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Why the fear of complex numbers? Just do a distinction of cases and generate solutions for the real and the complex case. $b-a$ in the denominator will always be real, as the imaginary parts will cancel out each other, so complex numbers will only be in the exponents, wich will lead to some nice sinusoidal functions, which is expected, as this is an ...


Your analog transfer function looks OK. For the sake of clarity - and to reduce the chance of making errors - I'd just rewrite it as $$H_a(s)=G\cdot\frac{s^2+as + b}{s^2+cs + d}\tag{1}$$ with $$\begin{align}G&=\frac{2R_g}{R_d+2R_g}\\a&=\frac{R_d}{L}\\b&=\frac{1}{LC}\\c&=G\left(a+\frac{1}{2R_gC}\right)\\d&=G\cdot b\frac{}{}\end{align}$$ ...


Does mixing brown noise and white noise create pink noise? No. Pink noise has a spectrum of that falls with 3dB/octave (or 10dB/decade). The spectrum of the sum of white and brown noise will be "brown" at low frequencies and "white" at high frequencies. The spectrum will have two slopes: below the transition frequency it will be -6dB/octave and above it, ...


Infinitely long. It's an exponential decay, so it never goes back to 0. The time constant for a 200 Hz filter is $\frac{1}{2 \pi f} \approx 0.8ms $. About every 0.8ms it drops by about $2/3$ or every 1.84 ms it drops by a factor of 10. If you define "almost zero" as one millionths you need to wait $6*1.8ms$ or about 11ms.

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