Cascade of Filters Solver

This software is a solver to choose the best configuration of FIR filters to perform a cascade of filters. Assuming a set of filters has been characterized and a cost function has been computed for each filter (number of coefficients and number of bits describing each coefficient), then the software will identify the optimum set of filters meeting a target, either of performance or resource usage.

Dependency

• Digital Signal Processing Simulator Only for build tools
• Gurobi v8.0.1 & 9.0.1 (Download and Licences: Gurobi Optimizer)

As described at https://www.gurobi.com/documentation/8.1/quickstart_linux/software_installation_guid.html, define the appropriate environment variables:

export GUROBI_HOME=/somewhere/gurobi901/linux64
export PATH=$PATH:$GUROBI_HOME/bin
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$GUROBI_HOME/lib

then compile manually the static library

cd $GUROBI_HOME/src/build
make
cp libgurobi_c++.a ../../lib

Coefficients file structure

To add your coefficients set, your file must be in binary format with:

• unsigned int 16 bits for the number of bits
• unsigned int 16 bits for the number of coefficients
• floating point double precision for the rejection

We provide the GNU Octave scripts to generate our filters coefficients in tools/.

CMake option

• LP_FIX_REJECTION_CONSTRAINT: Fix the rejection constraints (see Notes).
• LP_TOOLS: Compile the tool to simulate a cascaded filter

Compilation

git clone https://github.com/oscimp/cascade_filters_solver.git
git submodule update --init
mkdir build
cd build
cmake ..
make

Execution

# To maximize rejection
# ./fir-solver NUMBER_STAGE AREA_MAX FILTERS_JSON OUTPUT_FORMAT
./fir-solver --max_rej 3 500 ../fir_data/filters.json example

Will produce the results into example folder for 3 stages of filters with 500 a.u. of area.

# To minimize area
# ./fir-solver NUMBER_STAGE REJECTION_MIN FILTERS_JSON OUTPUT_FORMAT
./fir-solver --min_area 3 80 ../fir_data/filters.json example

Will be produce the results into example folder for 3 stages of filters with 80 dB of rejection.

The resuting files are

example.m example.sh example.tcl gurobi.lp sol.txt

with most significantly the Vivado tcl script for synthesizing the resulting FIR cascade using the OscimpDigital tools, the GNU/Octave file for simulating the filter cascade behaviour, and the bash script for automating the synthesis and running the resulting bitstream on a 14-bit Red Pitaya.

Notes

• The solver can produce some pessimistic result when the optimal number of stages is lower than the upper limit of considered stages. In such a case, take the best previous solution. You can also compile our project with LP_FIX_REJECTION_CONSTRAINT option but the solver will be twice slower.