Contains research objectives and summary of research.National Science Foundation (Grant GK-31353)U. S. Navy Office of Naval Research (Contract N00014-67-A-0204-0064

Allen, Jonathan

Crochiere, Ronald E.

Dudgeon, Dan E.

Mersereau, R. M.

Oppenheim, Alan V.

Portnoff, Michael R.

Tribolet, J. M.

Zue, Victor W.

DSpace@MIT

XV. DIGITAL SIGNAL PROCESSINGAcademic and Research StaffProf. A. V. Oppenheim Dr. R. M. MersereauProf. J. Allen T. AoyamaGraduate StudentsR. E. Crochiere H. Hersey E. VincentD. E. Dudgeon M. R. Portnoff V. W. ZueJ. M. TriboletRESEARCH OBJECTIVES AND SUMMARY OF RESEARCHThe general research aims of this group are directed toward the development andapplication of techniques for digital signal processing and digital filtering. There hasbeen a clear trend over the past several years toward increased use of digital ratherthan analog processing of signals, largely because of the inherent flexibility and reli-ability of digital processing. With the continuing development of integrated circuit tech-nology, faster digital hardware with reduced cost and size is constantly becomingavailable. Digital signal-processing techniques have found application in a wide varietyof areas including speech and picture processing, radar and sonar signal processing,and seismic data analysis. A summary of some of our present research projects andplans follows.1. Digital Network Theory and Filter StructuresNational Science Foundation (Grant GK-31353)R. E. Crochiere, A. V. OppenheimWhen implementing digital filters on large general-purpose computers, with floating-point arithmetic or long fixed registers, it is generally not necessary to pay closeattention to the filter structure that is used. In contrast, when a digital filter is imple-mented in special-purpose hardware, speed and filter behavior are closely related tothe type of structure used to implement the filter. In the past several years, a con-siderable amount of work has been done by our group and others with regard todeveloping and analyzing different filter structures. These include, for example, theanalysis of digital wave structures and the development of a filter analysis program thatpermits the analysis of arbitrary structures. Using this program, we have analyzedand compared several structures. In addition, we have developed a theoretical basis forthe design of digital filters to optimize the word length.Many techniques utilized in analyzing and comparing digital filter structures arebased on a somewhat more general theory relating to the properties of digital networksor signal flow graphs. Tellegen's theorem for signal flow graphs, for example, leadsto an important method for analyzing the sensitivity of filter structures, and this hasbeen utilized in our filter-analysis program. In a more general sense, we would hopethat the design of a filter structure with good finite register length characteristics couldbe incorporated directly into the filter-design problem. As an alternative, perhaps itwould be possible to modify a filter structure in the direction of minimizing the coeffi-cient sensitivity. Some indication about how this might be done is suggested by suchnetwork theorems as Tellegen's theorem, and it seems clear that as a better under-standing of digital network theory develops, the ways in which filter structures can bemodified will also become clearer.QPR No. 112(XV. DIGITAL SIGNAL PROCESSING)At present, in comparing filter structures, the primary emphasis is on their evalu-ation in terms of coefficient sensitivity and arithmetic round-off effects. In consideringthe details of digital filter implementation, however, a variety of other issues are atleast equally important. For instance, digital ladder structures appear to have goodproperties with respect to coefficient sensitivity. On the other hand, certain examplesof these structures require all serial computation, that is, much of the arithmetic cannotbe carried out in parallel. Since the degree of parallelism is generally related to com-putation speed, in some applications it may be attractive to sacrifice coefficient sensi-tivity to gain parallelism in the structure. Consequently, in evaluating filter structures,it seems important also to focus on other aspects of the structure such as the inherentparallelism. Issues such as this again relate to the topology of the digital network andfall within a framework that could appropriately be termed digital network theory.2. Multidimensional Signal ProcessingU. S. Navy Office of Naval Research (Contract N00014-67-A-0204-0064)National Science Foundation (Grant GK-31353)D. E. Dudgeon, R. M. Mersereau, A. V. OppenheimA class of problems that is becoming increasingly important and interesting involvestwo-dimensional digital processing. During the past year, we have completed a pro-ject directed toward the reconstruction of a multidimensional signal from its projections.In this work, a theorem has been determined that states that under specific conditionsa reconstruction can theoretically be made from a single projection. We areinvestigating design techniques for multidimensional digital filters. In image pro-cessing, for example, digital filtering is important in such problems as reducing noise,inverse filtering, matched filtering for pattern recognition, contrast enhancement, anddynamic range compression. In contrast with one-dimensional filters, however, theproblem of designing two-dimensional digital filters is for the most part unresolved. Thedifficulties arise from the fact that the system function is a ratio of two-dimensionalpolynomials, for which factorization theorems do not exist as they do for one-dimensionalpolynomials. Consequently, two-dimensional system functions cannot simply be charac-terized in terms of poles and zeros. Thus stability is considerably harder to guarantee.In one dimension, the approximation problem is generally concerned with the designof a squared magnitude function which is then factored. In two dimensions, the factor-ability of magnitude squared functions cannot be guaranteed. Furthermore, the generaltheory of approximation by two-dimensional polynomials is considerably less developedthan in the one-dimensional case. Thus the general area of two-dimensional digitalfiltering presents a number of interesting research problems that we propose to pur-sue.Our recent efforts have been directed toward developing algorithms that can be usedto design magnitude squared functions that approximate a given ideal frequency response.An algorithm has been developed that provides an optimum approximation in theTchebychev (minimax) sense on a limited pointed set. We shall continue this researchand also investigate the problem of implementing these designs recursively. Sinceno two-dimensional factorization theorem exists which allows straightforward splittingof these magnitude squared functions to obtain recursible systems, we are looking forother techniques that will perform this splitting for us. Ironically, our two-dimensionalrecursive filter design algorithm has also proved useful for the design of one-dimensionalfilters. We are exploring the use of this algorithm for one-dimensional filter design.Another approach to two-dimensional systems that we are exploring is that ofmapping the two-dimensional problem to a one-dimensional problem, performing thesignal processing in one dimension, and then mapping the output back to two dimensions.Such mappings exist, and are invertible. This approach is potentially rewarding becauseof the wide variety of available one-dimensional signal-processing techniques. Such anQPR No. 112(XV. DIGITAL SIGNAL PROCESSING)approach to processing two-dimensional signals is ideally suited to the processing ofdrum-scanned images and televisionlike signals, which are already somewhat one-dimensional in character.3. Applications of Digital Signal Processing to SpeechU. S. Navy Office of Naval Research (Contract N00014-67-A-0204-0064)A. V. Oppenheim, M. R. Portnoff, J. M. Tribolet, V. W. ZueIn this aspect of our research, we are interested in the applications of digital signal-processing techniques to speech processing and parameter extraction. One project isdirected toward studying in detail and summarizing in quantitative terms the acousticproperties of various speech sounds within and around stressed syllables. Thus far,our effort has been directed primarily toward those consonants preceding stressedvowels. The objective of the study is at least twofold. First, we aim to provide quanti-tative data of these speech sounds for immediate applications in such research areasas computer recognition of speech and speech synthesis by rule. Second, through a con-trolled study of this kind we hope to arrive at a better understanding of the encodingand decoding processes in the speech communication chain.Most of our effort has been directed toward the development of a good acoustic anal-ysis system. A speech analysis system centered around linear prediction analysis hasbeen implemented on a computer. This system has a highly interactive facility for on-line data display and playback.At present, linear prediction analysis is limited to extracting the poles of the vocal-tract transfer function. Another aspect of our research is to investigate the extensionof this set of techniques for the determination of zeros, as well as poles. One such pos-sibility, which we are now investigating, is based on applying linear prediction to thecepstrum, a technique that we have referred to as cepstral prediction.A third project, directed toward the application of digital signal processing tech-niques to speech, concerns speed transformations. There are many applications inwhich it is of interest to modify speech in such a way that its speed is changed whileretaining an intelligible, natural quality. In learning a second language, for example,it is common practice to have exercises available at several speeds, dependingon the level of the student. An eventual objective in learning a second language iscomprehension at natural speaking speeds. Preliminary training, however, is oftencarried out at slower speeds. At present, it is necessary to record the exercises ateach of several speeds. It would appear to be of considerable advantage if the speedtransformation could be implemented automatically and continuously under the con-trol of the student. Another class of applications arises in the consideration of readingmachines. It is commonly understood that it is possible to read text faster than nar-rating it. In many instances, however, it is more convenient to receive informationaurally. Other researchers have demonstrated that speed transformations of speechcan be implemented by factors of two or three without destroying the intelligibility. Inthe other direction, it is sometimes useful to reduce the speed of speech so that other-wise unintelligible speech becomes intelligible.One approach is the use of a vocoder which carries out the speed transformation bytime-scaling the synthesis parameters. In principle, this is a reasonable approach,which results in intelligible speech. The speech quality is degraded, however, becauseof the degradation inherent in the vocoder. While this degradation is tolerable in someapplications, in many, such as second-language learning, it is not. For this approachto be successful, an extremely high-quality speech analysis-synthesis system must bedeveloped. The specifications for the system constitute a departure from the tradi-tional point of view, in that efficient coding and bit-rate reduction is not a consider-ation. One aspect of our research is to develop such a system.QPR No. 112(XV. DIGITAL SIGNAL PROCESSING)Even with a high-quality, analysis -synthesis system, some important considerationsremain. To a first approximation, speech transformation can be implemented by time-scaling the synthesis parameters. In speaking at different speeds, however, we do notsimply change the speed of motion of the articulators, but, in fact, employ a set ofrules. For example, for vowels it is reasonable to assume that a simple time-scalingis applied. For plosives, on the other hand, the duration of the burst will remainapproximately constant. As a further consideration, coarticulation effects vary withspeed and we often employ contractions to effect a speed change. Many of these rules,at present, are not well understood and will comprise one aspect of the research.4. Digital Signal Processing Computer (The Black Box)U. S. Navy Office of Naval Research (Contract N00014-67-A-0204-0064)J. AllenA small fast processor called the "Black Box" is being built primarily for use asa peripheral processor for speech synthesis with a DEC PDP-9 host computer. Withthe exception of the host computer I/O interface, the detailed logic design of the BlackBox digital signal processing computer is complete.Following completion of construction, and hardware debugging, a set of test pro-grams will be written. We also plan to write a Black Box simulator on the PDP-9computer to check the detailed logical functioning of the machine. This is particularlyimportant for the Black Box multiplier, which is very complex, and must be checkedwith all possible bit patterns. During this period, we shall also write application pro-grams. The first example will be a vocal-tract model, but an FFT will also be written,and software for several functions, such as vector scalar and display generation, willbe completed. We expect that a large number of users will find the Black Box usefulfor their applications.QPR No. 112

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