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I suppose that you obtain a transfer function of the desired discrete-time system in the form $$H(z)=\frac{b_0+b_1z^{-1}+\ldots +b_Nz^{-N}}{1+a_1z^{-1}+\ldots +a_Nz^{-N}}\tag{1}$$ From that transfer function you compute the coefficients of the second-order sections. Before doing that, you can make sure that the DC gain of $(1)$ equals $1$ (which of course ...

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In general, what you are seeing is normal. Butterworth filters are designed in the analog domain where the frequency axis is unlimited. When discretizing the the freqyency axis stops at Nyquist. Both Matlab and Python use the bilinear transform to map analog frequency to the digital frequency. That means that the infinite analog frequency maps to the ...

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Quantization and encoding are largely independent. "Symbols" is another word for "pulses", and the line encoding can also play a role in how the information is transmitted. Say you quantize one sample to $256 = 2^8$ levels, or 8 bits/sample. In order to transmit those 8 bits, you can, among other options: use binary encoding, which requires transmitting ...

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