethora of fields. If you have any questions or thoughts, please leave a comment below! Page 3
Chapter 3 : Digital Signal Processing - Journal - Elsevier An important application of digital signal processing methods is in determining in the discrete-time do- main the frequency contents of a continuous-time signal, more commonly known as spectral analysis. Sampling signal processing To digitally analyze and manipulate an analog signal, it must be digitized with an analog-to-digital converter ADC. Sampling is usually carried out in two stages, discretization and quantization. Discretization means that the signal is divided into equal intervals of time, and each interval is represented by a single measurement of amplitude. Quantization means each amplitude measurement is approximated by a value from a finite set. Rounding real numbers to integers is an example. The Nyquistâ Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency component in the signal. In practice, the sampling frequency is often significantly higher than twice the Nyquist frequency. Theoretical DSP analyses and derivations are typically performed on discrete-time signal models with no amplitude inaccuracies quantization error, "created" by the abstract process of sampling. Numerical methods require a quantized signal, such as those produced by an ADC. The processed result might be a frequency spectrum or a set of statistics. But often it is another quantized signal that is converted back to analog form by a digital-to-analog converter DAC. Domains[ edit ] In DSP, engineers usually study digital signals in one of the following domains: They choose the domain in which to process a signal by making an informed assumption or by trying different possibilities as to which domain best represents the essential characteristics of the signal and the processing to be applied to it. A sequence of samples from a measuring device produces a temporal or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain representation. Time and space domains[ edit ] Main article: Time domain The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Digital filtering generally consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal. There are various ways to characterize filters; for example: A linear filter is a linear transformation of input samples; other filters are nonlinear. Linear filters satisfy the superposition principle, i. A causal filter uses only previous samples of the input or output signals; while a non-causal filter uses future input samples. A non-causal filter can usually be changed into a causal filter by adding a delay to it. A time-invariant filter has constant properties over time; other filters such as adaptive filters change in time. A stable filter produces an output that converges to a constant value with time, or remains bounded within a finite interval. An unstable filter can produce an output that grows without bounds, with bounded or even zero input. A finite impulse response FIR filter uses only the input signals, while an infinite impulse response IIR filter uses both the input signal and previous samples of the output signal. A filter can be represented by a block diagram, which can then be used to derive a sample processing algorithm to implement the filter with hardware instructions. A filter may also be described as a difference equation, a collection of zeros and poles or an impulse response or step response. The output of a linear digital filter to any given input may be calculated by convolving the input signal with the impulse response. Frequency domain Signals are converted from time or space domain to the frequency domain usually through use of the Fourier transform. The Fourier transform converts the time or space information to a magnitude and phase component of each frequency. With some applications, how the phase varies with frequency can be a significant consideration. Where phase is unimportant, often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared. The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to determine which frequencies are present in the input signal and which are missing. Frequency domain analysis is also called spectrum- or spectral analysis. Filtering, particularly in non-realtime work can also be achieved in the frequency domain, applying the filter and then converting back to the time domain. Page 4
This can be an efficient implementation and can give essentially any filter response including excellent approximations to brickwall filters. There are some commonly-used frequency domain transformations. For example, the cepstrum converts a signal to the frequency domain through Fourier transform, takes the logarithm, then applies another Fourier transform. This emphasizes the harmonic structure of the original spectrum. FIR filters have many advantages, but are computationally more demanding. The Z-transform provides a tool for analyzing stability issues of digital IIR filters. It is analogous to the Laplace transform, which is used to design and analyze analog IIR filters. The original image is high-pass filtered, yielding the three large images, each describing local changes in brightness details in the original image. It is then low-pass filtered and downscaled, yielding an approximation image; this image is high-pass filtered to produce the three smaller detail images, and low-pass filtered to produce the final approximation image in the upper-left. In numerical analysis and functional analysis, a discrete wavelet transform DWT is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: The accuracy of the joint time-frequency resolution is limited by the uncertainty principle of time-frequency. Page 5
Chapter 4 : Signal processing - Wikipedia Well Ideally the application is defined for the signal you are trying to process. It can be anything from audio, video, sensor output, data from the web, in short and simple words any sort of information. So processing it means making the information understandable i.e. like how discrete fourier. The following document describes the basic concepts of Digital Signal Processing DSP and also contains a variety of Recommended Reading links for more in-depth information. What is a DSP? Digital Signal Processors DSP take real-world signals like voice, audio, video, temperature, pressure, or position that have been digitized and then mathematically manipulate them. A DSP is designed for performing mathematical functions like "add", "subtract", "multiply" and "divide" very quickly. Signals need to be processed so that the information that they contain can be displayed, analyzed, or converted to another type of signal that may be of use. In the real-world, analog products detect signals such as sound, light, temperature or pressure and manipulate them. From here, the DSP takes over by capturing the digitized information and processing it. It then feeds the digitized information back for use in the real world. It does this in one of two ways, either digitally or in an analog format by going through a Digital-to-Analog converter. All of this occurs at very high speeds. During the recording phase, analog audio is input through a receiver or other source. This analog signal is then converted to a digital signal by an analog-to-digital converter and passed to the DSP. During the playback phase, the file is taken from memory, decoded by the DSP and then converted back to an analog signal through the digital-to-analog converter so it can be output through the speaker system. In a more complex example, the DSP would perform other functions such as volume control, equalization and user interface. Signals may be compressed so that they can be transmitted quickly and more efficiently from one place to another e. Signals may also be enhanced or manipulated to improve their quality or provide information that is not sensed by humans e. Although real-world signals can be processed in their analog form, processing signals digitally provides the advantages of high speed and accuracy. You can create your own software or use software provided by ADI and its third parties to design a DSP solution for an application. For more detailed information about the advantages of using DSP to process real-world signals, please read Part 1 of the article from Analog Dialogue titled: A DSP contains these key components: Stores the information to be processed Compute Engine: Serves a range of functions to connect to the outside world Recommended Reading Digital Signal Processing is a complex subject that can overwhelm even the most experienced DSP professionals. Although we have provided a general overview, Analog Devices offers the following resources that contain more extensive information about Digital Signal Processing: Page 6
Chapter 5 : Digital audio - Wikipedia Applications of DSP include audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, digital synthesizers, radar, sonar, financial signal processing, seismology and biomedicine. Blogging never been so electrical! Convolution is similar to cross-correlation. It has applications that include statistics, computer vision, image and signal processing, electrical engineering, and differential equations. The convolution can be defined for functions on groups other than Euclidean space. In particular, the circular convolution can be defined for periodic functions that is, functions on the circle, and the discrete convolution can be defined for functions on the set of integers. These generalizations of the convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing. Computing the inverse of the convolution operation is known as deconvolution. Convolution is a mathematical way of combining two signals to form a third signal. It is the single most important technique in Digital Signal Processing. Using the strategy of impulse decomposition, systems are described by a signal called the impulse response. Convolution is important because it relates the three signals of interest: This chapter presents convolution from two different viewpoints, called the input side algorithm and the output side algorithm. One of the most important concepts in Fourier theory, and in crystallography, is that of a convolution. Convolutions arise in many guises, as will be shown below. Because of a mathematical property of the Fourier transform, referred to as the convolution theorem, it is convenient to carry out calculations involving convolutions. But first we should define what a convolution is. Understanding the concept of a convolution operation is more important than understanding a proof of the convolution theorem, but it may be more difficult! Mathematically, a convolution is defined as the integral over all space of one function at x times another function at u-x. The integration is taken over the variable x which may be a 1D or 3D variable, typically from minus infinity to infinity over all the dimensions. So the convolution is a function of a new variable u, as shown in the following equations. The cross in a circle is used to indicate the convolution operation. This illustration shows how you can think about the convolution, as giving a weighted sum of shifted copies of one function: The top pair of graphs shows the original functions. The next three pairs of graphs show on the left the function g shifted by various values of x and, on the right, that shifted function g multiplied by f at the value of x. The bottom pair of graphs shows, on the left, the superposition of several weighted and shifted copies of g and, on the right, the integral i. You can see that the biggest contribution comes from the copy shifted by 3, i. If one of the functions is unimodal has one peak, as in this illustration, the other function will be shifted by a vector equivalent to the position of the peak, and smeared out by an amount that depends on how sharp the peak is. But alternatively we could switch the roles of the two functions, and we would see that the bimodal function g has doubled the peaks of the unimodal function f. The convolution theorem Because there will be so many Fourier transforms in the rest of this presentation, it is useful to introduce a shorthand notation. T will be used to indicate a forward Fourier transform, and its inverse to indicate the inverse Fourier transform. There are two ways of expressing the convolution theorem: The Fourier transform of a convolution is the product of the Fourier transforms. The Fourier tranform of a product is the convolution of the Fourier transforms. The convolution theorem is useful, in part, because it gives us a way to simplify many calculations. Convolutions can be very difficult to calculate directly, but are often much easier to calculate using Fourier transforms and multiplication. Any signal may be understood as consisting of a sequence of impulses. This is obvious in the case of sampled signals, but can be generalized to continuous signals by representing the signal as a continuous sequence of Dirac impulses. We may construct the response of a linear system to an arbitrary input signal as a sum over suitably delayed and scaled impulse responses. This process is called a convolution: Here f t is the input signal and g t the output signal; h t characterizes the system. We assume that the signals are causal i. The response of a linear system to an arbitrary input signal Page 7
can thus be computed either by convolution with the impulse response in time domain, or by multiplication with the transfer function in the Laplace domain, or by multiplication with the complex frequency response in frequency domain. A reason for choosing the FFT method is that responses are often specified in the frequency domain this is, as a function of frequency, so one would anyhow need a Fourier transformation to determine the impulse response. Moreover, the impulse response has an infinite duration, so it can never be used in full length. The FFT method, on the other hand, assumes all signals to be periodic, which introduces certain inaccuracies as well; the signals must in general be tapered to avoid spurious results. The interrelations between signal processing in the time and frequency domains. In digital processing, these methods translate into convolving discrete time series or transforming them with the FFT method and multiplying the transforms. For impulse responses with more than samples, the FFT method is usually more efficient. The convolution method is also known as a FIR finite impulse response filtration. A third method, the recursive or IIR infinite impulse response filtration, is only applicable to digital signals; it is often preferred for its flexibility and efficiency although its accuracy requires special attention. Digital signal processing and analog signal processing are subfields of signal processing. DSP includes subfields like: The world of science and engineering is filled with signals: Digital Signal Processing is the science of using computers to understand these types of data. This includes a wide variety of goals: DSP is one of the most powerful technologies that will shape science and engineering in the twenty-first century. Since the goal of DSP is usually to measure or filter continuous real-world analog signals, the first step is usually to convert the signal from an analog to a digital form, by using an analog to digital converter. Often, the required output signal is another analog output signal, which requires a digital to analog converter. Even if this process is more complex than analog processing and has a discrete value range, the stability of digital signal processing thanks to error detection and correction and being less vulnerable to noise makes it advantageous over analog signal processing for many, though not all, applications. DSP algorithms have long been run on standard computers, on specialized processors called digital signal processors DSPs, or on purpose-built hardware such as application-specific integrated circuit ASICs. Today there are additional technologies used for digital signal processing including more powerful general purpose microprocessors, field-programmable gate arrays FPGAs, digital signal controllers mostly for industrial apps such as motor control, and stream processors, among others. Specific examples are speech compression and transmission in digital mobile phones, room matching equalization of sound in Hifi and sound reinforcement applications, weather forecasting, economic forecasting, seismic data processing, analysis and control of industrial processes, computer-generated animations in movies, medical imaging such as CAT scans and MRI, MP3 compression, image manipulation, high fidelity loudspeaker crossovers and equalization, and audio effects for use with electric guitar amplifiers. Applications of the convolution theorem Atomic scattering factors We have essentially seen this before. We can tabulate atomic scattering factors by working out the diffraction pattern of different atoms placed at the origin. Then we can apply a phase shift to place the density at the position of the atom. Our new interpretation of this is that we are convoluting the atomic density distribution with a delta function at the position of the atom. B-factors We can think of thermal motion as smearing out the position of an atom, i. The B-factors or atomic displacement parameters, to be precise correspond to a Gaussian smearing function. At resolutions typical of protein data, we are justified only in using a single parameter for thermal motion, which means that we assume the motion is isotropic, or equivalent in all directions. Above, we worked out the Fourier transform of a 1D Gaussian. In fact, all that matters is the displacement of the atom in the direction parallel to the diffraction vector, so this equation is suitable for a 3D Gaussian. All we have to remember is that the term corresponding to the standard deviation refers only to the direction parallel to the diffraction vector. Since we are dealing with the isotropic case, the standard deviation or atomic displacement is equal in all directions. We replace the variance standard deviation squared by the mean-square displacement of the atom in any particular direction. The B-factor can be defined in terms of the resulting equation. Note that there is a common source of misunderstanding here. The mean-square atomic displacement refers to displacement in any particular direction. This will be equal Page 8
along orthogonal x, y and z axes. But often we think of the mean-square displacement as a radial measure, i. The mean-square radial displacement will be the sum of the mean-square displacements along x, y and z; if these are equal it will be three times the mean-square displacement in any single direction. So the B-factor has a slightly different interpretation in terms of radial displacements. Diffraction from a lattice The convolution theorem can be used to explain why diffraction from a lattice gives another lattice â in particular why diffraction from a lattice of unit cells in real space gives a lattice of structure factors in reciprocal space. The Fourier transform of a set of parallel lines is a set of points, perpendicular to the lines and separated by a distance inversely proportional to the space between the lines. This is related to the idea that diffraction from a set of Bragg planes can be described in terms of a diffraction vector in reciprocal space, perpendicular to the set of planes. In the figure below, one set of closely-spaced horizontal lines gives rise to a widely-spaced vertical row of points. A second set of more widely-space diagonal lines gives rise to a more closely-spaced row of points perpendicular to these lines. If we multiply one set of lines by another, this will give an array of points at the intersections of the lines in the bottom part of the figure. The Fourier transform of this lattice of points, which was obtained by multiplying two sets of lines, is the convolution of the two individual transforms i. Of course, the same argument can be applied to a 3D lattice. Diffraction from a crystal A crystal consists of a 3D array of repeating unit cells. Mathematically, this can be generated by taking the content of one unit cell and convoluting it by a 3D lattice of delta functions. The diffraction pattern is thus the product of the Fourier transform of the content of one unit cell and the Fourier transform of the 3D lattice. Since the transform of a lattice in real space is a reciprocal lattice, the diffraction pattern of the crystal samples the diffraction pattern of a single unit cell at the points of the reciprocal lattice. Resolution truncation Truncating the resolution of the data used in calculating a density map is equivalent to taking the entire diffraction pattern and multiplying the structure factors by a function which is one inside the limiting sphere of resolution and zero outside the limiting sphere. The effect on the density is equivalent to taking the density that would be obtained with all the data and convoluting it by the Fourier transform of a sphere. Now, the Fourier transform of a sphere has a width inversely proportional to the radius of the sphere so, the smaller the sphere i. In addition, the Fourier transform of a sphere has ripples where it goes negative and then positive again, so a map computed with truncated data will also have Fourier ripples. These will be particularly strong around regions of high density, such as heavy atoms. Missing data Similarly, leaving out any part of the data set e. Chapter 6 : A Beginner's Guide to Digital Signal Processing (DSP) Design Center Analog Devices Building from basic concepts to application of the material. Following the discussion of the basic signal processing methods, the book shows how speech algorithms can be built on top of various speech representations, and ultimately how applications to speech and audio coding, synthesis, and recognition can be realized based entirely on ideas discussed in earlier chapters of the book. Chapter 7 : Free DSP Books on the Internet - Rick Lyons Digital Signal Processing: A Review Journal is one of the oldest and most established journals in the field of signal processing yet it aims to be the most innovative. The Journal invites top quality research articles at the frontiers of research in all aspects of signal processing. Chapter 8 : Digital signal processing - Wikipedia Practical Applications in Digital Signal Processing begins with a review of basic DSP concepts such as frequency and sampling of sinusoidal waveforms. Clear diagrams accompany equations and the narrative, as the author describes the quantification and digitization of a waveform from both a theoretical and practical perspective. Page 9
Chapter 9 : An Introduction to Digital Signal Processing In this course you will learn about audio signal processing methodologies that are specific for music and of use in real applications. We focus on the spectral processing techniques of relevance for the description and transformation of sounds, developing the basic theoretical and practical. Page 10