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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determine the impulse response of given second order difference equation

$y[n]-3y[n-1]-4y[n-2]=x[n]$ i solved it as follows : 1.first calculated natural-response(ZIR i.e,zero input response) by using characteristic equation it came out as $y_n[n]=[c_1(-1)^{n}+c_2(4)^...
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125 views

Phase response for conjugate zeros

If a second order system has 2 poles/zeros that are conjugate symmetric, how does this affect the phase response? I know that if there are 4 zeros/poles that are conjugate reciprocals, then it is a ...
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781 views

How do I show if this system is time-varying? [closed]

$\displaystyle y(t) = x(t), t \ge 0$ and $-x(t), t \lt 0$ I can anticipate this system is time-varying. However, I cannot be sure it and prove it. please help me.
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BIBO stability and input at system's pole

My understanding of BIBO stability is that if a bounded input is applied to a discrete-time, linear, time-invariant BIBO system, the output will also be bounded. A sufficient condition for this is ...
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71 views

Output of system defined by differential equation

I don't fully understand how the output of a system can be derived from the system's differential equation and a given input. For example: $$y(0-) = 1 $$ $$y'(0-) = -2$$ $$ u(t) : \text{Heaviside ...
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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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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 ...
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312 views

How do I take the real part of this bandpass filter system's output?

I'm stuck on a final step in this problem. Essentially, there are the two systems above, which we'll call System 1 (Fig. 4.26, with ideal lowpass $H(jw)$) and System 2 (with $H_1(jw)$). The question ...
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244 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 ...
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285 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:...
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why exponential term neglected in equation?

where does that exponential term gone, is this because it is a constant term or it has to do something with stablity?
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Convolution of a signal by itself properties [closed]

I'm studying for a test and I can't really explain this question very well. If we convolve a signal by itself, will it have the same properties (time-invariant, linear, stable, casual)? I know how ...
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How does an LTI system produce multiple values from a unit impulse

I understand that in a discreet system, an impulse is 1 at the origin point and 0 everywhere else. I've seen many examples showing the impulse response of an LTI system to be many points, have many ...
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747 views

LTI system with Laplace transform

Given the input $$x(t)=u(t)$$ and the corresponding output signal measured as $$y(t)= 2 e^{-3t} u(t)$$ determine the impulse response $h(t)$. This what have done so far: $$ h(t)= \mathscr{L}^{-1} \...
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Why isn't option C correct answer for the given question?

W Please answer this question I am getting option c as my answer by putting input frequency of 3 radians in frequency response of system.
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1answer
457 views

Implementing FIR with MATLAB

There are several ways that MATLAB implements FIR. One of them is that convolution function conv directly implements the convolution equation and if the input is ...
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212 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) ...
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92 views

Modeling an infinite delay system

If black holes swallow everything and assumes that the black holes do not get out the things from them, then can we consider a black hole as an infinite delay system? It takes the input and it is a ...
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169 views

Are these Linear and Time Invariant Systems?

We were given the above systems and we were asked to tell whether they are linear (or not) and time invariant(or not). $y(m,n)=x(m,n)+c,\quad c>0$ $ y(m,n)=x(m,n)+x(m,-n)$ $y(m,n)=x(m,n+m)$ $y(m,n)...
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156 views

Is the system $L\{f[m,n]\}= c[m,n] f[m,n]$ shift invariant?

$c[m,n]$ is the spatially varying gain. My prof says that its not shift invariant. However if we put $m=m-k$ and $n=n-l$ we get $c[m-k,n-l] f[m-k,n-l]$ which is how a shift invariant system should ...
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1answer
134 views

classify the system if it's linear , non-linear , time variants or invariants [closed]

classify the system if it's linear , non-linear , time variants or invariants
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1answer
29 views

LTI system impulse response [closed]

I am learning signal processing and need some help with this question $h[n]=-x[n]+2x[n-1]-3x[n-3]$ Given the following input signal $x[n]$ calculate y[n] the output of the system $x[0]=2, x[1]=0, x[...
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LTI system output

I compute the output of a LTI system, can someone tell me if my answer is right..? and help me with my others questions? The impulse response is: $h(n) = \left(\frac{1}{2}\right)^nu(n)$ , entry is $x(...
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What Are Some Examples of Applications of LTI Systems

I'm giving a lecture on LTI systems. I encountered some questions: for a discrete LTI system H with impulse response h, is the system applied on signal x(t) equals x*h - normal discrete convolution ...
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1answer
271 views

Compute output of a LTI system

Is it possible to compute the output from one linear time invariant system which unit impulse sequence is: $$h(n) = \left(\frac{1}{3}\right)^nu(n)$$ and the entry in the system is: $$x(n)=u(n)-u(n-...
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Are there existing third system (linearity, non linear, !!!)?

I like to know your idea about is there any third system after linear, none linear classification. Could we consider more universe dimension than 4 dimensions (time, XYZ) like 11 dimensions of  ...
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550 views

Ideal BandPass Filter

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} = \...
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Is the following statement true or false?

Is the following statement true or false? For the input into this system: $x(t)=\delta(t)x ( t ) = δ ( t )$ the output from the integrator will be: $y(t)=u(t)$

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