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2 votes

Cross-correlation of two processes generated from the same signal through different LTI systems

You have to work through the calculation once and you'll remember forever. I hope you can fill in the details yourself. First, from the definition of cross-correlation (assuming real-valued filters ...
Matt L.'s user avatar
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4 votes

Does the impulse response of every stable system have finite energy?

In general, BIBO-stability doesn't imply finite energy of the impulse response. Neither does finite energy of the impulse response imply BIBO-stability. Example 1: BIBO-stable but infinite energy $$h(...
Matt L.'s user avatar
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3 votes

If the input of the system depends on the future outputs then is the system non-causal?

The equation $$x[n]=y[n-1]-\frac52y[n]+y[n+1]\tag{1}$$ is just a way of representing the input-output relation of a linear time-invariant discrete-time system. It does not mean that the input depends ...
Matt L.'s user avatar
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0 votes

Linear Constant Coefficient Differential Equations: Zero-Input and Zero-State responses

In system's engineering, the zero input response of a system described by a linear differential equation refers to the homogeneous solution of the differential equation. True False
Mohit Singh's user avatar
2 votes
Accepted

Is heat equation considered as LTI system?

An equation alone does not describe a system. You can define a linear system from it if you consider the heat equation as defining a system $h$ where $$u(\mathbf x, t) = h(f(\mathbf x, t)) \tag a$$ ...
TimWescott's user avatar
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3 votes
Accepted

Is $y(t) = y(t-4)+x(t-4)$ time invariant or not?

Let's re-write your difference equation: $$y(t) - y(t-4) = x(t-4)$$ Delaying the input gives the following difference equation for the output $y_1(t)$:$$y_1(t) - y_1(t-4) = x(t-m-4)$$ A delayed ...
Jdip's user avatar
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2 votes

Doubt on LTI systems (Zero input-Zero Output)

Note that for an LTI system the input can be zero at a certain time, and the output at that time can be non-zero. You can only conclude that a system is not LTI if you observe a non-zero output for ...
Matt L.'s user avatar
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2 votes
Accepted

How to find impulse response for the given system?

Since the system is causal, its impulse response has the form $$h(t)=c_1e^{-t/RC}u(t)+A_0\delta(t)\tag{1}$$ Note the unit step function $u(t)$ in $(1)$. From $(1)$ we obtain the derivative $$h'(t)=-\...
Matt L.'s user avatar
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