Time-Varying Direct-Form II Transpose Filter (DSP Blockset)

Time-Varying Direct-Form II Transpose Filter

Apply a variable IIR filter to the input.

Library

Filter Realizations, in Filtering

Description

The Time-Varying Direct-Form II Transpose Filter block is a version of the Direct-Form II Transpose Filter block whose filter coefficients can be updated during the simulation. The block applies a transposed direct-form II IIR filter to the top input (In), which must be a discrete-time signal.

This is a canonical form that has the minimum number of delay elements. The filter order is max(m,n)-1.

The block's two lower inputs (Num and Den) specify the filter's transfer function,

By default the filter coefficients are normalized by a₁. To prevent normalization by a₁, deselect the Support non-normalized filters check box.

The Filter type parameter specifies whether the filter is an all-zero (FIR or MA) filter, all-pole (AR) filter, or pole-zero (IIR or ARMA) filter:

Pole-zero

The block accepts inputs for both the numerator (Num) and denominator (Den) vectors.

Input Num is a vector of numerator coefficients,

[b(1) b(2) ... b(m)]

and input Den is a vector of denominator coefficients,

[a(1) a(2) ... a(n)]

All-zero

The block accepts only the numerator vector (Num). The denominator of the all-zero filter is 1.

All-pole

The block accepts only the denominator vector (Den). The numerator of the all-pole filter is 1.

For any of these designs, the coefficient vector inputs can change over time to alter the filter's response characteristics during the simulation.

Initial Conditions

In its default form, the filter initializes the internal filter states to zero, which is equivalent to assuming past inputs and outputs are zero. The block also accepts optional nonzero initial conditions for the filter delays. Note that the number of filter states (delay elements) per input channel is

max(m,n)-1

The Initial conditions parameter may take one of four forms:

Empty matrix

The empty matrix, [], causes a zero (0) initial condition to be applied to all delay elements in each filter channel.

Scalar

The scalar value is copied to all delay elements in each filter channel. Note that a value of zero is equivalent to setting the Initial conditions parameter to the empty matrix, [].

Vector

The vector has a length equal to the number of delay elements in each filter channel, max(m,n)-1, and specifies a unique initial condition for each delay element in the filter channel. This vector of initial conditions is applied to each filter channel.

Matrix

The matrix specifies a unique initial condition for each delay element, and can specify different initial conditions for each filter channel. The matrix must have the same number of rows as the number of delay elements in the filter, max(m,n)-1, and must have one column per filter channel.

The Frame-based inputs parameter allows you to choose between sample-based and frame-based operation.

Sample-Based Operation

When the check box is not selected (default), the block assumes that the input is a 1-by-N sample vector or M-by-N sample matrix. Each of the N vector elements (or M*N matrix elements) is treated as an independent channel, and the block filters each channel over time.

Frame-Based Operation

When the Frame-based inputs check box is selected, the block assumes that the input is an M-by-N frame matrix. Each of the N frames in the matrix contains M sequential time samples from an independent signal. The illustration below shows a 6-by-4 matrix input:

The Number of channels parameter specifies the number of independent channels (columns), N, in the matrix, and the block filters each channel independently over time. Frame-based operation provides substantial increases in throughput rates, at the expense of greater model latency.

In frame-based operation, the Filter update rate parameter determines how frequently the block updates the filter coefficients (i.e., how often it checks the Num and Den inputs). There are two available options:

One filter per sample time

The block updates the filter coefficients (from inputs Num and Den) for each individual scalar sample in the framed input. This means that each output sample could potentially be computed by a different filter (assuming that Num and Den inputs are updated frequently enough).

One filter per frame time

The block updates the filter coefficients (from inputs Num and Den) for each new input frame, rather than at each sample in the frame. This means that each output sample in a given frame is a result of an identical filtering process.

Note
If you expect to generate code for the Time-Varying Direct-Form II Transpose Filter block using the Real-Time Workshop, you should ensure that inputs are contiguous in memory. See the Contiguous Copy block for more information.

Dialog Box

Filter Type: The type of filter to apply: ARMA, MA, or AR. The Num and Den input ports are enabled or disabled appropriately.
Initial conditions: The filter's initial conditions, a scalar, vector, or matrix.
Support non-normalized filters: Normalizes the filter by a₁ when selected.
Frame-based inputs: Selects frame-based operation.
Number of channels: For frame-based operation, the number of channels (columns) in the input matrix.
Filter update rate: The frequency with which the block updates the filter coefficients; once per sample, or once per frame.

References

Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1989.

Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.