# Tag Info

### Are all LTI systems invertible? If not, what is a good counterexample?

You need to define what you mean by "invertible". Do you mean invertible by a causal and stable system? If yes, then any system that is not minimum-phase is not invertible (because the inverse system ...
• 91.3k
Accepted

### Auto-correlation function, an inverse problem

Let's look at the case $x[n] \in \mathbb{R}$, where $x[n]$ is real. Autocorrelation is basically convolution of the signal with it's time inverse. This can be easily expressed in the frequency domain....
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### Are all LTI systems invertible? If not, what is a good counterexample?

A necessary condition for invertibility is that any output has only one possible input (or injectivity, as proposed in comments). Since we are looking at counterexamples, we can look at when this ...
• 32.1k
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### Deconvolution of Synthetic 1D Signals - How To?

You cant't recover the original signal through deconvolution. A Gaussian kernel is in essence a lowpass filter, i.e. it will remove information at higher frequencies from the signal. Once it's gone, ...
• 47.1k
Accepted

### Can Principal Component Analysis (PCA) Solve the Cocktail Party Problem?

The Cocktail Party Problem is a Blind Source Separation (BSS) problem. Given a linear mixture of signals: $$\boldsymbol{y} \left[ n \right] = A \boldsymbol{x} \left[ n \right]$$ We're trying to ...
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### How Is the Formula for the Wiener Deconvolution Derived?

The Wiener Filter can also be derived by another (Easier) way. Let's assume the following model: $$y = h \ast x + n$$ Namely the data is a result of a linear combination (Convolution) of $x$ with ...
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### Auto-correlation function, an inverse problem

There is in general, as @Hilmar's answer points out, no unique solution to the question of a sequence that has the given perodic autocorrelation function. In the simplest case, that a shifted ...
• 20.7k
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### Deconvolution of a 1D Time Domain Wave Signal Convolved with Series of Rect Signals

Solving a deconvolution isn't easy even in simulated environment not to mention in practice. The main trick to solve it is using the proper model / prior for the problem and very good measurements (...
• 20.2k
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### Estimating the Signal by Deconvolution with a Prior on the Filter Coefficients and the Signal Samples

I would take approach based on Blind Deconvolution. Since we're dealing with ill posed problem some assumptions should be made. The intuitive approach would be using the information as a prior for ...
• 20.2k
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### Estimating Convolution Input Under the Assumption of Sparsity and Constant Non Zero Values Using Compressive Sensing Approach

Basically your problem is called Blind Deconvolution. It means we want to estimate both the operator and the input given the output. You model is Linear Time Invariant Operator so we have LTI Blind ...
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### Solving Inverse Problem of Multiple Pulses Over Multiple Channels with Convolution Kernel and Cross Channel Mix

Crosstalk between channels is small and well-conditioned, at least in the example you provided. Your matrix A has a condition number of 1.85, which is really good. It means you can invert it and it ...
• 531
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• 20.2k