Questions tagged [differential-equation]

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Characterizing an unknown LTI system

What are the best approaches to characterize an unknown discrete time LTI system? I believe one of the approaches is to input a known input and measure the output to find a transfer function. What are ...
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Is non-causal, non-LTI solution to difference equation correct?

Find a solution to the difference equation $y[n]-\frac{5}{6}y[n-1]+\frac{1}{6}y[n-2]=\frac{1}{3}x[n-1]$ that is neither casual nor LTI, where $y[0]=y[1]=1$ and $x[n]=\delta[n]$ The homogenous ...
3
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1answer
42 views

Proof for the solution of homogenous difference equation

Suppose the output $y_h[n]$ of a linear, time-invariant system is described by by the following equation for input $x[n]=0$, $$\sum_{k=0}^{N}a_k y_h[n-k] = 0$$ My book states the $y_h[n]$ is in fact ...
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1answer
34 views

Difference equation with variable coefficients in MATLAB

Given the following difference equation $$y[n]-\left(\dfrac{n}{n+1}\right)y[n-1] = n\cdot x[n]$$ How can we use MATLAB to solve it? I know if the coefficients are constant we can simply use ...
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1answer
92 views

Determine the system function H(s) of a system and find out the differential equation

I have created the following system for practice purposes. From this system I want to determine the system function H(s). In the picture I have worked with auxiliary (dummy) variables, which should ...
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2answers
98 views

LCCDE in simple words?

What is LCCDE?I only know its abbreviation/full form :linear constant-coefficient difference equation I know that in s domain we have differential equations and in z domain we have difference ...
4
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1answer
47 views

Damped spring mass system - parameter estimation

I've tried to calculate the parameters of a damped spring mass system of the form $m~ y''(t)+d~y'(t)+c~y(t)=F(t)$ but I have some problems determining the mass m of the system. The damped ...
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1answer
210 views

Transform a Continuous Time Differential Equation of a Low Pass Filter to Discrete Time

Assuming I have a linear differential equation of first order low pass filter: $$RC*y(t)'+y(t) = x(t) $$ And Assuming i know now that the input x(t) is being sampled at a rate of $T_s$ how can now ...