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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.
TimWescott's user avatar
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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 ...
Matt L.'s user avatar
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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 ...
Dan Boschen's user avatar
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If the convolution of two signals is a unit impulse, what does this tell us?

Well Hilmar is 100% correct but I want to give a practical application of 2 such systems. If 2 systems are inverse of each other you can use them to make a noise removing system: The block with $H_{1}...
Cerise's user avatar
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If the convolution of two signals is a unit impulse, what does this tell us?

It tells us that the systems are inverses of each other. The DFT of $$h_1[n]*h_2[n]= \delta[n]$$ is $$H_1[k] \cdot H_2[k] = 1 $$ so we get $$H_2[k] = \frac{1}{H_1[k]}, H_1[k] = \frac{1}{H_2[k]}$$ In ...
Hilmar's user avatar
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Why does convolution give the output of a passing a signal through a filter?

You can describe the system with an operator acting over an input $x(t)$ transforming it into $z(t)$. If $L$ is the operator, $z(t)=L[x(t)]$. Remember that the system and the operator are linear and ...
Andy R's user avatar
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1 vote
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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 ...
Ahsan Yousaf's user avatar
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