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If the filter has a fixed order then increasing the sampling rate will make its response scale with frequency, thus the transition width increases relative to the sampling frequency. For example: if $f_s=1\;\mathrm{kHz}$ and $\omega_{tw}=10\;\mathrm{Hz}$ for a given order then keeping the order and increasing $f_s$ tenfold will make $\omega_{tw}$ increase ...


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