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1

You are trying to mimic what I did at time $t$. You'll be $y$ for now, say I'm $x$. Now suppose that our are mimicking my actions with your own modification pattern (called $f$), at the very same time. Then, your location, depending on mine, is: $$y(t) = f(x(t))\,. $$ Here, you only need the current observation $x(t)$. Now, suppose that you are ...


1

Y and Z should show the same values clear; %Create random vector x x = randn(32,8); %take ifft along each column y = ifft(x); Y = reshape(y,[],1); z = reshape(x,[],1); % d=conj(dftmtx(32))/32; X = kron(eye(8),d); Z = X*z;


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Since for a transmission line, the system is distributed since RLC is distributed in infinitesimally small sections in the line. The t values can be assumed to be infinitesimally small sections of the unit time delay system.


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However, for me, a distributed system is something like a transmission line, where the parameters can't be modeled accurately by "discrete" and finite elements. I can't grasp why this system is classified as distributed just because there are an infinite number of points describing the initial state. It's not just that you need an infinite number of ...


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You are right that a distributed system could be "something like a transmission line". Note that the system $$y(t)=x(t-T)\tag{1}$$ is a simple model of a transmission line, where just a frequency-independent delay $T$ is taken into account, and the attenuation is neglected. Note that lumped electrical systems, described by resistors, capacitors and ...


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The reason x[n] must be white is because the solution will effectively spectrally weight the channel response based on the amount of energy present in each spectral frequency location. A white noise source provides equal weight to all frequencies. If energy is not present in any particular frequency bin, a proper solution cannot be found for that frequency. ...


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Actually, we have two kinds of autocorrelation functions. One is defined for stochastic signals and the other for deterministic ones. If $x(t)$ is a stochastic signal, then its autocorrelation function will be $$R_x(t+\tau,t)=\Bbb E\{x(t+\tau)x^*(t)\}$$where $\Bbb E(\cdot)$ denotes the mathematical expectation. If x(t) is a deterministic signal, then its ...


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