Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

# Tag Info

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 $$H(... 1 The problem that recursive least squares (RLS) can solve can be formulated as recursively solving for \hat{\theta}, such that it is the least squares solution to$$ \hat{\theta}_n = \arg\min_x \sum_{k=0}^n w[k]\,\|z[k] - \phi[k]^\top x\|_2^2, $$where w[k] are weights, z[k] and \phi[k] are known and z[k] is assumed to be generated by using \phi[... 1 You're overcomplicating things here. There's no need for sines and cosines and squares. Note that \omega=0 corresponds to z=1, and \omega=\pi corresponds to z=-1. From the definition of the \mathcal{Z}-transform you should be able to figure out that the DC term of the transfer function H(z) is given by$$H(1)=h_1+h_2+h_3\tag{1} and the value ...