What sort of algorithm would effectively notice this?
What you are describing, is an online algorithm that uses a small set of "past" measurements to make an inference, in this case, about the slope of the signal.
Since you are keeping track of the current beginning and end of the rolling buffer, it is essentially like having access to a linear buffer of N ...
To be honest, I don't think CNNs, RNNs and LSTM are useful for this kind of problem – a bandpass filter followed by a threshold would be.
Now, that would have three parameters:
Lower cutoff frequency
Upper cutoff frequency
and what is usually called "Machine Learning" is nothing but finding local minima over some (loss) function with real ...
The term LTI system is a bit broad, so perhaps restricting ourselves to single input-single output systems makes sense. Let's just look at $s$ (Laplace) for now. The $Z$ transform follows in a straightforward way.
Also, if the system is not stable, a practical inverse filter will not recover the input. Convolution commutes so following a stable filter with ...
You have to be clear what you mean by "invertible". Commonly, you want the inverse system to be causal and stable, and that puts certain restrictions on the original system.
In the case of systems with rational transfer functions, you just have to look at the zeros of the transfer function, because they become the poles of the inverse system. If all zeros ...
In general LTI System is invertible if it has neither zeros nor poles in the Fourier Domain (Its spectrum).
The way to prove it is to calculate the Fourier Transform of its Impulse Response.
The intuition is simple, if it has no zeros in the frequency domain one could calculate its inverse (Element wise inverse) in the frequency domain.
Few remarks for the ...