*MDNAP* is a comprehensive CAD tool for discrete-domain
1, 2 or
3-dimensional filters and in a limited capacity for
continuous-domain filters. Based on the Signal-Flow
Graph (SFG) description of the filter,
*MDNAP* is capable of performing frequency-domain
and sensitivity
analysis for both discrete-domain and continuous-domain
filters and spatiotemporal-domain analysis for
discrete-domain filters. In addition to a SFG description
of the filter, *MDNAP* offers a means
for incorporating fixed-point precision of filter coefficients
and node variables.

**Frequency-domain Analysis:**

- fully symbolic state-space difference equation
- fully symbolic transfer function
- 1, 2 or 3-D frequency response
- rendering of 3-D frequency response as shaded, solid contour volumes (Example: 3D Lowpass with three equi-gain surfaces, 256x256 19k GIF)

**Sensitivity Analysis:**

- symbolic first-order sensitivity function (of the transfer function w.r.t. any coefficient)
- 1, 2 or 3-D first-order sensitivity (of the frequency response w.r.t. any coefficient)
- rendering of 3-D sensitivity as shaded, solid contour volumes

**Spatiotemporal-domain Analysis** of
discrete-domain filters:

- scheduling information for parallel and sequential implementations
- hardware simulation with control over:
- quantization methods
- overflow methods
- boundary conditions
- processing orders

- both, delay and advance operators supported

**Linear-Trajectory Filter Example:**

Linear-trajectory (LT) 3-D filters are capable of being tuned to pass
objects moving at a particular velocity in a video sequence.
Here is an example of using *MDNAP*
to examine quantization effects in a particular implementation of
a LT filter.

**Beer cases**

One of the critical parameters in filter hardware implementations is data wordlength, which determines the precision and dynamic range of the signals. Choosing a too-short data wordlength can result in filter instability; choosing a too-long data wordlength makes the hardware too expensive.

The input sequence (256x240, 53 frames, MPEG, 499k) was filmed at a local brewery. Note that it contains several objects moving with different velocities.

A filter structure capable of implementing a LT filter was designed, and the coefficients were tuned to pass the diagonally-moving beer cases. In order to investigate the effects of changing wordlength, a simulation (256x240, 53 frames, MPEG, 120k) of a 16-bit hardware implementation of this filter was performed, and the filter was found to perform very well. However, a simulation (256x240, 11 frames, MPEG, 44k) of an 8-bit implementation showed that filter becomes unstable.

See this paper for more details.

*MDNAP* source is written in *C* and, to date,
has been compiled for
*SUN SPARCstations*, *NeXTstations* and DOS-based
*Intel* 386-and-up machines. *MDNAP* is not
public software. If
you are interested, contact
me
or
Dr. L.T. Bruton.