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The original use appears to be in this paper, which is referenced in your linked paper. The part that's missing in your explanation is explained in that paper: Specifically, the notch-filtered signal is not removed from the original signal, but from another processing of it: the ANC-de-noised version of it. Otherwise, you are correct, you might just as well ...

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I'm not quite sure what you're asking, but it looks like you have three second order sections. The [1.0000 0 -1.0000] are the numerators and the remaining numbers on each line are the denominators. Does that help? If I do [b,a] = sos2tf(filter.sosMatrix) freqz(b,a) then I get this plot, which looks right to me, based on your plot above. I've not used the ...

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How can i get the difference equation from the impulse response That's easy enough to do  y[k] = \sum_{n=-\infty}^\infty x[k-n] \cdot \left[ \frac{2 f_1}{F_s} \left ( {\rm sinc}(2 \pi f_1 n T_s) (g_1-g_2) \right )+ \frac{2 f_2}{F_s} \left ( {\rm sinc}(2 \pi f_2 n T_s) (g_2-g_3) \right )+ \frac{2}{F_s} \left ( f_3 g_3 {\rm sinc}(2 \pi f_3 n T_s)-f_0\...

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Big simplification can be done on equations of first answer (fraction-saving) as follows: Original: temp = afixedpoint∗x[n] + (32768-afixedpoint)∗y[n-1] - error[n-1] y[n] = round(temp/32768) error[n] = y[n]∗32768−temp Proposed: temp = temp + afixedpoint*(x[n]-y[n-1]) y[n] = round(temp/32768) Coded was tested giving same results Proof The (32768-a) term in ...

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