Constructing a lowpass digital differentiator such that maximum error is $n$ dB for passband - Signal Processing Stack Exchange most recent 30 from dsp.stackexchange.com 2019-11-12T16:03:28Z https://dsp.stackexchange.com/feeds/question/54575 https://creativecommons.org/licenses/by-sa/4.0/rdf https://dsp.stackexchange.com/q/54575 0 Constructing a lowpass digital differentiator such that maximum error is $n$ dB for passband Jacob Macherov https://dsp.stackexchange.com/users/39838 2019-01-03T09:59:47Z 2019-01-03T09:59:47Z <p>I want to construct a lowpass digital differentiator with uniform-interval samples such that error from ideal differentiator is <span class="math-container">$n$</span> dB in magnitude at maximum for the passband up to frequency <span class="math-container">$\omega_c$</span>. (The reference for dB here is amplitude of <span class="math-container">$1$</span>.)</p> <p>This error magnitude is not magnitude of frequency response of a lowpass differentiator subtracted from magnitude of frequency response of an ideal differentiator. The error magnitude literally is magnitude of the subtraction of frequency response of a lowpass differentiator from frequency response of the ideal differentiator.</p> <p>Also, I want the lowpass differentiator to roll off close to zero for frequency response of frequency from <span class="math-container">$\omega_c$</span> to <span class="math-container">$\pi$</span>. </p> <p>It is hard to find an article that shows how to construct such a filter as a function of <span class="math-container">$n$</span> and <span class="math-container">$\omega_c$</span>. Can anyone show me any reference? There surely must be such a filter construction. I do not care if it is IIR or FIR filter, Savitzky-Golay or not, though the error magnitude restriction seems to favor zero-phase filters such as Savitzky-Golay.</p>