# 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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### Do Causal Discrete-time systems have proper transfer functions?

In the case of continuous-time systems, if the system is causal, its Laplace transfer function is strictly proper (the degree of the numerator is less than the degree of the denominator). Is this ...
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### What is the difference between natural response and zero input response?

I am new to DSP and was going through different responses of a system subjected to an input. My understanding of zero input response is: it is the response/output of the system when the input signal ...
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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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### Are complex exponentials the only eigenfunctions of LTI systems?

Is there an example of an eigenfunction of a linear time invariant (LTI) system that is not a complex exponential? Justin Romberg's Eigenfunctions of LTI Systems says such eigenfuctions do exist, but ...
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### Is this system linear?

I have this system: $$y[n] = -\frac{1}{2} x[n+2] - y[n+1]$$ I have no idea how to prove if the system is linear or not, because, it depends on future outputs... Thanks for the help
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### Output of a discrete-time LTI system different form than input?

This question is related to this one. I'm going through old exams for a 2nd year systems and transforms course, and came across this question. I'm posting this question just in case my other question ...
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### A system that perfoms Fourier Transform operation - is it an LTI system?

If a system takes input as the time domain signal and outputs the frequency domain signal, is such a system an LTI system? For if the input time domain signal can be represented as a linear ...
449 views

### Does instability make an otherwise LTI system nonlinear (or time-variant)?

I am spinning this question off from the question from johnny. Matt L. and I have had directly opposite conclusions to johnny's question. I want to decouple the question from issues of causality and ...
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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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### Why unit impulse function is used to find impulse response of an LTI system?

Hello i am working in digital image restoration field, recently i have studied concept of convolution, i studied that to find the impulse response/point-spread function of an LTI system, an unit ...
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### Beginner level : Help with terminologies : smooting length, length of channel, channel equalization delay, blind system identification, equalization

Say the channel model is an univariate FIR filter with true coefficients $h=[1,a_1, a_2 ]$. I am learning algorithms for system identification and channel equalization. For this, I am implementing ...
231 views

### should this be viewed as an impulse response or step response

I'm trying to teach myself the relation between simple discrete ODE's and the impulse response-step response concept. Getting back to the question: I don't expect anyone to read the whole thing but I'...
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### System Identification with a Limited Bandwidth Input Signal and Region of Interest

Given a FIR filter $h[n]$. Its action can described as: $$\mathbf{y} = \mathbf{H} \mathbf{x} \\ \mathbf{y} = \mathbf{X} \mathbf{h}$$ where $\mathbf{H}$ and $\mathbf{X}$ is a Toeplitz matrix. If $h$...
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### Causal system and Physical Systems

According to the Paley-Wiener criterion, a system is causal if satisfies: $$\int\limits_{-\infty }^{+\infty }{\frac{\ln (|H(f)|)}{1+{{f}^{2}}}}df<\infty$$ So I want to know This equation is ...
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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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### 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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### Design a LTI system which returns DC value of the input signal

Suppose that $h(t)$ is the impulse response of LTI system. The input signal $x(t)$ is periodic with period $T$. Determine $h(t)$ so that the output signal $y(t)$ only be the DC component of $x(t)$. Is ...
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### Exponential decaying step response in LTI System

I'm attempting to better understand the relationship between step responses, impulse responses, and convolutions. Say that I have a system where if I apply a constant input, my output decays from a ...
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### Alternative to BIBO stability of a system

In DSP textbooks a system is stable in the BIBO (Bounded-Input, Bounded Output) sense if and only if every bounded input sequence produces a bounded output sequence. After stating this definition ...
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### Moving average and linearization of two piecewise linear systems

I have 2 oversampling ADC's running parallelly, each to process data in a specific range of the input as shown below: Each ADC can process only half cycle range of a sine wave. Each ADC adds its own ...
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### Why is the total signal response response of zero input + zero state, $y(t) = y_0(t) + h(t)\star x(t)$, not an LTI?

For the zero input + zero state response in continuous time linearly time-invariant systems, why is the $y(t)$ equation not "technically" considered an LTI? I read this in a journal and there was no ...