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5

If you remove (for the time being) that leading factor $A$ as a constant gain factor: $$H(s)=\frac{s^2+\left(\frac{\sqrt{A}}{Q}\right)s + A}{As^2 + \left(\frac{\sqrt{A}}{Q}\right)s + 1}$$ what you get then is a symmetric, but otherwise general shelf that could be equally described as "LowShelf" or "HighShelf". In dB, the gain at the low ...


3

If you use a parameterization with a (pole or zero) frequency and a Q-factor for numerator and denominator of a biquadratic function you get the following general second-order transfer function $$H(s)=G_{\infty}\frac{s^2+\frac{\omega_z}{Q_z}s+\omega_z^2}{s^2+\frac{\omega_p}{Q_p}s+\omega_p^2}\tag{1}$$ For a low shelving filter we want $H(\infty)=1$, i.e., $G_{...


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