New answers tagged linear-systems
0
votes
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.
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4
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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 ...
- 87.2k
4
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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 ...
- 48.2k
1
vote
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}...
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14
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Accepted
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 ...
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4
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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 ...
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1
vote
Accepted
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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