I don't have a thorough background in Signal processing and require some information for an application pertaining to computer science. Minimum Entropy Blind Signal Deconvolution with Non Minimum Phase FIR Filters paper proposes to use entropy for blind system identification. My questions are the following based on terms that I cannot follow in the paper and shall be grateful for detailed explanation
Q1: What does minimum phase filter mean? In my understanding phase of a signal means the angular displacement or the angle $\theta$ that appears in an equation like $x=A sin (\omega*t + \theta)$
Q2: What is an inverse filter? How is it related to convolution and deconvolution?
Answer
We will be talking about linear time-invariant systems.
1) A minimum phase filter is one which is causal and stable and its inverse is causal and stable. In the case of a discrete time system, you have all the poles and zeros of the transfer function within the unit circle.
2) An inverse filter of a filter with transfer function $H(z)$ is a filter $G(z)$ such that $H(z) G(z) = 1$ -- that is, when you cascade the filter with its inverse filter, its the identity filter. In the z-transform domain, multiplication corresponds to convolution in the time domain. So, if your input is $X(z)$, and your filter is $H(z)$ and your output is $Y(z)$, the relation is $Y(z) = H(z) X(z)$ in the z-transform domain, while in the time domain, $y[n] = h[n] * x[n]$ where $*$ denotes convolution and $h$ is the impulse response of the filter. The inverse filter convolves with the impulse response corresponding to $1/H(z)$ (that is, you take the output $y$ and find an input which when convolved with $h$ gives the output -- i.e. deconvolution).
You can find more details in any introductory Digital Signal Processing text like Discrete-Time Signal Processing by Oppenheim, Schafer and Buck (now in its 3rd edition).
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