Abstract:
A system and a method for signal processing by employing parallel paths ( 107  and  110 ) for processing separate parts of the signal. The method effectively doubles operating speed by providing at least two processing paths. Where two paths are used, each operates at approximately one-half of the data rate of the incoming data signal. By using parallel paths to process signals through a FIR filter ( 100 ), for example, the method can take full advantage of a high order encoding system, such as Radix-8. Further, because of relaxed clock speeds, a preferred embodiment allows use of smaller and faster latches ( 103 ), instead of flip-flops, for the retiming stages. Finally, when used with a FIR filter ( 100 ), the method makes use of the normal irregularity of critical path delays at various stages by borrowing retiming slacks from less time-critical taps ( 101 ) of the FIR filter ( 100 ).

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention relates to a system and a method for increasing throughput rate of a signal processor, for example, one that uses a finite-impulse-response (FIR) filter. In particular, it provides a system a for parallel processing of a digital signal encoded in Radix-N.  
         BACKGROUND  
         [0002]    A FIR filter may be included in the general class of devices referred to as digital signal processors (DSP). This does not mean that the FIR can operate only on digital signals, however.  
           [0003]    A “digital signal” is a signal that conveys a discrete number of values at discrete times. Contrast the “analog signal,” i.e., a signal that conveys an infinite number of values whether continuous time or discrete time. A signal having a digital form may be generated from an analog signal through sampling and quantizing the analog signal. Sampling an analog signal refers to “chopping” the signal into discrete time periods and capturing an amplitude value from the signal in selected ones of those periods. The captured value becomes the value of the digital signal during that sample period. Such a captured value is referred to as a sample.  
           [0004]    Quantizing refers to approximating a sample with a value that may be represented on a like digital signal. For example, a sample may lie between two values characterized upon the digital signal. The value nearest (in absolute value) to the sample may be used to represent the sample. Alternatively, the sample may be represented by the lower of the two values between which the sample lies. After quantization, a sample from an analog signal may be conveyed as a digital signal. This is the resultant signal upon which the FIR filter may operate.  
           [0005]    A DSP transforms an input digital signal to an output digital signal. For the digital FIR filter, the transformation involves filtering out undesired portions of the received digital signal. An original analog signal may be represented as a sum of a plurality of sinusoids. Each sinusoid oscillates at a particular and unique frequency. Filtering is used to remove certain frequencies from an input signal while leaving other frequencies intact.  
           [0006]    A FIR filter is a device in which an input sample produces a finite number of output samples. After the finite number of samples expires, the FIR filter output is no longer affected by that particular input sample. Transversal filters, of which FIR filters may be a class, are filters in which a certain number of past samples are used along with the current sample to create each output sample.  
           [0007]    Programs executing on a FIR filter are real-time programs in that the instructions are manipulating a sample of a digital signal during the interval preceding the receipt of the next sample. If the program cannot complete manipulating a sample before the next sample is provided, then the program will eventually begin to “lose” samples. A lost sample does not get processed, and therefore the output signal of the FIR filter no longer contains all of the information from the input signal provided to the FIR filter. This potential for losing samples is reduced by a preferred embodiment of the present invention, while maintaining a required throughput rate.  
           [0008]    Besides considering a FIR filter&#39;s throughput, all design parameters have an associated cost. One important cost factor is the silicon area needed to “house” the FIR filter. Those that are manufactured on a relatively small silicon chip are less expensive than those requiring a large chip. Therefore, an easily manufacturable, small (low cost) FIR filter is desirable.  
           [0009]    Some features of FIR filters that are important to the design engineer include phase characteristics, stability (although FIR filters are inherently stable), and coefficient quantization effects. To be addressed by the designer are concerns dealing with finite word length and filter performance. When compared with other filter options such as infinite impulse response (IIR) filters, only FIR filters have the capability of providing a linear phase response and are inherently stable, i.e., the output of a FIR filter is a weighted finite sum of previous inputs. Additionally, the FIR filter uses a much lower order than a generic Nyquist filter to implement the required shape factor. FIR filters are subject to non-negligible inter-symbol interference (ISI), however.  
           [0010]    Coefficient quantization error occurs as a result of the need to approximate the ideal coefficient for the “finite precision” processors used in real systems. The result of coefficients being approximated is a deviation from ideal in the frequency response.  
           [0011]    Quantization error sources due to finite word length include:  
           [0012]    a) input/output (I/O) quantization,  
           [0013]    b) filter coefficient quantization,  
           [0014]    c) uncorrelated roundoff (truncation) noise,  
           [0015]    d) correlated roundoff (truncation) noise, and  
           [0016]    e) dynamic range constraints.  
           [0017]    Input noise associated with the analog-to-digital (A/D) conversion of continuous time input signals to discrete digital form and output noise associated with digital-to-analog conversion are inevitable in digital filters. Propagation of this noise is not inevitable, however.  
           [0018]    Uncorrelated roundoff errors most often occur as a result of multiplication errors. For example, in attempting to maintain accuracy for signals that are multiplied, only a finite length can be stored and the remainder is truncated, resulting in “multiplication” noise being propagated. Obviously, any method that minimizes the number of multiplication steps will also reduce noise and increase inherent accuracy.  
           [0019]    Correlated roundoff noise occurs when the products formed within a digital filter are truncated. These include the class of “overflow oscillations.” Overflows are caused by additions resulting in large amplitude oscillations. Correlated roundoff also causes “limit-cycle effect” or small-amplitude oscillations. For systems with adequate coefficient word length and dynamic range, this latter problem is negligible. However, both overflow and limit-cycle effects force the digital filter into non-linear operation.  
           [0020]    A typical example of a high-speed FIR with five or more coefficients is a Type II FIR. A Type II FIR is based on an array of costly Multiply and Add (MAC) accumulation stages. A conventional system using MAC is constrained to a minimum number of gates to achieve a given partial product accuracy. Digital implementation of an FIR filter is also limited by the maximum number of logic gates that can be inserted between reclocking stages established by the filter&#39;s clock cycle. Thus, for a given digital process, a minimum time to process is established by the propagation time through the critical path. To achieve very high speeds of processing, the critical path is broken into a number of shorter paths that can be addressed at higher clock speeds, i.e., processed within a short clock cycle. A preferred embodiment of the present invention implements an alternative using parallel processing of an interleaved signal.  
           [0021]    Some conventional high-speed systems employing FIR filters use an analog FIR filter placed before an analog-to-digital converter (ADC). This prevents the FIR filter&#39;s latency from accumulating in the sampled timing recovery loop. This method is inherently not well suited to digitally intensive designs.  
           [0022]    Some existing designs always include the FIR filter in the timing recovery loop, increasing latency ab initio, and decreasing stability of the embedded loops, both the timing recovery and gain loops, for example.  
           [0023]    Other designs bypass the FIR filter during acquisition but require the coefficients of the FIR filter to be symmetric in order to avoid a phase hit when switching back the FIR filter at the end of the acquisition period.  
           [0024]    In magneto-resistive (MR) heads using FIR filters, with their inherent response nonlinearities, this constraint is becoming even more unacceptable. There are more modern methods that achieve a fully digital solution, but these are extremely complex while covering a disproportionately large area on a silicon chip. In one design, discrete time analog values are entered in memory as are weights, some of which are set to zero to improve throughput. In this architecture neither pass through delay lines.  
           [0025]    There have been several novel approaches to achieving performance improvement of FIR filters. One involves converting a digital signal to log values, thus avoiding the use of multipliers. A second more traditional technique uses oversampling. Yet another approach uses variations of multiplexing, i.e., a multiplexed data stream is input to a tapped delay line and the filter provides a multiplexed output of alternated samples.  
           [0026]    For those data streams that have a high dynamic range, a method involving splitting the sampled input signal into two portions and addressing each separately in separate filters has been proposed. Of course, this doubles the number of operations and the hardware required.  
           [0027]    Some of the above introduce additional complexity not required in the preferred embodiments of the present invention while others may not be suitable for high-speed applications.  
           [0028]    In a magnetic disk data storage system, for example, information is recorded by inducing a pattern of magnetic variations on the disk, thus encoding the information. The magnetic variations are recorded along concentric circular tracks on the disk. The linear density with which the magnetic flux changes may be recorded along a track as well as the radial density of tracks on the disk is ever increasing.  
           [0029]    As the recording density is increased, however, the magnetic readback signal from the disk becomes more and more difficult to read and interpret due in part to inter-symbol interference (ISI). ISI results from process-time overlaps and the reduced spacing between neighboring magnetic flux patterns along an individual track as well as between those on adjacent tracks. For drives with interchangeable disks, in particular, each disk may introduce its own irregularities into the readback signal due to naturally occurring variations within manufacturing tolerances. Moreover, the irregularities are not uniform even over an individual disk, but depend to some degree on radial position.  
           [0030]    Increased data density has prompted the use of digital signal processing techniques to extract data from noisy, distorted or otherwise irregular readback signals. In one commonly used technique, a sequence of consecutive raw data samples read from the disk is passed through a filter that continuously monitors the expected error in the signal and corrects data accordingly. A popular class for this purpose comprises the adaptive FIR filters.  
           [0031]    These filters provide time-varying signal processing that adapts signal characteristics, in real time, to a sensed error measure. The characteristics are defined by time-varying coefficients, the values of which are adjusted at regular intervals, again in real time, in order to minimize cumulative error.  
           [0032]    An adaptive FIR filter may be thought of as having two parts: a filter structure that uses coefficients to modify data, and an adaptation circuit that updates the values of the coefficients. Existing implementations of filter structures and adaptation circuits are subject to design compromises.  
           [0033]    The dynamic power dissipated in conventional filter circuit implementations (assuming the use of CMOS ICs) is given by the relationship: 
             Pα∝C×V   2   ×f×N   Gate   (2) 
           [0034]    where:  
           [0035]    C=the average loading capacitance of a gate in the IC chip,  
           [0036]    V=the power supply voltage level,  
           [0037]    f=the operating frequency, and  
           [0038]    N gate =the number of gates that are switching at frequency, f.  
           [0039]    Improved performance is generally realized with a higher operating frequency, f, but comes at the expense of higher power dissipation levels.  
           [0040]    From Eqn. (2), power consumption also increases in proportion to the number of gates. A common IC embodiment of FIR filters is a tapped delay line, in which each of the coefficients characterizing the filter corresponds to a separate “tap” along a delay line. The number of gates goes up in proportion to the number of taps. The number of taps dictates the overall time delay for data (in Type I FIR structure) to pass through the filter and thus limits the operating frequency (data rate). To compensate for this delay, data pipelining is introduced to increase the FIR filter&#39;s operating frequency and the effective system throughput. However, pipelining calls for more gates, resulting in even greater power consumption.  
           [0041]    In addition to the power demand, conventional FIR filter coefficient adaptation circuits can introduce a bottleneck. To provide updated filter coefficients in successive clock cycles as new data are latched through, conventional adaptation circuits require computations to be performed within a single clock cycle. This makes it difficult to increase the overall speed of the data detection system as a whole and limits the circuitry and algorithms that may be employed for updates.  
           [0042]    Existing filter adaptation circuits also experience updated coefficients that wander from optimal when the coefficient adaptation process is operated simultaneously with a “decision-directed” timing recovery loop. This prevents consistent convergence to optimal values and impedes the performance.  
           [0043]    A “pipelining” method is normally used to achieve better FIR performance at high input data rates. The cost of using this method is increased latency, however. At very high speeds, such as are being seen with newer systems, conventional pipelining falls subject to the law of diminishing returns. The pipelining “overhead” now consumes a larger percentage of the benefits gained from higher clock speeds. The overhead consists of a required latching or reclocking stage for every pipelining command. Generally, the performance improvement for one level of pipelining is less than two while the hardware cost increase is greater than two. All the while this is occurring at the very high clock rate of the input data. A preferred embodiment of the present invention addresses this clock rate limitation.  
         SUMMARY  
         [0044]    A preferred embodiment of the present invention provides a system and method for increasing the speed of operation of FIR filters by “parallelizing” operation of the filter. By providing parallel paths for operation, without increasing hardware, in conjunction with adopting a high order Radix-N number encoding system, such as Radix-8, for encoding input data, the operations speed is doubled.  
           [0045]    By having each path of the parallel operation operate at half the input data rate, taking advantage of the slack time borrowing at less critical taps of the FIR filter during retiming, and providing for certain operations to be made common to each path, required silicon area on the chip is also significantly reduced.  
           [0046]    This is accomplished by de-interleaving the digitized input signal to the FIR filter proper and making available two paths for processing a single signal. See FIG. 1 for an example of a 5-tap FIR filter  100  in a preferred embodiment of the present invention. Data stream “samples” of the input signal DTI are provided to separate buses  107  and  110  in FIG. 1 a . For sake of easy identification the signal is said to be split into “odd” bits, processed on bus  110 , and “even” bits processed on bus  107 . If a higher order numbering system is used the encoder could be Radix-4, or preferably, Radix-8.  
           [0047]    FIR filter coefficients  105  of FIG. 1 a  are supplied to both paths from a memory device (not shown). A clock signal (not shown) is provided from a timing recovery loop (not shown) to insure that the “samples” are being taken at the appropriate instance. A processing period of 2T, where T is the clock rate of input data signal DTI, is made available by processing odd bits on the “rising edge” of the clock signal at delay lines  103  along bus  110  and  110   a . Of course, the opposite is the case for the even bits processed on the “falling edge” of the clock signal at delay lines  103  along buses  107  and  107   a . In a preferred embodiment of the present invention the delay lines  103  can be configured using simple latches (not shown) and incorporate a multiply and accumulate (MAC) function for each tap  101 . This alternating processing of even and odd bits on two different buses and at opposite levels of a clock signal provides the 2T processing period that differentiates a preferred embodiment of the present invention from existing designs, including those using separate FIR filters to accomplish the same end.  
           [0048]    Some of the salient advantages of the present invention are that it:  
           [0049]    significantly increases throughput.  
           [0050]    reduces required silicon area on the chip, considering the performance improvement.  
           [0051]    reduces overhead.  
           [0052]    reduces latency.  
           [0053]    reduces fabrication cost.  
           [0054]    uses simpler, more reliable components.  
           [0055]    uses a clock speed that is half the input data rate.  
           [0056]    facilitates borrowing of the slack time at non-critical taps.  
           [0057]    makes selected operations common to each path.  
           [0058]    applicable to both adaptive and fixed FIR filters. 
       
    
    
     BRIEF DESCRIPTION OF DRAWINGS  
       [0059]    [0059]FIG. 1 a  is a block diagram of the preferred embodiment employing a 5-tap FIR filter showing the optional input stream de-interleaver.  
         [0060]    [0060]FIG. 1 b  depicts a timing sequence of processing at a series of taps for an 5-tap FIR filter of a preferred embodiment of the present invention.  
         [0061]    [0061]FIG. 2 is a diagram of a representative parallel layout of a preferred embodiment employing a 5-tap FIR filter showing the optional input stream de-interleaver, Radix-N encoder, and output stream re-interleaver.  
         [0062]    [0062]FIG. 3 is a block diagram similar to FIG. 1 for a preferred embodiment of the present invention using an even number of taps (8) in the FIR filter.  
         [0063]    [0063]FIG. 4 is a detailed block diagram of the last tap of the FIR filter used in FIG. 1 with an option of the programmable reduction of the filter length by two taps.  
         [0064]    [0064]FIG. 5 a  depicts processing, coupled with use of the Radix-8 numbering system, at a single tap of a FIR filter employed in a preferred embodiment of the present invention  
         [0065]    [0065]FIG. 5 b  depicts timing, interleaving, and processing times, as well as slack times for the single tap of FIG. 5 a.    
         [0066]    [0066]FIG. 6 a  depicts timing sequence of a middle tap of a 5-tap FIR filter of a preferred embodiment of the present invention.  
         [0067]    [0067]FIG. 6 b  depicts timing sequences for parallel processing of even and odd bit streams for the middle tap of the 5-tap FIR filter of FIG. 6 a.    
         [0068]    [0068]FIG. 7 depicts timing sequences for parallel processing of even and odd bit streams in a 5-tap FIR filter employed in a preferred embodiment of the present invention.  
         [0069]    [0069]FIG. 8 depicts the efficient rectangular layout available for chip layout of an 8-tap embodiment of the present invention.  
         [0070]    [0070]FIG. 9 provides a sample timing sequence as in FIG. 7 , but using four-way processing of parallel circuits.  
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0071]    The class of FIR filters with k coefficients fulfills the relationship:  
               Y        (   n   )       =       ∑     j   =   0       k   -   1              C        (   f   )       ×     X        (     n   -   j     )                   (   3   )                               
 
         [0072]    Where:  
         [0073]    C(j)=coefficient of the filter with X(n) as an input sample and Y(n) as an output sample  
         [0074]    Y(n)=sum of the products over the interval, j=0 . . . k−1  
         [0075]    j=the index  
         [0076]    X(n)=the most recent value of the input sample  
         [0077]    X(n−j)=the delayed sample value associated with delay, j  
         [0078]    [0078]FIG. 1 a  shows a preferred embodiment of the FIR filter  100  that includes five taps, tap no.  3  shown as  101 , with Multiply-and-Accumulate operations carried out at each tap as shown for tap no.  3   101 . A coefficient C 3    105 , provided from an external memory (not shown), is multiplied with even bits of the 6-bit input signal (or its encoded representation) provided on buses  107  and  107   a  from de-interleaver  108  at multiplier  102 . The product from the multiplier  102  is accumulated and provided to delay line  103 , a latch in a preferred embodiment, from which it is transferred to the next tap&#39;s summer  104  and then accumulated. The output DTO_E from even delay element  112 , a flip-flop in a preferred embodiment, is then sent to an optional re-interleaver (not shown in FIG. 1 a ) where it is combined with the output DTO_O from the odd delay element  111 , a flip-flop in a preferred embodiment, of the parallel circuit handling odd bits along buses  107   a  and  110  of FIG. 1 a  for forwarding to a detector (not shown in FIG. 1 a ). As depicted in FIG. 1 a , the latches  103  along buses  107  and  107   a  are clocked with a logic LOW. The converse occurs along the buses  110  and  110   a  carrying odd bits in that the latches  103  on buses  110  and  110   a  are clocked with a logic HIGH.  
         [0079]    [0079]FIG. 1 b  depicts a timing sequence used with part of the series of taps for an 5-tap FIR filter, leading to the last tap (associated with c 0 ). Line  1  of FIG. 1 b  depicts the bit stream DTI. Line  2  of FIG. 1 b  shows the 2T clock on which each path  107  and  110  of FIG. 1 a  of the de-interleaved signal is timed. Line  3  of FIG. 1 b  shows the even bit stream of path  107  in FIG. 1 a  to be processed while Line  4  of FIG. 1 b  shows the odd bit stream of path  110  in FIG. 1 a  to be processed.  
         [0080]    Line  5  of FIG. 1 b  shows shaded areas at the output of tap  5 , during which time a bit stream is most likely being processed. Looking down the slanted lines  112  drawn on this figure provides a view of the “sequential ripple effect” available for borrowing in a preferred embodiment of the present invention. Lines  6  through  10  of FIG. 1 b  provide timing sequence for the outputs by tap for each tap associated with coefficients 4 through 0. In addition, the slanted shaded areas provide a sense of the “carry propagation” from the LSB to an MSB.  
         [0081]    [0081]FIG. 2 shows the de-interleaving stage and separate even and odd encoders lumped as  209  for the odd and even bit streams transported on paths  201  and  202 , respectively. The filter  200  has five cascaded taps  203 . The five taps  203  are associated with coefficients, c 0  through c 4 ,  204  provided by a coefficient memory (not shown), to be multiplied internally in taps  203 . Also shown in FIG. 2 is the optional re-interleaver  210  for combining signals DTO_E and DTO_O, outputs from paths  202  and  201 , respectively, into DTO, the output from re-interleaver  210  that is further provided to a detector (not shown).  
         [0082]    A preferred embodiment of the present invention uses latches rather than flip-flops at each tap  203 , with the possible exception of the last tap  111  and  112  in FIG. 1 a  of each path (that may use flip-flops instead of latches without performance degradation). The advantage of using latches instead of flip-flops is faster operation, smaller size, and allowed borrowing between taps.  
         [0083]    [0083]FIG. 3 shows a preferred embodiment of the present invention using an 8-tap FIR filter  300 . Note that the first latches  301  and  302  initiate the processing beginning with a different path than that of the odd numbered 5-tap filter of FIG. 1. FIG. 3 also does not show the optional de-interleaving and re-interleaving stages  209  and  210  as shown in FIG.2.  
         [0084]    [0084]FIG. 4 shows an expanded view of the last tap latching operation prior to output of the separate odd and even bits for an even number of taps (in this case 8) as used with a FIR filter. Note the use of flip-flops  403  and  404  in the final stage and that single flip-flops could be used for latches  403  and  404  if the optional reduction from 8 taps to 6 taps (in this case) is not implemented.  
         [0085]    A single tap of a FIR filter is illustrated in FIG. 5 a  as a summary of actions at each tap of a FIR filter when using a preferred embodiment of the present invention. The odd bits are placed on path  501 , latched on logic LOW of the clock as provided on path  503 , and the even bits are placed on path  502 , clocked on path  504  with a logic HIGH. The odd and even 6-bit signals are then fed to encoders  505  (odd bits) and  506  (even bits), along paths  501  and  502  respectively, for encoding in a high order numbering system such as Radix-8. From each encoder  505  and  506 , each signal stream (odd and even bits) is then split into the 9 higher order bits (EH)  507  and  509  and 8 lower order bits (EL)  508  and  510  of the 17-bit encoded signal. From the encoders  505  and  506 , the odd and even higher and lower order bit streams  507  through  510  control the multiplexed inputs of the tap&#39;s coefficients  511  in pairs of multiplexers  512  and  513 , respectively. In turn, these mulitplexed product outputs, B_E  514 , A_E  515 , B_O  516  and A_O  517  are added together appropriately with the odd and even bit streams of the previous tap values X_E  518  and X_O  519  to form the tap outputs Y_E  520 , clocked with a logic LOW, and  521 , clocked with a logic HIGH, provided as tap output signal S_E on path  522  and signal S_O on path  523 .  
         [0086]    [0086]FIG. 5 b  provides yet another picture of timing. Line  1  of FIG. 5 b  shows the “natural sampling frequency” CLK using square samples of period T. Line  2  of FIG. 5 b  depicts the input data bit stream signal DTI emerging from an ADC clocked with a period of T. The DTI_E bit stream of line  4  might be sampled by the rising edge of a 2T clock and the other DTI_O line  5  the falling edge of the same 2T clock.  
         [0087]    The shaded areas of Line  6  of FIG. 5 b , output, S_E, and Line  7  of FIG. 5 b , output, S_O, depict an approximation of the time actually needed for processing within the processing period available, 2T, for each tap output Line  6  of FIG. 5 b , output, S_E, and Line  7  of FIG. 5 b , output, S_O.  
         [0088]    [0088]FIG. 6 a  depicts timing occurrence at a single tap (no.  2 , whose coefficient is c 2 ,) of a 5-tap FIR filter of a preferred embodiment. The portion carrying the odd bit stream  601  is shown paralleling the portion carrying the even bit stream  602 . Note that latches are logic configured oppositely for each bit stream  601  and  602 .  
         [0089]    [0089]FIG. 6 b  shows the timing sequence for the single parallel taps of FIG. 6 a . Line  1  of FIG. 6 b  shows clock period, 2T, for each path. Line  2  of FIG. 6 b  shows the signal DTI_E along the even bit stream&#39;s path  602  in FIG. 6 a  and Line  3  of FIG. 6 b  shows the signal DTI_O along the odd bit stream&#39;s path  601  in FIG. 6 a  . Lines  4  and  5  of FIG. 6 b  provides a comparison of time available for processing with time most likely needed for processing for the signals S 3 _E and S 3 _O approaching the summer  604  in each of paths  601  and  602 , i.e., the shaded areas. Likewise, Lines  6  and  7  of FIG. 6 b  provide a comparison of time available for processing with time most likely needed for processing for the signals S 2 _E and S 2 _O approaching the summer for the next tap, tap  2  (not shown in FIG. 6 a  ) in each of paths  601  and  602 , i.e., the shaded areas.  
         [0090]    [0090]FIG. 7 shows a timing diagram for a 5-tap preferred embodiment of the present invention. For line number  701  of FIG. 7, x i &#39;s are the bit sample values at i while the c j &#39;s are the coefficient values at tap j, where j=0, 1, 2, 3, 4 for the 5-tap example of FIG. 7.  
         [0091]    Now, comparing line  703  of FIG. 7 with line numbers  701  and  702  of FIG. 7, the overlap of processing the x 1 c 1  partial product while the x 0 c 0  operation is being completed is evident. Even samples (bits) are processed within a clock period of 2T in lines  702 ,  704 ,  706 ,  708 , and  710  of FIG. 7, while odd samples (bits) are processed within a clock period of 2T in Lines  703 ,  705 ,  707 ,  709 , and  711  of FIG. 7. The overall process, including de-interleaving and re-interleaving, takes little more time than a straightforward single path full “natural sampling rate” processing, while allowing a higher natural data rate (e.g., faster rotation of the disk or higher density on the disk, or both). Further it does not require separate filter or processing sections be added to the silicon area.  
         [0092]    The key point to note is that the least significant bit (LSB) can be used as soon as the latch opens at a tap, thus completing “pre-calculation” by the time the MSB arrives from the previous tap. Since there are now available two full “natural sampling rate” clock cycles for multiplication and accumulation of the partial products, less than one full cycle is needed for accumulation with the previous tap. Note line  702  of FIG. 7 compared to the natural sampling rate of samples on line  701  of FIG. 7. There are fully two “natural sampling rate” clock cycles in which to perform the necessary multiplication and accumulation of c 0  times x 0 .  
         [0093]    [0093]FIG. 8 depicts an advantage of a preferred embodiment of the present invention when laying out integrated circuits (ICs). The preference is for regular and rectangular layouts. This preferred embodiment of the present invention readily lends itself to a rectangular layout. FIG. 8 shows the products accumulating at the 8 taps of an 8-tap FIR filter  800  of a preferred embodiment of the present invention with the encoded data even and odd bit streams  801  and  802 , respectively, laid side by side and the encoders  803  and  804 , respectively, orthogonal thereto with the coefficient sources  805  running between the two parallel processing paths. The products along the top horizontal half  806  are latched when the clock is logic LOW, while those along the bottom horizontal half  807  are latched when the clock is logic HIGH.  
         [0094]    [0094]FIG. 9 shows another preferred embodiment of the present invention for a 3-tap FIR so as to illustrate the concept only. A preferred embodiment is not limited to parallelism by a single pair. In FIG. 9, a four-way parallelism can be seen laid out for taps  0 ,  1 , and  2  of FIG. 9, expanding on the concept shown in FIG. 7.  
         [0095]    The foregoing describes the salient features of the present invention&#39;s parallel structure and modified architecture, and should not be interpreted as limiting the application of, method of operation, or uses for the present invention to that specified in the foregoing. While the invention has been shown with specific components and circuits, and further described with regard to specific number system types, it will be understood by those skilled in the art that various other changes in the selection of components and use with different combinations of circuit components, or other details may be changed without departing from the spirit and scope of the invention.