Abstract:
Filter-chain-creating, digital signal-processing structure, for performing frequency band analysis and selection, which structure features a time-slice-based digital fabricating/instantiating engine, and engine-software-operating structure designed to operate the engine in a time-slice-based fabrication mode to create a chained arrangement of at least one of (a) Type-I, and (b) combined Type-I and Type-I wave digital filter (WDF) agencies in an overall, composite WDF structure to function for frequency band analysis and selection.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation from currently co-pending U.S. patent application Ser. No. 11/895,538, filed Aug. 24, 2007, for “Digital Signal-Processing Structure and Methodology Featuring Engine-Instantiated, Wave-Digital-Filter Componentry, and Fabrication Thereof”, which is a continuation from currently co-pending U.S. patent application Ser. No. 10/651,233, filed Aug. 28, 2003, for “Digital Signal-Processing Structure and Methodology Featuring Engine-Instantiated, Wave-Digital-Filter Componentry, and Fabrication Thereof”. The entire contents of these currently co-pending parent applications are hereby incorporated herein by reference. 
    
    
     BACKGROUND AND SUMMARY OF THE INVENTION 
     This invention relates generally to digital signal processing, and in a more specific sense to the creation, configuration and implementation of wave digital filter (WDF) structure and activity. As will become apparent to those generally skilled in this art, the various facets, the novel methodology, and the novel structure of this invention are adaptable to a very wide range of applications, just a few of which are specifically, but only generally, mentioned herein. 
     By way of background regarding this field of technology, most signal-processing systems employ two fundamental types of processing algorithms—fixed-function and data-dependent. Typical signal-processing systems use very high-throughput, fixed-function algorithms for front-end processing, such as band selection filtering or fast Fourier transforming. This front-end processing step is typically followed by the use of data-dependent algorithms for feature extraction and data classification. Front-end processes are typically implemented on high-performance, programmable, digital signal processors (DSPs), and micro-processor based architectures are commonly used to implement the front-end algorithms since they provide great flexibility. 
     High-performance filter functions are needed in most signal-processing applications. One common use of signal-processing systems is in signal filtering. Typical end-use requirements include decimation and filtering for sigma-delta modulator-based analog-to-digital converters for signal acquisition, for digital sample-rate converters to match signal parameters to various processing algorithms, and for spectral or frequency band analyses and selection for signal extraction. 
     Classically, finite impulse response filters (FIRs) are used in the above-identified applications. FIRs have the advantage of ease of design and unconditional stability. However, FIRs usually require considerable hardware resources, particularly in high dynamic range, multi-channel systems. Wave digital filters (WDFs) are attractive alternatives in these applications because of their low coefficient sensitivity and simple design. Additionally, by constraining the ratio of a filter&#39;s cut-off frequency to the clock rate in a filter algorithm, WDFs with low arithmetic complexity of only one or two multiplications per data input sample may be realized. These types of filters are approximately five to six times more hardware-efficient than the best FIR implementations for a given filter specification. Furthermore, by systematically searching constrained coefficient space, a number of WDF structures have been developed where a multiplication operation reduces to a simple hard-wired binary shift and add operation, an approach which reduces hardware complexity still further. 
     In this setting, where WDF circuitry is sought to be used as a preferential approach to signal processing, the WDF signal-processing technology of the present invention offers a significant new advance. 
     In accordance with the present invention, included among the several digital signal-processing advances which are offered by this invention are (1) a newly proposed WDF agency, (2) a newly proposed cascade, or chained, series arrangement of WDF filter agencies, referred to herein as a composite WDF, one of which composite-contributing agencies is the just-mentioned, newly proposed WDF agency (1), and (3) a computer-based digital fabricating engine (and related methodology) which operate to generate (realize) on the fly, so-to-speak, by time-based instantiation in time-spaced phases, all of this agency (and agency-composite) structure (also referred to herein as phase-instantiated WDF structure). Among the “WDF agency structure” thus created by this engine, significantly, is a foundation filter “building block” which is referred to herein as a branch of a 5 th -Order WDF elliptical filter section. Such a branch, and its different, specific, useful configurations, are illustrated and described hereinbelow in relation to a selected, dedicated drawing figure ( FIG. 6 ) which is presented especially to highlight this feature of the invention. The proposed WDF-based structure and methodology of this invention are simple in construction and implementation, are adaptable to many applications, and offer, generally in the “world” of signal filtering, an impressive, steep (or short, or fast) transition-bandwidth performance which allows for sophisticated operation in, for example, multi-channel filtering environments, such as the environment mentioned above associated with the frequency band analyses and selection. 
     For illustration purposes, a preferred and best-mode embodiment of, and manner of implementing and practicing, the present invention are disclosed herein in the setting of a multi-channel WDF implementation employing a unique, and especially short(fast)-transition-bandwidth, composite WDF made up of two, concatenated WDF agencies, referred to herein as Typed and Type-II WDF agencies. The Type-II WDF agency discussed herein is one of the new and unique contributions (to the art) of the present invention. As will be seen, it is the fast transition bandwidth of this new Type-II WDF agency which causes the mentioned composite WDF to exhibit the unique and special, overall, fast “composite” transition bandwidth offered by the present invention. 
     This multi-channel WDF implementation exploits the generally fast-transition bandwidth of WDF technology, and uniquely uses time-division, or time-sliced, multiplexing in the transitory, instantiated forming of various WDF building blocks (functional digital circuitry) to process multiple channels of data using the mentioned, effectively single, composite WDF. In a multiple-channel filtering system, and among many of the advantages offered by the invention, the cost, for example, of an employed arithmetic logic unit (ALU) can be spread over the total number of processed channels. This is possible because the speed of operation of the proposed, new Type-II WDF agency is much faster than counterpart, conventional WDF agencies, due, at least in part, to the new agency&#39;s very simple, effective hardware structure. Hence, an ALU which is used with the WDF structure of the present invention can easily and very efficiently be time-multiplexed (sliced) over, and offered transitorily to, a number of input signal channels. 
     Thus, included among the important and unique contributions of this invention are (1) a new type of fast-transition-bandwidth, decimating WDF agency, referred to herein as a Type-II agency, constructed with four, concatenated (in a cascade series), 5 th -Order elliptical signal-processing sections, and (2) a new type of decimating, composite WDF filter which is formed of a concatenated combination (also in a cascade series) of a single Type-II agency, and upstream therefrom, at least one decimating WDF agency, referred to herein as a Type-I agency, constructed with a pair of concatenated 5 th -Order elliptical sections. The four elliptical sections in the new Type-II agency include three upstream, non-decimating sections, and a fourth, downstream decimating section. The two elliptical sections in the Type-I agency include an upstream, non-decimating section, and a downstream, decimating section. More than a single Type-I agency may be employed in a composite WDF structure formed in accordance with the invention, and the preferred embodiment of the invention is illustrated herein in a setting which employs four such agencies—concatenated. 
     Each elliptical section in each type agency is formed with a parallel pair of branches, referred to herein as upper and lower branches, and every such branch includes a twin-summing-node-connected, parallel arrangement formed with a defined Z-transform function block bracketed by a pair of Gamma-factor multipliers. Within each elliptical section, the Gamma factors associated respectively with these “function blocks” in the upper and lower branches are different, but are the same within each branch, per se, and the specific Gamma factors which are associated respectively with the elliptical sections forming the Type-I and Type-II agencies differ from one another. There are four Gamma factors employed herein, and these are referred to as Gamma 1 and Gamma 2 (used in each Type-I WDF agency), and Gamma 3 and Gamma 4 (used in each Type-II WDF agency). 
     Non-decimating elliptical sections distinguish generally from decimating elliptical sections by the facts that their lower branches (in the non-decimating sections) include an additional, series-connected, Z-function, delay element, and that they possess but a single “input terminal”. Decimating sections do not possess such a delay element, and are characterized, effectively, by a pair of individually, and mutually exclusively, selectable “input terminals”. 
     Further contributed by the present invention is the earlier-mentioned, computer-based, digital fabricating engine which operates in an on-the-fly, time-sliced manner to instantiate all of the above-discussed signal-processing structure (and functionality) just as such are needed to perform signal processing. A signal presented to the environment of this invention “passes through” that environment in a manner “managed” by this engine so as to be “engaged” by the various branches, sections and agencies mentioned above, and in the correct order, so as to become appropriately processed. 
     What this engine, an instantiation engine, thus does during operation is to create, in effect, to represent as instances, a seriatim secession of 5 th -Order elliptical-section branches (upper and lower), also referred to herein as instances of such branches, appropriately ordered in time, and organized, with respect to signal flow, so as to create a succession of whole elliptical sections, which are, in turn, organized in time to produce the correct concatenated arrangement of Type-I and Type-II agencies. This engine can thus be thought of fundamentally as being provided, via code-control instructions, with a basic template for the creation, over a defined time span within a particular extent of time, of 5th-Order elliptical-section branches, and then sequentially furnished with appropriate data informing it (a) whether it is to create a Type-I or a Type-II agency, (b) whether, within such a singularly defined agency, it is to create, during a particular short span of time, a decimating or a non-decimating elliptical section, (c) what appropriate Gamma factor should be used to define the multipliers in the upper and lower elliptical-section branches, and (d), with regard to a lower branch, whether it is to include the above-mentioned, additional Z-function delay element, Effectively, the engine creates these “things” as structural and functional portions of itself between what are referred to herein as signal input and output zones. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block/schematic illustration of the overall WDF structure and methodology of the present invention. 
         FIG. 2  shows, in an isolated manner, a composite WDF portion of what is pictured in  FIG. 1 . 
         FIG. 3  illustrates the transfer function of the composite WDF portion shown in  FIG. 2 . 
         FIG. 4  is a block/schematic diagram generally illustrating a non-decimating Order elliptical section which is employed in the practice of the present invention. 
         FIG. 5  is a block/schematic diagram generally illustrating a decimating (decimate-by-two) 5 th -Order elliptical section which is employed in the practice of the invention. 
         FIG. 6  is a block/schematic diagram generally illustrating the make-up of each of the blocks in  FIGS. 4 and 5  which are labeled, respectively, Upper and Lower WDF Gamma 1, 3, and Upper and Lower WDF Gamma 2, 4. 
         FIG. 7  is a high-level block/schematic diagram of what is referred to herein as a Typed WDF agency. 
         FIG. 8  is a high-level block/schematic diagram of what is referred to herein as a Type-II WDF agency. 
         FIG. 9  provides a somewhat more detached view of the Type-I WDF agency pictured in  FIG. 7 . 
         FIG. 10  illustrates the transfer function of the Typed agency shown in  FIGS. 7 and 9 . 
         FIG. 11  furnishes a somewhat more detailed view of the Type-II WDF agency shown in  FIG. 8 . 
         FIG. 12  illustrates the transfer function of the Type-II agency shown in  FIGS. 8 and 11 . 
         FIG. 13  provides a high-level block/schematic illustration of a time-slice-based, computer-based, digital fabricating engine which operates in accordance with the present invention to instantiate the various functional structures that are presented in  FIGS. 4-9 , inclusive, and  11 . 
         FIG. 14  is provided as an aid to understanding the names given herein to identify different structural and methodologic regions in the overall configuration of the present invention. 
         FIG. 15  presents a complete block/schematic diagram fully illustrating the operation of the fabricating engine proposed by the present invention, and thus fully describing the basic operational practice of the invention. 
         FIG. 16  is a view which is provided as an aid to understanding how  FIGS. 17-19 , inclusive, may be arranged physically to display certain engine-performed actions which are implemented by the engine of  FIG. 13  to instantiate the upper and lower branches of a 5 th -Order elliptical section, such as those sections shown in  FIGS. 4 and 5 . 
         FIGS. 17-19 , inclusive, describe, in row-and-column form, the upper and lower branch-instantiation activities mentioned in relation to the description of  FIG. 16 . 
         FIGS. 20-24 , inclusive, detail, in block/schematic forms, the make-up of a memory and counter structure which is employed in the operation of the fabricating engine of  FIG. 13 . 
         FIGS. 25-27 , inclusive, present detailed micro-code listings for the read and write, memory-access addressing activities of the components of the structures shown in  FIGS. 20-24 , inclusive, in specific relation to the operative engagements that take place with two dual-port RAM memories which form part of the engine pictured in  FIG. 13 . These listings are directly related to the upper and lower, branch-formation engine steps which are presented in  FIGS. 17-19 , inclusive. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Turning now to the drawings, and referring first of all to  FIGS. 1 ,  2 ,  4  and  14 , let us note at the outset that a consideration of  FIG. 14  is useful throughout the invention description provided herein to aid in visualizing how certain terminology employed in this description relates both to the structural and to the methodologic features of the invention. In  FIG. 1 , a digital signal-processing system (or structure) and methodology of the present invention, in their respective preferred and best-mode forms, are indicated generally at  30 . Speaking from a systemic point of view, system  30  effectively includes a time-slice-based, and computer-based, digital fabricating engine  32  which operates under the control of an appropriate micro-code to create, on an instantiation basis, what are referred to herein as concatenated Type-I (early-stage) and concatenated Type-II (later stage) wave digital filter (WDF) agencies, such as those shown at  36 ,  38 ,  40 ,  42  (each an identical Type-I agency), and  44  (a Type-II agency). Block  34  which represents the just-mentioned control micro-code is also referred to herein both as software operating structure, and as control code structure. 
     Collectively, these Type-I and Type-II WDF agencies constitute what is referred to herein both as a composite WDF, and as a time-slice instantiated, wave digital filter assembly (WFDA), indicated generally at  46 . This composite WDF, or WDFA, is segregated and isolated for focus in  FIG. 2 . 
     Each WFDA includes at least one Type-I agency, and only one Type-II agency. Each WDFA may include plural Type-I agencies, and system  30  is shown herein including four such agencies (mentioned above as agencies  36 ,  38 ,  40 ,  42 ).  FIGS. 1 and 2  clearly show that plural Type-I agencies, called an arrangement of such agencies, are concatenated in a manner whereby the output sides (the right sides) of certain ones of the Type-I agencies are connected to the input sides (the left sides) of certain other ones of these agencies. 
     Selectable output taps  36   a ,  38   a ,  40   a ,  42   a  for agencies  36 ,  38 ,  40 ,  42 , respectively, are provided for selective connection to the input side (the left side) of Type-II agency  44 . A solid arrow-headed line  47   a  is shown connecting the output side of agency  36  (tap  36   a ) to the input aide of agency  44 . A dash-dot arrow-headed line  47   b  is shown connecting the output side (tap  40   a ) to the input side of agency  44 . Such Type-I to Type-II agency connections are specifically selectable by engine  32  for each created WDFA, depending upon how many “stages” of Type-I-agency signal processing are called for. 
     The entire collection of output taps for the Type-I agencies is referred to herein as an output region. The right side of Type-II agency  44  constitutes its output side. 
     As will be pointed out later with reference to  FIGS. 10 and 12 , the Type-I and Type-II agencies provide different, respective filtering transfer functions which are characterized with different transmission bandwidths. The transfer function of each Type-I agency is referred to herein as a first transfer function, and its transmission bandwidth is referred to as a first transmission bandwidth. The transfer function of a Type-II agency is referred to herein as a second transfer function, and its transmission bandwidth is referred to as a second transmission bandwidth. The transition bandwidth of Type-II agency  44  is less than the like transmission bandwidths of Type-I agencies  36 ,  38 ,  40 ,  42 . The transfer function, and overall transmission bandwidth, of WDFA (composite WDF)  46  are illustrated in  FIG. 3 . 
     WDFA  46  is appropriately connected to signal input and output structures  48 ,  50 , respectively, and, in the invention form now being described, is appropriately supplied with time-successive digital signals for processing, on a channel-by-channel basis, from a plurality of channels  52   a - 52   h , inclusive, through an associated, respective plurality of generally conventional, decimate-by-four, finite impulse response filters  54   a - 54   h , inclusive. Channels  52   a - 52   h  and filters  54   a - 54   h , inclusive, are collectively referred to as plural-channel signal feed structure, and the right-side of this feed structure in  FIG. 1  is called an output side for this structure. Structures  48 ,  50  herein are also referred to as signal input and output zones, respectively. 
     With regard to what has been generally described so far in system  30 , it is important to note that, whereas all of the basic, high-level schematic views of the system “components” are shown in a “simultaneous existence” manner in  FIGS. 1 and 2 , they actually do not ever exist fully at the same moment in time. Rather, they are created in a staged, time-selected, instantiated way, by engine  32 , as they, and constituent portions of them, are needed to implement the processing of a signal passing through a WDFA. Stylized block  56  in  FIG. 1 , which is shaded into different laterally displayed regions, such as the three, left-to-right displaced regions shown at  56   a ,  56   b ,  56   c  within this block, represents such time-slice instantiation for the creation of an appropriate, single WDFA, Relative to block  56 , an input signal which is to be processed is shown at  58   a , and the resulting processed output signal is shown at  58   b . According to practice of the present invention, each such signal to be processed is presented in its various stages of “intermediate” processing, and ultimately and in the correct processing manner, to the various signal-processing constituent elements of a single, instantiated WDFA. 
     For illustrative and explanatory purposes herein, operation of system  30  is described simply in the context of the instantiated creation of a single WDFA “possessing” a single Type-I WDF agency. 
     Directing attention now to  FIGS. 4-9 , inclusive, and  11 , these figures, with somewhat differing degrees of specificity, illustrate the fundamental building blocks (the componentry) of the high-level illustrations furnished in  FIGS. 1 and 2  for the Type-I and Type-II WDF agencies, Specifically, these building blocks are described in the structural context of previously mentioned Type-I agency  36  and Type-II agency  44 . 
     Beginning with  FIGS. 4 and 5 ,  FIGS. 4 and 5  diagram, respectively, what are referred to herein as a non-decimating, 5 th -Order elliptical, signal-processing section  60 , and a decimating (decimate-by-two), 5 th -Order elliptical, signal-processing section  62 , which are created transitorily by engine  32 , and associated in different ways with one another to generate the above-described Type-I and Type-II agencies. 
     Section  60  includes upper and lower, parallel, all-pass branches  63 ,  64  respectively, which connect at a pair of spaced summing nodes  66 ,  68 . Summing node  68  is actually a SUM/2 node. Included in each of upper and lower branches  63 ,  64  is a block  70  which is referred to herein as an all-pass transform block (or “function”), the details of which are shown in  FIG. 6 , and which performs in accordance with the equation: 
               H   ⁡     (   Z   )       =       Gamma   +     Z     -   2           1   +     Gamma   ⁢           ⁢     (     Z     -   2       )                 
Lower branch  64  additionally includes, in series with block  70 , and on the node- 66  side of block  70 , a Z −1  transform function block  72  which performs in accordance with the equation:
 
 H ( Z )= Z   −1  
 
Block  72  constitutes what is also called a delay element herein.
 
     Decimating elliptical section  62  includes identical upper and lower parallel all-pass branches  74 ,  76 , respectively, each of which includes a transform block  70  (previously mentioned), and neither of which includes a delay element  72 . In section  62 , branches  74 ,  76  are referred to herein also as mutually exclusive through paths, the left ends of which (as seen in  FIG. 5 ) provide selectable inputs  74   a ,  76   a , respectively. One or the other of these inputs is selected appropriately by engine  32  for signal-flow connection to a singular, upstream input  78 . The right ends of branches  74 ,  76  in  FIG. 5  are connected at a summing (SUM/2) node  79  which is like previously mentioned node  68 . 
     As was mentioned above, greater details of construction of each block  70  are pictured in  FIG. 6 . Each of these blocks  70  includes a central Z −2  transform function block  80 , the left and right sides of which in  FIG. 6  connect with summing nodes  82 ,  84 , respectively. Node  82  includes plus (+) and minus (−) input terminals  82   a ,  82   b , respectively, and an output terminal  82   c , Node  84  includes a pair of plus (+) input terminals  84   a ,  84   b , and an output terminal  84   c . Block  80  performs in accordance with the equation:
 
 H ( Z )= Z   −2  
 
     Functionally bracketing block  80  are two fixed-Gamma-factor multipliers  86 ,  88 . In  FIG. 6 , the left side of multiplier  86  connects with the interconnection which exists between block  80  and node  82 , and the right side of this multiplier connects with the upper-shown input terminal  84   a  in node  84 . The left side of multiplier  88  in  FIG. 6  connects with minus (−) input terminal  82   b  in node  82 , and the right side of this multiplier connects with lower input terminal  84   b  in node  84 . 
     The fixed-value Gamma factors (Gamma 1, Gamma 2, Gamma 3 and Gamma 4) associated with multipliers  86 ,  88  are always the same within a given single block  70 . However, the fixed-value Gamma factors per se have different values depending upon (a) whether block  70  is being created for use in an upper or in a lower section branch, and (b) whether block  70  is to be employed either a Type-I or in a Type-II WDF agency. 
     In a Type-I agency, the upper branch Gamma factors are all the same (Gamma 1), and preferably have the value ⅛, and the lower branch Gamma factors are also all the same (Gamma 2), and preferably have the value ½+ 1/16. In a Type-II agency, all of the upper branch Gamma factors (Gamma 3) preferably have the same value ¼+ 1/64, and all of the lower branch Gamma factors (Gamma 4) preferably have the same value ½+¼. 
     An interesting feature of the preferred embodiment of this invention is that the Gamma multipliers represented in  FIG. 6  by blocks  86 ,  88  are implemented, effectively, as hard-coded sums of binary number shifts. All of the actual Gamma multipliers which have this hard-coded characteristic herein are more specifically illustrated as individuals in  FIG. 13  of the drawings (still to be discussed) which details the structure of engine  32 . 
     Within the elliptical sections and structures shown in  FIGS. 4 ,  5  and  6 , arrowheads on lines indicate signal-flow “directions”. 
       FIGS. 7 and 8  picture the constructions of previously mentioned Type-I and Type-II WDF agencies  36 ,  44 , respectively. Specifically, these two figures show how the two, different 5 th -Order elliptical sections presented in  FIGS. 4 and 5  are assembled by engine  32  to form agencies  36 ,  44 . What can be seen clearly here is that each Type-I agency is formed as a concatenated series of two different 5 th -Order elliptical sections, including an upstream section, which is a non-decimating section  60 , and a decimating, downstream section  62 . Each Type-II agency is formed as a concatenated series of four 5 th -Order elliptical sections, including three upstream (or input), non-decimating sections  60  coupled to one downstream, decimating section  62 . 
     From the system description which has now been given above, and looking now especially at  FIG. 15 , one can see that the entirety of a WDFA, such as a WDFA  46 , can be fabricated by the activity of operating engine  32  so as to create a seriatim, time-phased series of upper and lower elliptical-section branches (a) having the correct Gamma multiplier factors defined for them, and (b) including (or not including) a delay element  72 . To create a Type-I agency, the engine, utilizing the correct Gamma factors, creates a simple succession including, first, a non-decimating 5 th -Order elliptical section  60 , followed by a decimating 5 th -Order elliptical section  62 . If more than one Type-I agency is required to process a particular signal, the engine simply repeats this process an appropriate number of times. This total number of times is represented by N in  FIG. 15 . 
     To create a Type-II agency, engine  32 , again utilizing the correct Gamma factors, generates, first, a series of three non-decimating 5 th -Order elliptical sections  60 , followed by the formation of a single, decimating elliptical section  62 . 
       FIGS. 10 ,  12 , and  3  describe the respective transfer functions and transition bandwidth characteristics of (a) a Type-I WDF agency, like agency  36 , (b) a Type-II WDF agency, like agency  44 , and (c) a WDFA, like WDFA  46 . 
     Beginning with  FIG. 10  which illustrates the transfer function of a Type-I WDF agency, the x-axis represents scaled frequency lying within a range from 0.0 to 0.5. Frequency values are scaled by normalizing the frequency with the appropriate clock rate. The y-axis in this figure represents relative output in decibels (dB). As can be seen from the plotted information in  FIG. 10 , attenuation of an input signal is approximately 0-dB until the scaled frequency reaches approximately 0.2. Attenuation above this scaled-frequency value increases relatively slowly, following a parabolic path, until it reaches about 120-dB attenuation, where the scaled frequency reaches approximately 0.39. Thus, the transfer frequency range over which a Type-I agency attenuates a signal from 0-dB attenuation to 120-dB attenuation is approximately 0.2 to 0.39 on a scaled-frequency scale. This defines a transfer frequency band which, when normalized to dock rate, is approximately 0.19. 
       FIG. 12  presents a similar graphical representation of the transfer function of a Type-II WDF agency constructed in accordance with practice of the present invention. Here also the x-axis plot represents scaled frequency lying within a range from 0.0 to 0.5. Again, frequency is scaled by normalizing the frequency with the appropriate dock rate. The y-axis represents relative output in decibels (dB). As can be seen here, attenuation of an input signal is approximately 0-dB until the scaled frequency reaches approximately 0.22. Signal output then decays rapidly, following an exponential pattern, until it reaches 120-dB attenuation, where the scaled-frequency value reaches approximately 0.28. Thus the transfer frequency range over which a Type-II agency attenuates a signal from 0-dB attenuation to 120-dB attenuation is approximately 0.22 to 0.28 on the scaled-frequency scale. This results in the transfer frequency band, normalized to dock rate, being about 0.06. Thus, the Type-II WDF agency proposed by the present inventions furnishes an extremely fast (or short, or steep) transfer function. 
       FIG. 3  provides a graphical representation of the transfer function provided by a composite (Type-I/Type-II) wave digital filter (WDFA) formed in accordance with practice of the present invention. The x-axis in this figure represents scaled frequency in the range from 0.0 to 0.5. Again, frequency is scaled by normalizing the frequency with the appropriate clock rate. The y-axis expresses relative signal output in decibels (dB). As can be seen here, attenuation of an input signal is approximately 0-dB until the scaled frequency reaches approximately 0.015, beyond which signal output decays rapidly, following a near asymptotic path, until in reaches 120-dB attenuation, where scaled-frequency reaches approximately 0.022. Thus the transfer frequency range over which a WDFA prepared in accordance with the invention attenuates a signal from 0-dB attenuation to 120-dB attenuation is approximately 0.015 to 0.022 on a scaled-frequency scale. This represents a transfer frequency band, normalized to dock rate, of about 0.007. 
     Completing a description now of the structure and methodology of this invention, the composition and operation of instantiating engine  32  are described. Beginning with  FIG. 13 , here, engine  32  is shown occupying most of the space of this figure. To the left of engine  32  in  FIG. 13  is a memory and counter structure  90  which includes a 512×16 read only memory  90   a  (PROM), and a clock-pulse driven counter  90   b . Structure  90  functions, with respect to the operation of engine  32 , to generate control addresses for each one of a pair of memories, still to be described, which form parts of engine  32 . More will be said shortly about structure  90  and its components  90   a ,  90   b  in relation to drawing  FIGS. 20-27 , inclusive. 
     Engine  32  includes at  92 ,  94  (DPRAM  1 , DPRAM  2 , respectively) these two, just-mentioned memories, a pair of four-input multiplexers  96 ,  98  (MUX  1 , MUX  2 , respectively), four registers  100 ,  102 ,  104 ,  106  (Reg  1 , Reg  2 , Reg  3 , Reg  4 , respectively), three two-input summing nodes, or adders,  108 ,  110 ,  112  (SUM  1 , SUM  2 , SUM  3 , respectively), and a two-input multiplexer  114  (MUX  3 ). Directly associated with the four inputs in multiplexer  96  are four Gamma-factor multipliers  96   a ,  96   b ,  96   c ,  96   d . Similarly, directly associated with the four inputs in multiplexer  98  are four Gamma-factor multipliers  98   a ,  98   b ,  98   c ,  98   d . Multipliers  96   a ,  98   a  utilize Gamma 1, multipliers  96   b ,  98   b  Gamma 2, multipliers  96   c ,  98   c  Gamma 3, and multipliers  96   d ,  98   d  Gamma 4. Arrowheads provided on the various interconnecting lines shown in  FIG. 13  describe signal-flow directions. Input and output structures  48 ,  50  are shown connected to multiplexer  114 . 
     As was mentioned earlier, all of these now individually pictured Gamma multipliers are implemented in engine  32  in the forms of hard-coded sums of binary number shifts. The respective “values” of these several multipliers, as set forth above in this text, are directly reflected in these hard-coded “sums” and “shifts”. This advantageous approach to effecting “multiplication” produces great simplicity and efficiency in the preferred implementation of the invention. 
     While different specific implementation approaches may be used for engine  32 , the preferred embodiment illustrated herein is implemented in a commercially available FPGA Xilinx XCV50 device. Memory  92  is configured as a 256×24 dual-port random access unit, and memory  94  as a 512×24 dual-port random access unit. 
     All control and memory addresses involved in engine operation are generated by and from memory and counter structure  90 . 
       FIG. 13  in the drawings, along with  FIGS. 4-9 , inclusive,  11 , and  15 - 27 , inclusive, are presented herein in manners which will fully equip those skilled in the art to implement and practice this invention. 
       FIG. 15 , as has been mentioned earlier, is a fully explanatory, high-level block representation of the “flow” of the operation of engine  32  during (and focused upon) the creation of a single WDFA, such as WDFA  46 . This operation is repeated to create an appropriate plurality of time-successive WDFA functional structures, on a successive channel-by-channel basis, so long as channel input signals are presented for processing. 
       FIG. 16  shows how  FIGS. 17-19 , inclusive, may be spatially assembled to be read in an integrated fashion.  FIGS. 17-19 , inclusive, when assembled as pictured in  FIG. 16 , collectively describe, in detailed, darkened text, various engine- 32  operations which typically take place during five successive clock signals. During these five “pictured” clock signals, one can observe, among other things, instantiated assembly by engine  32  of one complete 5 th -Order elliptical section, performed in accordance with preferred practice of the invention. Instantiation of this elliptical section is “readable” from  FIGS. 17-19 , inclusive, effectively by “reading” downwardly and to the right along the angularly deployed dash-dot line L which can be visualized as being threaded as a continuum through the left-to-right lateral assembly of these three figures as shown by  FIG. 16 . 
     Providing now a somewhat more detailed narrative description of the structure and operation of this invention, engine  32  uses a fixed-topology, pipelined, signal-flow architecture to generate an all-pass transfer function (performed by an elliptical-section branch) every clock cycle. 
     The all-pass transfer function is expressed as follows: 
     
       
         
           
             
               
                 
                   
                     H 
                     ⁡ 
                     
                       ( 
                       Z 
                       ) 
                     
                   
                   = 
                   
                     
                       Gamma 
                       + 
                       
                         Z 
                         
                           - 
                           2 
                         
                       
                     
                     
                       1 
                       + 
                       
                         Gamma 
                         × 
                         
                             
                         
                         ⁢ 
                         
                           Z 
                           
                             - 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   1 
                   ] 
                 
               
             
           
         
       
     
     Where Gamma is selected by the micro-code out of the sparse set:
 
Gamma 1=(⅛)=0.125)
 
Gamma 2=(½+ 1/16)=(0.5625)
 
Gamma 3=(¼+ 1/64)=(0.265625)
 
Gamma 4=(½+¼)=(0.75)
 
     Also included in the engine is a delay/summation stage that allows two contiguous all-pass section branch outputs to be summed together to calculate a 5 th -Order WDF filter elliptical section of the form: 
     
       
         
           
             
               
                 
                   
                     H 
                     ⁡ 
                     
                       ( 
                       Z 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           Gamma 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         + 
                         
                           Z 
                           
                             - 
                             2 
                           
                         
                       
                       
                         1 
                         + 
                         
                           Gamma 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           × 
                           
                             Z 
                             
                               - 
                               2 
                             
                           
                         
                       
                     
                     + 
                     
                       
                         Z 
                         
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             Gamma 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                           + 
                           
                             Z 
                             
                               - 
                               2 
                             
                           
                         
                         
                           1 
                           + 
                           
                             Gamma 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                             × 
                             
                               Z 
                               
                                 - 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   2 
                   ] 
                 
               
             
           
         
       
     
     Five stages of pipeline registers are used in the signal-flow path of the engine to maintain speed of operation, and a result is that the engine provides an all-pass filter-section branch every clock cycle (or equivalently a 5 th -Order WDF elliptical section every two clock cycles), with a latency of five clock cycles. 
     Engine  32  is programmed to operate as a multi-channel decimation filter by correctly sequencing the read/write addresses that are used to provide the register banks for the filter sections. These addresses are pre-calculated, and are stored appropriately in a small PROM ( 90   a ) look-up table. 
     The basic operation of the engine is now described on a cycle-by-cycle basis, under circumstances with the engine generating a single WDF 5 th -Order elliptical filter section. In this context, one should note that the two dual-port RAM memories  92 ,  94  (DPRAM  1 , DPRAM  2 , respectively) in the engine have completely independent read and write ports. As a consequence, reading and writing from different RAM locations can be carried out simultaneously in the same clock cycle. 
     The RAM addresses are organized so that (a) two contiguous samples of the required filter channel time series are processed sequentially, and (b) the WDF filter transform functions for that channel are generated properly. Data from a different filter channel or for a different decimation stage of the same channel can then be processed in the next-following, two time slots. The related engine- 32  operation is basically as follows: 
     DPRAM  1  ( 92 ), MUX  1  ( 96 ) and SUM  1  ( 108 ) are used to form the recursive part of the transfer function detailed in equation [1] above, i.e., they calculate; 
     
       
         
           
             
               
                 
                   
                     H 
                     ⁡ 
                     
                       ( 
                       Z 
                       ) 
                     
                   
                   = 
                   
                     1 
                     
                       1 
                       + 
                       
                         Gamma 
                         × 
                         
                           Z 
                           
                             - 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   3 
                   ] 
                 
               
             
           
         
       
     
     Thus, during clock cycle 1:
         (a) Input data is read from DPRAM  1  ( 92 );   (b) registered data is read from DPRAM  2  ( 94 ) and scaled by the Gamma weighting (multiplication) selected via MUX  1  ( 96 ); and   (c) The MUX  1  ( 96 ) output and the Z −2  DPRAM  1  ( 92 ) outputs are added together in SUM  1  ( 108 ) to form the all-pass filter output to generate the transfer function given in equation [3] above.       

     The output from SUM  1  ( 108 ) and from DPRAM  2  ( 94 ) are registered into pipeline registers Reg  1  ( 100 ) and Reg  2  ( 102 ), respectively, ready to form the numerator part of equation [1] using MUX  2  ( 98 ) and SUM  2  ( 110 ), i.e. to calculate:
 
 H ( Z )=Gamma+ Z   −2   [4]
 
     During clock cycle 2:
         (a) The recursive-section output generated from SUM  1  ( 108 ) in cycle 1 is written back into DPRAM  2  ( 94 ) to provide for delayed data needed for later calculations;   (b) Data is registered into Reg  1  ( 100 ) and Reg  2  ( 102 );   (c) Reg  1  ( 100 ) data is scaled by the Gamma weighting (multiplication) selected via MUX  2  ( 98 ) and added to the registered DPRAM  2  ( 94 ) output from Reg  2  ( 102 ) to generate equation [4], so the overall transfer function generated thus far through the processing is given in equation [1] above; and   (d) At the same time, DPRAM  1  ( 92 ), MUX  1  ( 96 ) and SUM  1  ( 108 ) form another sample of the all-pass filtered data, using different data samples of the same input channel time series data.       

     The output from SUM  2  is loaded into pipeline register Reg  3  ( 104 ) during clock cycle 3, and into Reg  4  ( 106 ) in clock cycle 4. Because of the pipelined nature of the engine and the continuous processing cycles being calculated by that engine, at the end of clock cycle 4, there exist two time-contiguous samples of the required all-pass filter functions stored in Reg  3  ( 104 ) and Reg  4  ( 106 ). When added together by SUM  3  ( 112 ), these form the required 5 th -Order WDF transfer function (elliptical section) defined in equation [2]. The output of SUM  3  ( 112 ) is scaled by 0.5 (by a hard-coded shift) to avoid excessive word-length growth through the various processing activities. 
     The scaled SUM  3  ( 112 ) output, selected via MUX  3  ( 114 ) is written back into DPRAM  1  ( 92 ) during dock cycle 5 so that this data can be re-cycled through the engine to cascade filter sections, and to allow further decimation. Because SUM  3  ( 112 ) provides valid filter output data only on alternate cycles, every other cycle is available for MUX  3  ( 114 ) to select input data to update DPRAM  1  ( 92 ). Hence DPRAM  1  ( 92 ) is used to store both the unprocessed input data, as well as partially processed data to be used for further filter/decimation processing. 
     The basic operation of the WDF engine thus provides a succession of all-pass filter sections, and, as described above, decimation filtering normally works by using two all-pass sections performed sequentially on each channel to implement a 5 th -Order WDF elliptical filter section. 
     According to practice of the present invention, and as has been mentioned, two types of WDF filters (the Type-I and Type-II agencies described above) are needed for high-performance decimation. The Typed agency, with a moderate transition bandwidth and a minus 120-dB stop-band attenuation, uses a cascade of two 5 th -Order elliptical sections. The Type-II agency, with sharper transition bandwidth and, again, a minus 120-dB stop-band, uses a cascade of four 5 th -Order elliptical sections. 
     The input data rate to engine  32  needs to support samples from eight data-acquisition channels, each sampled at 500-kHz, giving an available time slot of 250-nSecs per channel. For a 32-mHz WDF engine clock rate, this allows eight dock cycles per channel for processing. 
     In order for processing to take place appropriately under these circumstances, it is necessary to provide a Type-I agency on each channel at the input data rate, the output of which is decimated by a factor of two. This first Type-I agency requires two 5 th -Order elliptical sections, and so uses up four of the eight dock cycles, leaving four cycles for further filtering. If one were simply to cascade multiple, decimate-by-two, Type-I agencies, then, because each Type-I agency decimates the sample rate by a factor of two, one could continue cascading decimation filters within the mentioned, remaining, four-clock-cycle slot ad infinitum. 
     Initially with the un-decimated input data, the illustration now being described provides eight clock cycles in total which are available per channel for processing. After the first stage of decimation by two, four of the eight available cycles have been used-up. However, since the output data rate is now reduced by a factor of two, there is actually a total of sixteen clock cycles per output sample available in the processing sequence, of which eight are unused. 
     If one decimates by a further factor of two, there exists a total of thirty-two clock cycles per output sample available in the processing sequence, again, eight of which are unused. Thus, one can continue cascading decimate-by-two sections, and after decimations, will always have eight free clock cycles in the sequence length defined by the decimated output sampling rate for the (D+1) th  decimation. 
     Accordingly, one has available essentially a geometric sum for the number of clock cycles per channel slot needed overall having the form: 
     
       
         
           
             
               
                 
                   N 
                   = 
                   
                     4 
                     + 
                     
                       
                         ∑ 
                         
                           d 
                           = 
                           1 
                         
                         D 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         4 
                         ⁢ 
                         
                           / 
                         
                         ⁢ 
                         
                           2 
                           d 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   5 
                   ] 
                 
               
             
           
         
       
     
     Where N=number of clock cycles per time slot, and 
     D=total number of Type-I decimate-by-two agencies. 
     In the limit, as D approaches infinity, N approaches eight. Thus, eight clock cycles per channel allows one essentially to cascade Type-I agencies forever. 
     In practice, it seems most appropriate to filter/decimate signals down to around a 16-kHz sample rate, and thus require a total decimation of x32. The final stage of decimation needs to be performed with a Type-II agency to provide a sufficiently steep transition bandwidth, and this is furnished by providing a cascade of four Type-I agencies, followed by a Type-II agency. After the first four Type-I decimations, there are eight dock cycles remaining. These remaining cycles are used to calculate the cascade of four 5 th -Order elliptical sections required for the Type-II final filter stage. 
     Consequently, the micro-code sequence length for a complete decimate-by-32 system, using four Type-I WDF agencies followed by a final Type-II agency requires 32×8 cycles per channel, requires 256-states per channel 
     Each 5 th -Order elliptical section requires two RAM locations for intermediate data storage, and so, a total of sixteen locations is needed for the Type-I agencies required per channel, plus a further four for the final Type-II agency—a grand total of twenty locations per channel. Hence the size required for the DPRAM  2  memory for eight channels of signal data is 192-locations. To simplify addressing, the DPRAM size would normally by rounded up to the nearest convenient ‘whole binary number’, i.e. to 256-locations. Similarly, each 5 th -Order elliptical section needs one RAM location for storage in DPRAM  1 , thus giving a required DPRAM size of 128-locations. 
     As was mentioned previously, engine  32  uses a fixed topology, and is essentially programmed by controlling the two DPRAM read/write address sequences. The DPRAM addresses are pre-calculated for the number of channels and the decimation sequencing required, and the resultant address sequences are stored in PROM  90   a . The “regional sizes” within PROM  90   a  that are appropriately made available in the particular system described herein are 512×6 for DPRAM  2  read/write addresses, and two of the size 512×5 for DPRAM  1  read and write addresses. 
     One should note that the same address information can be used for read and write addressing for DPRAM  2 , since the recursive part of the all-pass elliptical section operates on a read/modify/write cycle, and only one effective register is needed for each all-pass through-path. However, because of the pipeline delay of one cycle in calculating this recursion, the write address must also be delayed to compensate. 
     For DPRAM  1 , separate read and write address sequences are needed, and so, separate addressing PROM sites in PROM  90   a  are needed. The sites are sequenced using a straight binary counter ( 90   b ), driven by the 32-mHz system clock. Because the same processing operations are required on eight data channels in the system illustrated herein, the DPRAM addresses are broken essentially into two fields—(1) a channel-address field (the three Most Significant Bits (MSBs) of the address), driven straight from the sequence binary counter ( 90   b ), and (2) a “register” field (the remaining bits), driven with PROM data. The basic topology for these address generation systems is shown schematically and tabularly in  FIGS. 20-27 , inclusive. 
     Turning particular attention now to these several drawing figures, these figures effectively illustrate the important sequential addressing activities which take place during operation of engine  32 .  FIGS. 20-24 , inclusive give schematic structural/functional views of these activities, and  FIGS. 25-27 , inclusive, illustrate specific RAM address sequencing—one figure each for DPRAM  1  WRITE ADDRESS sequencing ( FIG. 25 ), DPRAM  1  READ ADDRESS sequencing ( FIG. 26 ), and DRAM  2  WRITE—READ ADDRESS sequencing ( FIG. 27 ). These latter three figures show the actual addresses supplied to these RAM structures in a length-512 sequence, and thus illustrate composites of ROM output and sequential count, as depicted in  FIGS. 20-24 , inclusive. 
     The following text describes how to read each of  FIGS. 25 ,  26  and  27 . In the left-most column (thirty-two rows long) of four digits, the first three digits in each row in this column are the MSBs of an address, and the fourth digit in this column, in all cases a 0, can be thought of as being a “placeholder” for the “insertion” of a series of fourth, Least-Significant-Bit (LSB) digits which complete a four-digit address. Thus this “three-plus-one” pattern forms a two-dimensional depiction of a length-512 sequence. The 512 locations so accessed are, therefore, 0000 to 01 F0, or 0 to 511. The main block/matrix of numbers, any member of which is identified by the coincidence of any four-digit row designator (0000-01F0), and any column digit (0-F), is the address value presented to one of the DPRAMs for that point in an operating sequence. 
     Using DPRAM  1  READ ADDRESS ( FIG. 26 ) as an example, the first row immediately below the above-mentioned upper-most row is read as 0000, with a content (the address supplied to DPRAM  1 ) of 0; the next address is 0001, with a content of 1; and so on up to, at the end of the first row, the address 000F, with a content of B (decimal 11, or pure binary 1011). 
     One can thus see that the matrix of numbers for each DPRAM READ or WRITE sequence ( FIGS. 25-27 , inclusive), is therefore a two-dimensional representation of a complete eight-channel processing sequence of length 512. 
     Accordingly, a preferred and best mode embodiment of, and manner of practicing, the invention are thus described. The invention, as stated earlier, offers a number of significant advances in the field of digital signal processing, and does so through presenting this field with several unique practices and resulting structures. Introduced by the invention is a novel digital-instantiating fabricating engine which operates, inter alia, to generate in time sliced manners, a new, fundamental, all-pass branch for the construction, ultimately, of a new 5 th -Order elliptical WDF section, which, in turn, is employed by the engine to generate a new Type-II WDF agency possessing a notably “steep and fast” transition-bandwidth characteristic. Also proposed by the invention, instantiated preferably by the engine of the invention, is a new composite Type-I/Type-II wave digital filter formed as a concatenation of decimating and non-decimating 5 th -Order elliptical sections organized into the composite structure. This concatenation, combining, as it does, the cooperating transition bandwidths of a Type-I and the new Type-II agencies, offers an extremely short and fast collaborative transition-bandwidth performance. Each composite structure includes at least one (but may include many) “initial” Type-I agency(ies), depending upon the number of “pre-Type-II” decimations which are desired, and but a single, final Type-II agency. 
     The structure and practice of the invention can easily accommodate multiple input channels of signals for processing, and in conjunction with performing processing efficiently and effectively, employs simple hard-coded binary “sums and shifts”, the Gamma factors described herein, to perform “multiplications”. 
     Accordingly, while preferred structures and practice modalities are specifically described and illustrated herein to disclose the various facets of this invention, we appreciate, as will those generally skilled in the relevant art, that variations and modifications thereof may be made without departing from the spirit of the invention.