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The filter is a discrete FIR filter, so the transfer function would be given as: $$H(z) = .0287 + 0.1430z^{-1} + 0.3283z^{-2} + 0.3283z^{-3}+0.1430z^{-4}+0.0287z^{-5}$$ With the frequency response given by using the unit circle for the complex variable $z$, as in $z = e^{j\omega}$ for $\omega \in [0, 2\pi)$, with the sampling rate normalized to $\omega = 2\...


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You have 2 right-half plane zeroes : 0.012 and 18. The zero at +18 is "fast" and will not affect the performance much, but your slow zero at 0.012 will severely limit your performance. You can't cancel this right-half plane zero with a right-half plane pole in your controller, your controller output will be unbounded. Is this homework or a real ...


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The roots of the quadratic equation $s^2 + 2\xi \omega_n + \omega_n^2=0$ are $s_{1,2} = -\xi w_n \pm \omega_n \sqrt{\xi^2 - 1} = -\xi w_n \pm i\omega_n \sqrt{1 - \xi^2}$ where we define the damping frequency $\omega_d = \omega_n \sqrt{1 - \xi^2}$ when $\xi < 1$. Therefore, the usual second order transfer function $\frac{\omega_n^2}{s^2 + 2\xi \omega_n + \...


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To examine the behavior of the system when noise is added would only make sense to apply the noise to the input of the system. To do this you would determine the power spectral density (spectrum) of your noise process (which for the white noise case the OP describes would be constant across the entire frequency range, so in that case the spectrum is constant ...


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I don't think it's a good idea to add random noise to frequency response. In general, noise is added to the input or output signal. You should be clear that at which stage the noise is introduced. According to the different stages of noise introduction, there are two main transfer function estimators, $H_1$ estimator and $H_2$ estimator. $H_1$ assumes that ...


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For $|\zeta| \le 1$, let $\zeta= \cos\theta$, so $\theta=\mathrm{arccos}\,\zeta$ $$\begin{align*}g(s) &= K\frac{\omega_n^2}{s^2 + 2\zeta \omega_n s + \omega_n^2}\\ \\ &= K\frac{\omega_n^2}{s^2 + 2\omega_n s \cos\theta+ \omega_n^2(\cos^2\theta +\sin^2\theta)}\\ \\ &= K\frac{\omega_n^2}{(s + \omega_n \cos\theta)^2+ \omega_n^2\sin^2\theta}\\ \\ &...


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Assuming you have an input signal $ u = A cos(2\pi ft) $ and you measure an output signal $y = B cos(2\pi ft + \theta) $ The $\frac{B}{A}$ ratio is the gain and $\theta$ is the phase shift for frequency $f$. You could simply demodulate $y$ by multiplying by $x = cos(2\pi ft) - jsin(2\pi ft)$ $$ z(t) = y*x = \frac{B}{2}(cos(4\pi ft) + cos(\theta) + j(sin(4\pi ...


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