Lattice Allpass Structures (Digital Filter Design Toolkit)

For an allpass filter, you can implement one of the following section types of lattice allpass filter structures:

• Basic section type
• One multiplier section type
• Normalized section type

The following figure represents the basic section type of a lattice allpass filter structure. Refer to the Understanding Filter Structure Graphs topic for information that helps you read and understand a filter structure graph.

The total number of the lattice reflection coefficients k is M, where M is the filter order. The total number of multipliers is 2M.

The following figure represents the one multiplier section type of a lattice allpass filter structure.

The total number of the lattice reflection coefficients k is M, which is the same as in the basic section type. However, the total number of multipliers is only M, which is half the number that the basic section type requires. Therefore, the one multiplier section type of a lattice allpass structure involves fewer multipliers than other section types. Fewer multipliers require less hardware resources.

The following figure represents the normalized section type of a lattice allpass filter structure.

You can derive k' from k in the normalized section type by using the formula .

One advantage of the normalized section type structure is that this structure automatically scales the internal signals in each lattice section. Unfortunately, scaling the internal signals increases the implementation complexity.