# Tag Info

Accepted

### Why LTI system cannot generate new frequencies?

One of the definitive features of LTI systems is that they cannot generate any new frequencies which are not already present in their inputs. One way to see why this is so, comes by observing the ...
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### What is the difference between natural response and zero input response?

First it's important to realize that many authors use the terms zero-input response and natural response as synonyms. This convention is used in the corresponding wikipedia article, and for instance ...

### 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 ...

### Are there any real world applications for complex-valued signals or impulse responses?

Absolutely! Conjugates are mentioned in textbooks because conjugation has no effect on real signals, but it does on complex ones. This way, formulations are more general and apply to both real and ...
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### Do Causal Discrete-time systems have proper transfer functions?

Note that a stable and causal continuous-time transfer function does not need to be strictly proper but only proper, i.e. the degree of the numerator does not exceed the degree of the denominator, but ...
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### How to determine if the system is invertible

It depends on what exactly you mean by "invertible". In system theory, what is often meant is if there is a causal and stable system that can invert a given system, because otherwise there might be an ...
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### Discrete State Space Model - Why Are We Calculating $x \left[ k + 1 \right]$ Instead of $\dot{\boldsymbol{x}} \left( t \right)$?

I will ask you something that will give you intuition. How would you calculate the Gradient of an image? Image is a discretization of reality, so how would you estimate the gradient of the "Reality" ...

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### Negative group delay and envelope advance

Answer : No, any causal LTI system with frequency response $H(f)$ cannot produce the output $y(t)$ in advance. And, the answer lies in the causality of input signal $x(t)$ being applied to $h(t)$. Any ...

### Are the output functions of a continuous-time LTI system necessarily continuous (in the calculus sense) for any given input functions?

Consider the identity system $y(t) = x(t)$. This system is LTI. If the input $x(t)$ is discontinuous, then the output $y(t)$ will be discontinuous too.

### What's the Difference between Convolution Kernel and Point Spread Function in the Context of Image Convolution?

The PSF (Point Spread Function) is the system response to Impulse Signal (Point). If your system model is LSI (Linear Spatially Invariant) then the output image of the system is applying the PSF as a ...
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### Why is the output of an LTI system expressed as the convolution of the input with its impulse response?

it takes more work to do this for continuous-time systems, so i'll just do it for discrete-time and we can all wave our arms to extend to continuous-time. a general discrete-time input signal can be ...