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Note that this is not about general limitations of FIR filters, but about the special case of linear-phase FIR filters. If you understand why a type-II linear-phase FIR filter has a zero at $z=-1$, then the limitations of the other types should be obvious too. It's always about zeros at either $z=1$ (DC) or $z=-1$ (Nyquist). Given the transfer function $$H(...


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The problem that recursive least squares (RLS) can solve can be formulated as recursively solving for $\hat{\theta}$, such that it is the least squares solution to $$ \hat{\theta}_n = \arg\min_x \sum_{k=0}^n w[k]\,\|z[k] - \phi[k]^\top x\|_2^2, $$ where $w[k]$ are weights, $z[k]$ and $\phi[k]$ are known and $z[k]$ is assumed to be generated by using $\phi[...


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A real, 1D DFT is fully described by the non-negative frequencies, since real DFTs are symmetric about the 0 frequency bin. The function you linked is only computing the FFT along one dimension, and is only returning the non-negative frequency bins. From the manual page: "Notice how the final element of the fft output is the complex conjugate of the ...


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You're overcomplicating things here. There's no need for sines and cosines and squares. Note that $\omega=0$ corresponds to $z=1$, and $\omega=\pi$ corresponds to $z=-1$. From the definition of the $\mathcal{Z}$-transform you should be able to figure out that the DC term of the transfer function $H(z)$ is given by $$H(1)=h_1+h_2+h_3\tag{1}$$ and the value ...


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From what I can glance : The chattering seems to be high-frequency compared to your signal of interest, it should not be hard to filter this chattering noise. You simply need to identify the frequency band of your signal and the frequency band of this noise. Could your perform an FFT to analyze the frequencies of your noise? Then design a filter that will ...


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Does gradient vector of pole zero carry useful information? Yes. The partial derivatives can be used in creating iterative search algorithms for fitting IIR filters to arbitrary targets. Examples of algorithms that use the derivatives are Steepest Descent or Conjugate Gradient. It's not a trivial process though and there are lot of details to be worked ...


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The purpose of an anti-alias filter is to remove signal and noise from frequency bands that would otherwise "fold" or alias into the band of interest during the sampling process. This can occur when going from an analog signal to digital (and thus would be the filter just prior to the A/D converter), or when resampling a digital signal such as done in multi-...


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Suppose if your sampling rate is fs, then the corner frequency of the Anti Aliasing filter would be fs/2


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