Questions tagged [linear-systems]

A linear system operates on inputs with only linear operators so the response to a complex input can be analysed as the sum of the response to a set of simpler inputs. This mathematical property makes the analysis of linear systems much simpler than non-linear systems where this summation or superposition does not hold. Linear systems are generally further classified as time invariant, meaning that there characteristics do not change over time.

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Conversion from stationarity to non-stationarity

Is there any way to convert a non-stationary signal to a stationary one, perform operations on it meant for a stationary signal and then convert it back to the non-stationary one?
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How do you determine the properties of a differential equation?

If I was given a differential equation of the form $$y'(t) + a(t)y(t) = x(t)$$ how would I be able to decide its linearity, time-invariance, and causality?
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time invariance concept?

if a time varying input like cos is given to a time invariant system,how will it behave? I have a system $x^2(t)$ Apparently from equation it seems to be time invariant But when i give it input x=...
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Confusion in linearity?

I am studying linear systems from the book "Signals and Systems Laboratory with MATLAB". I have performed an example on MATLAB myself in this regard. Code is as follow: ...
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How does one describe the “frequency response” of a mixer?

Suppose one uses a vector network analyzer to measure the $S_{21}$ parameter of an RF mixer over a frequency range. Would it be appropriate to call this the “frequency response” of the mixer? I find ...
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What does this notation $g(x) = S\{\delta(t) \}(x)$ mean?

What does this notation mean $g(x) = S\{\delta(t) \}(x)$ mean, where $S$ is a "system", $\delta(t)$ is the impulse function and $g(x)$ the output function of the system? I am really not familiar with ...
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ROC of inverse system function

If the region of convergence (ROC) for system function $H(z)$ is $R_h$, what is the ROC of the inverse function $G(z)=\frac{1}{H(z)}$? 
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System indentification different inputs

I have peformed different form for input/output relation to determine a system, but seem to be missing some theory which input will be the most will excite enough modes such that the models which i ...
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Perfect system identification or am i doing something wrong?

I am using MATLAB to identify a system. The problem with my method is that my result is perfect. I get a nearly 100% fit, which make me wonder if what I am doing is correct. I feed a sine sweep with ...
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Solving linear system and find impulse response

I have this linear system that is defined by the differential equation $$y''(t) + 4y'(t) + 5y(t) = 2x(t) + 3x'(t)$$ with x(t) the input and y(t) the output. I'm asked to find two things:...
$\dot{\boldsymbol{x}}(t)=\boldsymbol{Ax}(t)+\boldsymbol{Bu}(t)$ $\boldsymbol{y}(t)=\boldsymbol{Cx}(t)+\boldsymbol{Du}(t)$ but say that $y(t)=\frac{Y(t)}{u_1(t)}$, where $u_1(t)$ is one of the system ...