# 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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### Discretizing my continuous system in Matlab

I was hoping someone could help me with conducting my discretization in MATLAB. I have a linear system with known data: sampling interval $T$, system matrix $\mathbf{A}$, input matrix $\mathbf{B}$, ...
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I've got an LTI-system such as follows: $$y'(t)+{2} y(t)={5} x(t-{3}), t>0, \\ \\ y(0)=0 \ \text{ ja } x(t)=0, \ t<0.$$ From this i've already figured out the transfer function: $$H(f)=\frac{5\... 0answers 24 views ### Inversion problem for big dataset Suppose my goal is to solve for x in Ax = b using CG method and A is Toeplitz. The problem is that b is extremely large in size and I can't just read in the whole vector b and then solve for ... 1answer 96 views ### 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 ... 0answers 50 views ### Co-prediction of signals Is there any plausible method to estimate or predict one signal, on the basis of known value of another signal, provided the two signals bear a strong correlation? For instance, the audio amplitude ... 0answers 107 views ### Frequency Response Question on LSI System Someone please explain me the question its seems very complicated to me. I just want know what the question asking and how to solve it i dont want fully solved solution. Thank you!! 0answers 77 views ### should block diagrams in Direct Form 1/2 contain empty branches to fit structure? When creating a block diagram in a well-recognized structure (Direct Forms 1&2 in particular), does one remove branches where the coefficient is 0? This picture includes a coefficient of b_1=0.... 0answers 27 views ### 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 ... 0answers 72 views ### 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 ... 1answer 258 views ### Issues in generating AR model with a constraint I am new to the topic of system identification and looking for a large Autoregressive (AR) model. Can anybody point out a large stable AR model which has more than 2 coefficients AND there should be a ... 0answers 291 views ### 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) $$with x(t) the input and y(t) the output. I'm asked to find two things:... 1answer 300 views ### The Spectrum of the Impulse Response of Linear Time Invariant (LTI) System Consider an LTI system with impulse response$$h[n] = \frac{1}{5^n} u[n]. (a) Determine and sketch the magnitude and phase response $|H(\omega)|$ and $\arg(H(\omega))$ respectively. (b) ...
Let suppose x(t)=$\sum\limits_{k=-∞}^∞ R(t-kT)$ $R(t) = \begin{cases}1 &[0,2T] \\ 0 & \text{otherwise} \end{cases}$ x(t) is the input to an ideal bandpass filter with \$\text{BandWidth} = \...