diff --git a/ifcs2018_proceeding.tex b/ifcs2018_proceeding.tex index 368a810..9bc6ca6 100644 --- a/ifcs2018_proceeding.tex +++ b/ifcs2018_proceeding.tex @@ -119,7 +119,7 @@ will result in some precision loss. \begin{figure}[h!tb] \includegraphics[width=\linewidth]{images/demo_filtre} \caption{Impact of the quantization resolution of the coefficients: the quantization is -set to 6~bits -- with the horizontal black lines indicating $\pm$1 least significant bit -- setting +set to 6~bits -- with the horizontal black lines indicating $\pm$1 least significant bit -- setting the 30~first and 30~last coefficients out of the initial 128~band-pass filter coefficients to 0 (red dots).} \label{float_vs_int} @@ -187,7 +187,7 @@ constraints in the initial statement of the problem leave little room for findin \begin{figure}[h!tb] \begin{center} \includegraphics[width=.5\linewidth]{schema2} -\caption{Shape of the filter transmitted power $P$ as a function of frequency: +\caption{Shape of the filter transmitted power $P$ as a function of frequency: the bandpass BP is considered to occupy the initial 40\% of the Nyquist frequency range, the stopband the last 40\%, allowing 20\% transition width.} @@ -207,11 +207,11 @@ Following these considerations, the model is expressed as: To explain the system \ref{model-FIR}, $\mathcal{R}_i$ represents the rejection of depending on $N_i$ and $C_i$, $\mathcal{A}$ is a theoretical area occupation of the processing block on the FPGA, and $\Delta_i$ is the total rejection for the current stage $i$. Since the function $\mathcal{F}$ cannot be explictly expressed, we run simulations to determine the rejection depending -on $N_i$ and $C_i$. However, selecting the right filter requires a clear definition of the rejection criterion. Selecting an -incorrect criterion will lead the linear program solver to produce a solution which might not meet the user requirements. +on $N_i$ and $C_i$. However, selecting the right filter requires a clear definition of the rejection criterion. Selecting an +incorrect criterion will lead the linear program solver to produce a solution which might not meet the user requirements. Hence, amongst various criteria including the mean or median value of the FIR response in the stopband as will be illustrated lated (section \ref{median}), we have designed -a criterion aimed at avoiding ripples in the passband and considering the maximum of the FIR spectral response in the stopband +a criterion aimed at avoiding ripples in the passband and considering the maximum of the FIR spectral response in the stopband (Fig. \ref{rejection-shape}). The bandpass criterion is defined as the sum of the absolute values of the spectral response in the bandpass, reminiscent of a standard deviation of the spectral response: this criterion must be minimized to avoid ripples in the passband. The stopband transfer function maximum must also be minimized in order to improve the filter @@ -329,7 +329,7 @@ with no consideration for the ripples in the bandpass. The results of the optimi in these cases, are shown in Figs. \ref{compare-mean} and \ref{compare-median}. \begin{figure}[h!tb] -\includegraphics[width=\linewidth]{images/fir-mono-vs-fir-series-noise-fixe-mean.pdf} +\includegraphics[width=\linewidth]{images/fir-mono-vs-fir-series-noise-fixe-mean-light.pdf} \caption{Comparison of the rejection capability between a series of FIR and a monolithic FIR with a cutoff frequency set at half the Nyquist frequency.} \label{compare-mean} @@ -347,7 +347,7 @@ the reasons stated previously and much poorer than those found with the maximum selected earlier (Fig. \ref{compare-fir}). \begin{figure}[h!tb] -\includegraphics[width=\linewidth]{images/fir-mono-vs-fir-series-noise-fixe-median.pdf} +\includegraphics[width=\linewidth]{images/fir-mono-vs-fir-series-noise-fixe-median-light.pdf} \caption{Comparison of the rejection capability between a series of FIR and a monolithic FIR with a cutoff frequency set at half the Nyquist frequency.} 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