# 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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### Is this system linear or non linear? $y[n]=cos(\frac{5\pi}{8}*n+\frac{\pi}{4})$ [closed]

$y[n]=cos(\frac{5\pi}{8}*n+\frac{\pi}{4})$ If I let $(\frac{5\pi}{8}*n+\frac{\pi}{4})=x[n]$, I get the system as non linear. But one of my teacher says it is linear, whereas another teacher says it is ...
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### Can we tell if a system is linear and time-invariant from its frequency response?

Given a system with a known frequency response in the S-domain. Is there a way to find whether the system is linear and time invariant? My current understanding is that we need to take the inverse ...
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### What are the characteristics of a smartphone speaker?

What are the characteristics of a smartphone speaker? Whether it is linear or non-linear?
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### FInd the amplitude function to a system

I'm studying a course in signal analysis and have come across an exercise where I find the analytical part a bit tricky. I am to find the amplitude function $|H( f )|$ for a system with the impulse ...
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### Difference equation to FIR filter coefficients

I have a difference equation $$y[n] = y[n-1] + 0.5x[n] - 0.5x[n-2] \text{.}$$ According to this answer, the filter should have finite impulse response. I just can't figure out how to get the FIR ...
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check time variance of this system $$y (t) = x(\frac{t}{3})$$ my solution $$y_1(t) = x_1(t/3)\\ y_2(t) = x_2(t)= x_1(\dfrac{t}{3}-t_o)$$ where $$x_2(t) = x_1(t-t_o)\\ y_1(t - t_o) = x_1(\dfrac{t-... 1answer 43 views ### How to prove that this system is an invertible system or not? How could i go throw proving that this system y(t)=\int_{-\infty}^{t}e^{-(t-\tau)}x(\tau)d\tau is invertible system or not ? 1answer 60 views ### Linear system stability criteria Suppose we have a closed-loop system H(s)=\frac{A(s)}{1+A(s)f(s)}=\frac{A(s)}{1+T(s)}. I've seen the stability of the system stated a couple ways: If H(s) has any poles in the RHP, then it is ... 1answer 52 views ### When is a LTI IIR H(z) system minimum phase EDIT: I failed to mention that the system's inverse also needs to be causal and stable. I cannot wrap my mind around on how when a system and its inverse are both causal and stable and LTI IIR it is ... 0answers 20 views ### Please explain the following Linear Prediction estimate graph I am reading this doc https://librosa.org/doc/latest/generated/librosa.lpc.html#librosa.lpc? I can't understand the graph for linear prediction coefficients. Please help explain it as I a new to this ... 0answers 40 views ### Signal separation This is probably a blind signal separation problem of sorts, but it seems like it should be easier than I am finding it. Let’s say I have N time series, each of length [M x 1] that are a superposition ... 1answer 84 views ### Why is particular solution zero for an impulse excitation signal? We were being taught the impulse response for a series RC Circuit- consisting of simply one resistance, one capacitor, and an impulse excitation all in series. I get that the homogeneous part of the ... 2answers 190 views ### Where to start with DSP? I have a DSP exam coming up this summer and I got an abysmal mark on an assignment earlier this year. Obviously, the lecture slides are not enough for me to understand DSP, so I am wondering where can ... 1answer 129 views ### Impulse response for an LTI system I'm new to signal processing and working my way through a textbook. There is an exercise where a causal LTI system is given that responds to a rectangular pulse. I have an exercise where a causal LTI ... 2answers 87 views ### Under what conditions is the convolution of an input signal with the system's impulse response periodic? I'm currently solving the following convolution problem from Oppenheimer's book: In the solution, it was stated that "x(t) periodic implies y(t) is periodic" So I wondered if it's ... 1answer 37 views ### How do i know it is will be periodic (system is LTI and Casual) 1)If a periodic signal is applied to the input of this system. Does output always have to be periodic ? 2)What conditions are required for this system to be linear? thanks ... 1answer 72 views ### Output of a stable LTI system (discrete) Consider an LTI (linear and time invariant) system that is BIBO (bounded input bounded output) stable and is such that x[n] = 0 for all n < 0 (note: this is sometimes referred to as a relaxed ... 1answer 56 views ### Understanding LTI systems graphically I'm currently working on this problem from Oppenheimer's book: Given x_{1}(t) and y_{1}(t) I should figure out y_{2}(t) and y_{3}(t) given that the system is LTI. My progress so far: I'm ... 3answers 163 views ### How do I check for linearity for the following piecewise-defined system? The problem at hand: Where I'm currently stuck: I'm not entirely sure about how to move on from this point, I'm trying to find the superposition of the responses of the two individual signals so I ... 2answers 44 views ### Physically, what does the usage of two variables mean for convolution My intuition of convolution is that it is just a way to depict multiplication of two signals where each signal is made up of various frequencies and phases. Since it isn't easy to find the value of \... 1answer 92 views ### Scaling the input vs scaling the impulse response for an LTI system Two different cases: We pass x(t) to an LTI system with impulse response h(2t) and get the output y(t). We pass x(2t) to an LTI system with impulse response h(t) and get the output z(t). ... 0answers 26 views ### Stable and causal system How many stable and causal systems with the same magnitude response are there? I know this relates to an all pass system for two rational transfer functions but am not sure about the specifics of this 2answers 36 views ### Z-transform of an affine function What is the transfer function of the system described by the following affine input (x)-output (y) relationship:$$ y[n] = \alpha x[n] + \beta. $$Using the Z-transform we find:$$ Y[z] = \alpha X[...
I can solve problems without imaginary numbers, but when exponential contain imaginary numbers, I can't solve the problem. For example, $x(t)=e^{3jt}+e^{4jt}$, $y(t)=(e^{-3t}-e^{-4t})u(t)$ (where $j$ ...