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Your diagram looks correct. Let's call the transfer function in the feedback loop $G(z)$. Consider the signal $w[n]$ at the input to the delay line. Its $\mathcal{Z}$-transform satisfies $$W(z)=X(z)+G(z)Y(z)\tag{1}$$ where $X(z)$ and $Y(z)$ are the $\mathcal{Z}$-transforms of the input and output sequences, respectively. The output is just a delayed ...

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The simplest solution is probably window design method FIR filter. Even though literature mostly only tells about designing lowpass filter, window design method is actually capable of creating any arbitrary frequency response FIR filter. Here is a reference Arbitray Frequency Response.

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I might consider doing a complex modulation of the frequency you want to notch down (or up) to 0 Hz. Then run your favorite deep DC blocker (plus phase adjustment if needed). Then complex remodulate the result back to the original unshifted spectrum. DC block: For non real-time, just subtract the entire signal’s average. Or a long (weighted?) moving ...

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If you need to discriminate between 60 and 65 Hz signals, the fact that you're sampling at 25 kHz means that you're basically doing real time signal processing: the Nyquist Frequency is far above the frequencies of interest. Thus, from classical Fourier theory, you're going to need on the order of 1.0/5 Hz = 0.2 seconds of data, no matter how you process it....

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In general your result match expectations, I don't see anything in there that's unusual or unexpected. Filter design is a complicated trade off between complexity/cost, stopband attenuation, pass band ripple, transition steepness, phase distortion, time domain ringing, non-causality, latency, etc. The best way to go about is to clearly articulate the ...

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