2 IIR6
         Name: IIR6.ASM
         Type: Assembler Macro
      Version: 1.0
 Date Entered:  15-Jul-87
  Last Change:  15-Jul-87

  Description: Arbitrary Order Direct Canonic Filter

 This macro implements a direct form filter with a minimum
 number of delay elements using looped code to allow a filter
 of arbitrary order.

     Input                w(n)
 x(n) >----(+)--------------------------(+)-----> Output
            ^              |             ^        y(n)
            |     a(1)    1/z    b(1)    |
           (+)<-- 0.8 -----|---- 0.1 -->(+)
            ^              v             ^
            |     a(2)    1/z    b(2)    |
           (+)<-- -0.7 ----|---- 0.2 -->(+)
            ^              v             ^
            |     a(3)    1/z    b(3)    |
           (+)<-- 0.6  ----|---- 0.3 -->(+)
            ^              v             ^
            |     a(4)    1/z    b(4)    |
           (+)<-- -0.5 ----|---- 0.4 -->(+)
            ^              v             ^
            |     a(5)    1/z    b(5)    |
           (+)<-- 0.4  ----|---- 0.5 -->(+)

                 Direct Form Canonic Filter

  This filter is described by the difference equation:

 y(n)  =
 x(n)  +  a(1)y(n-1)  +  a(2)y(n-2)  +  ...  +  a(r)y(n-r) +
          b(1)x(n-1)  +  b(2)x(n-2)  +  ...  +  b(r)x(n-r)

 with z transform:

                      -1         -2               -r
   Y(z)      1 + b(1)z    + b(2)z   +  ... + b(r)z
 -------  =  --------------------------------------
   X(z)               -1          -2              -r
            1 - a(1)z    - a(2)z      ... - a(r)z

  where:
    x(n)  = input sample at time nT
    y(n)  = output of the filter at time nT
    a(n)  = filter coefficient n (magnitude less than one)
    b(n)  = filter coefficient n (magnitude less than one)
      T   = sample period
      r   = order of filter

  This filter can be described in terms of its "order" where the
  order  of  the filter refers to the highest power of z in the
  polynomial describing the system.  In this example, the filter
  is a 5th order filter.

  The memory map for this filter is shown below.   

          r0          m0=order  (=5, mod 6)
          |
          v
        -------------------------------------------
   X:   |      |      |      |      |      |      | Filter States
        |w(n)  |w(n-1)|w(n-2)|w(n-3)|w(n-4)|w(n-5)|
        -------------------------------------------
             

           r4       m4=2*order-1  (=9, mod 10)
           |
           v
         ------------------------------------
    Y:   |  a(1)| a(2) | a(3) | a(4) | a(5) |
         |  .8  | -.7  |  .6  | -.5  |  .4  |
         ------------------------------------


         ------------------------------------
         |  b(1)| b(2) | b(3) | b(4) | b(5) |
         |  .1  | .2   | .3   | .4   | .5   |
         ------------------------------------
            
      Memory Map for the Direct Form Canonic Filter

  For an example of how to use this filter see the
  test program IIR6T.ASM