# Tag Info

### Sine as input to an LTI system

There is a trigonometric identity To this problem it brings much clarity To shift from sine to cosine add degrees 10 times nine Then your problem answers itself, uh, ity.

### Sine as input to an LTI system

It's important to understand the response of an LTI system to a complex exponential $$x(t)=e^{j(\omega_0 t+\phi)}\tag{1}$$ (as pointed out in Dan's answer). The response to the input signal $(1)$ is ...

### Sine as input to an LTI system

Either sin, cos, or exp can be used and they are all related by Euler's formula as: $$e^{j\omega t} = \cos(\omega t) + j \sin(\omega t)$$ My guess as to why educators may favor using cosine is that it ...
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### Why does convolution give the output of a passing a signal through a filter?

The convolution operation essentially computes a weighted sum of the input signal's values, with the weights determined by the filter. This process allows filters to capture patterns, features, or ...

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