# 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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### What is meant by a system's “impulse response” and “frequency response?”

Can anyone state the difference between frequency response and impulse response in simple English?
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### Can every type of linear filter be modelled by a convolution?

I have an input time series going through a filter that creates another time series as output. If I assume in first approximation that my filter is linear, does it necessarily mean that I can model ...
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### Negative group delay and envelope advance

I am having a doubt reading about delays in signal processing. Let there be an input to a LTI system with frequency response $H(f)$, given signal $x(t) = a(t)\cos(2\pi f_ot)$, where $a(t)$ is a ...
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### What Is the Transfer Function of a Moving Average (FIR Filter)?

To make post-processing easier, I export scope measurements as CSV files, which are then post-processed (mostly in Microsoft Excel, which is not the best tool for the job, but it is all I have at my ...
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### Initial conditions for the LTI systems described as a difference equations

Why do we need the initial conditions to be zero for the LTI systems described as a difference equations? First question is why do we need it for linearity? I can't think of any example of the non ...
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### Given the input and the output, how to determine the impulse response?

I would like to find the impulse response, $h[n]$, of an LTI system given the input $$x[n] = [1,-3,2]$$ and the output $$y[n] = [1,-1,-4,4]$$ I know that $y[t]=x[t]*h[t]$, but I am having hard ...
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### Finding the Wiener filter transfer function

I am trying to understand the mechanism of finding the transfer function for a Wiener function. ...
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### Eigen Function of Linear Time Invariant (LTI) System

Whenever I try to find the derivation of eigen signal of a LTI system, they always start with assumption that the input signal is complex exponential. Is there any other way to prove that this is the ...
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### Does “improper” imply that a system cannot be stable and causal?

This answer and the comments in it made me wonder whether the following statement is true: If a transfer function is improper, then that system cannot be causal and stable at the same time. I had ...
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### Difference between convolving before/after discretizing LTI systems

Suppose I have transfer functions for two continuous causal linear-time invariant (LTI) systems: $F_1(s)$ and $F_2(s)$. Let $D\left\{\cdot\right\}$ denote the function that maps a transfer function ...
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### How to perform model fitting for system identification

I am having a really hard time in understanding how to formulate a model say linear AR model to represent a communication channel or maybe any motion. I have the experimental data representing the ...
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### Concept of finding forced response from difference equation?

I know how the process works, first from difference equation make a homogeneous equation and then find natural response , then find a particular response (in the form of input) substitute it back in ...
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### Why does reversing the order of these two transfer functions give me different outputs?

Consider these two systems: \begin{align} &u\ {\longrightarrow}\boxed{s}{\longrightarrow}{\boxed{\frac 1s}}{\longrightarrow}\ y\\ &u\ {\longrightarrow}\boxed{\frac 1s}{\longrightarrow}{\boxed{...