diff --git a/ifcs2018_journal.tex b/ifcs2018_journal.tex index f2330f0..c473f0f 100644 --- a/ifcs2018_journal.tex +++ b/ifcs2018_journal.tex @@ -1,9 +1,9 @@ -% fusionner max rejection a surface donnee v.s minimiser surface a rejection donnee -% demontrer comment la quantification rejette du bruit vers les hautes frequences => 6 dB de +% fusionner max rejection a surface donnee v.s minimiser surface a rejection donnee +% demontrer comment la quantification rejette du bruit vers les hautes frequences => 6 dB de % rejection par bit et perte si moins de bits que rejection/6 % developper programme lineaire en incluant le decalage de bits -% insister que avant on etait synthetisable mais pas implementable, alors que maintenant on -% implemente et on demontre que ca tourne +% insister que avant on etait synthetisable mais pas implementable, alors que maintenant on +% implemente et on demontre que ca tourne % gwen : pourquoi le FIR est desormais implementable et ne l'etait pas meme sur zedboard->new FIR ? % Gwen : peut-on faire un vrai banc de bruit de phase avec ce FIR, ie ajouter ADC, NCO et mixer % (zedboard ou redpit) @@ -169,7 +169,6 @@ We will apply our methodology on very simple DSP chain. We generate a digital si thanks at generator of Pseudo-Random Number (PRN) or thanks at an Analog to Digital Converter (ADC). Once we have a digital signal, we filter it to decrease the noise level. Finally we stored some burst of filtered samples before post-processing it. -% TODO: faire un schéma In this particular case, we want optimize the filtering step to have the best noise rejection for constrain number of resource or to have the minimal resources consumption for a given rejection objective. @@ -250,8 +249,6 @@ the FIR magnitude exhibits two parts. \draw[dashed] (12,8) -- (16,8) ; \end{tikzpicture} - -% \includegraphics[width=.5\linewidth]{images/fir_magnitude} \caption{Shape of the filter transmitted power $P$ as a function of frequency $f$: the passband is considered to occupy the initial 40\% of the Nyquist frequency range, the stopband the last 40\%, allowing 20\% transition width.} @@ -276,6 +273,22 @@ A second criterion considers the maximum rejection within the stopband minus the \label{fig:custom_criterion} \end{figure} +Thanks to this criterion we are able to automatically generate lot of fir coefficients +and estimate their rejection. The figure~\ref{fig:rejection_pyramid} exhibits the +rejection in function of the number of coefficients and their number of bits. +We can observe it looks like a pyramid so the edge represents the best +coefficient set. Indeed if we choose a number of coefficients, increasing the number +of bits over the edge will not improve the rejection. Conversely when we choose +a number of bits, too much increase the number of coefficients will not improve +the rejection. Hence the best coefficient set are on the edge of pyramid. + +\begin{figure} +\centering +\includegraphics[width=\linewidth]{images/rejection_pyramid} +\caption{Rejection as a function of number of coefficients and number of bits} +\label{fig:rejection_pyramid} +\end{figure} + Although we have a efficient criterion to estimate the rejection of one set of coefficient we have a problem when we sum two or more criterion. 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