From 8a48cee5806b39457cd429dc2c488a9eaea99b0e Mon Sep 17 00:00:00 2001 From: Arthur HUGEAT Date: Mon, 21 May 2018 10:55:46 +0200 Subject: [PATCH] Rajout de la definition de D_i --- ifcs2018_proceeding.tex | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) diff --git a/ifcs2018_proceeding.tex b/ifcs2018_proceeding.tex index deb6bb6..ba377ce 100644 --- a/ifcs2018_proceeding.tex +++ b/ifcs2018_proceeding.tex @@ -171,11 +171,12 @@ computational resources: optimizing some criteria within finite, limited resources indeed matches the definition of a classical optimization problem. Specifically the degrees of freedom when addressing the problem of replacing the single monolithic -FIR with a cascade of optimized filters are the number of coefficients $N_i$ of each filter $i$ and -the number of bits $C_i$ representing the coefficients. Because each FIR in the chain is fed the output of the previous stage, +FIR with a cascade of optimized filters are the number of coefficients $N_i$ of each filter $i$, +the number of bits $C_i$ representing the coefficients and the number of bits $D_i$ representing +-the data fed to the filter. Because each FIR in the chain is fed the output of the previous stage, the optimization of the complete processing chain within a constrained resource environment is not trivial. The resource occupation of a FIR filter is considered as $C_i \times N_i$ which aims -at approximating the number of bits needed in a worst case condition to represent the output of the +at approximating the number of bits needed in a worst case condition to represent the output of the FIR. Indeed, the number of bits generated by the FIR is $(C_i+D_i)\times\log_2(N_i)$ with $D_i$ the number of bits needed to represent the data $x_k$ generated by the previous stage, but the $\log$ function is avoided for its incompatibility with a linear programming description, and @@ -231,9 +232,9 @@ rejection capability. Weighing these two criteria allows designing the linear pr \label{noise-rejection} \end{figure} -The objective function maximizes the noise rejection ($\max(\Delta_{i_{\max}})$) while keeping resource -occupation below a user-defined threshold, or as will be discussed here, aims at minimizing the area -needed to reach a given rejection ($\min(S_q)$ in the forthcoming discussion, Eqs. \ref{cstr_size} +The objective function maximizes the noise rejection ($\max(\Delta_{i_{\max}})$) while keeping resource +occupation below a user-defined threshold, or as will be discussed here, aims at minimizing the area +needed to reach a given rejection ($\min(S_q)$ in the forthcoming discussion, Eqs. \ref{cstr_size} and \ref{cstr_rejection}). The MILP solver is allowed to choose the number of successive filters, within an upper bound. The last problem is to model the noise rejection. Since filter noise rejection capability is not modeled with linear equations, a look-up-table is generated -- 2.16.4