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.
4
votes
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 ...
4
votes
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 ...
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}...
14
votes
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 ...
4
votes
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 ...
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 ...
Top 50 recent answers are included
Related Tags
linear-systems × 649discrete-signals × 129
impulse-response × 83
convolution × 75
continuous-signals × 73
filters × 66
signal-analysis × 47
fourier-transform × 47
z-transform × 45
transfer-function × 45
causality × 40
stability × 38
homework × 37
frequency-response × 35
laplace-transform × 35
control-systems × 32
system-identification × 25
state-space × 20
matlab × 16
linear-algebra × 16
finite-impulse-response × 15
digital-filters × 15
differential-equation × 15
infinite-impulse-response × 14
filter-design × 13