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  1. D

    General solution to differential equations

    I’m reviewing differential equations after taking the course about 5-6 years ago and I have a couple of questions about the solutions of differential equations. 1) First why is the general form of the solution to linear homogenous differential equations, with non-equal and real roots to the...
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    Impulse response of recursive DT system

    1. Homework Statement y[n] - 1.8\cos (\frac{\pi }{{16}})y[n - 1] + 0.81y[n - 2] = x[n] + 0.5x[n - 1] Determine the impulse response h[n] by calculating the zero-state response with x[n] = \delta [n] 2. Homework Equations y[n] - 1.8\cos (\frac{\pi }{{16}})y[n - 1] + 0.81y[n - 2] =...
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    Joint expectation of two functions of a random variable

    Ok I am not sure if I should put this question in the homework category of here but it’s a problem from schaums outline and I know the solution to it but I don’t understand the solution 100% so maybe someone can explain this to me. Let X and Y be defined by: \begin{array}{l} X = \cos \theta...
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    N-dimensional RV vs DT Random process

    Thanks mathman. I think I get it now.
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    Help learning Signal Processing/Communication Systems

    Here is a website that has some simulink tutorials that pertain to communications systems http://www.csun.edu/~skatz/ece561/561hmk.html. They are labeled matlab tutorial but there mostly simulink. The have some labs that are easy to work through with the solutions posted. I dont know many books...
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    N-dimensional RV vs DT Random process

    Thanks for your reply mathman. So the two are very similar but they are just interpreted diffrently? Is there any diffrence other than that which someone might know about?
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    Help learning Signal Processing/Communication Systems

    I think to build some intuition in the relm of signal processing i would recomend getting a copy of simulink and learning to use that. You can set up simulation of signal processing systems and learn a lot from doing that.
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    N-dimensional RV vs DT Random process

    If a discrete random process can be viewed as a collection of random variables indexed by a value n and a discrete N dimensional random variable can be viewed as N random variables with with a joint pmf. In these cases it seems like there is not much difference between a N dimensional random...
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    Expected value of stationary independent increments.

    1. Homework Statement Let \{ X(t),t \ge 0\} be a random process with stationary independent increments and assume that X(0)=0 . Show that: E[X(t)] = {\mu _1}t 2. Homework Equations 3. The Attempt at a Solution I tried to work backwards by argueing that the mean between...
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    Exact search

    How do i perform a search for and exact phrase? For example i want to search posts that have the phrase "Independent Increments" in it, but when i put quotes it still returns reasults that have only indepedent in the title.
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    Meaning of Independent Identically distributed random variables

    I am a little fuzzy on the meaning of Independent Identically distributed random variables. I understand the independent part but still not 100% on the identically distributed part. I understand that identically distributed means they have the same pdf and cdf but does this mean that they have...
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    Function of random variable

    1. Homework Statement Let X and Y be two independent random variables each exponentially distributed with parameter 1. Define a new random variable: z = \frac{x}{{x + y}} Find the PDF of Z 2. Homework Equations 3. The Attempt at a Solution \begin{array}{l} {F_Z}(z) = P(Z...
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    Autocorrelation and ESD/PSD

    Ahhh haa... I just found that in one of my books. Thanks. I just needed someone to point me in the right direction.
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    Autocorrelation and ESD/PSD

    Does anyone here have a good explanation of why the fourier transform of the autocorrelation function equals the ESD of the the original signal. It kind of make sense intutively because functions that have a autocorrelation that drops of quickly are high frenquency and the fourier transform of...
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    Inegral evaluation

    Thanks... I am a little rusty...
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    Inegral evaluation

    This is not a homework question but I am trying to follow the proof on wolfram that \int_{-\infty }^{ \infty }{e}^{{x}^{-2}} dx = \sqrt{\pi} and I am haveing trouble at one point where they state \int_{0 }^{ \infty }r{e}^{{r}^{-2}} dr = \left[- \frac{ 1}{ 2} {e }^{ {-r }^{2 } }...
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    Why are random variables needed?

    Ahh this is what i suspected... So its fair to say that the RV helps keeps the pdf independent of each expirment
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    Why a ring?

    Ok so I am not a math major and i haven't taken an abstract algebra class but i am curoius about the subject. I have been watching video lectures at UCCS at http://cmes.uccs.edu/Fall2007/Math414/archive.php?type=valid and the proffessor talks about groups and rings. In the introduction the...
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    Why are random variables needed?

    please corret me if i am incorrect in my understanding of a RV,PMF or anything else but as i understand it a random variable simply maps a expirmental outcome to a real number. And a probability mass function simply gives the probabilty that a number will occur. Now my question is this: why...
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    Virtual short concept

    well the differential voltage doesn't actualy reach "0". That is just the ideal. In reality it will be really small and thus there will be very little feedback to change the differential voltage. Since V2 - V1 = very very small V0 = very very very small since V0 = (V2 - V1)/A. And there will...
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    Virtual short concept

    First think about what the opamp does. It creates a "Large" differential gain A(V2- V1) = Vo. For the ideal opamp A is considered infinate. In real life its real big around 10000 or 100000. Think what would happen if there was a small diffrence between V2 and V1: (V2- V1) = .01V for example the...
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    Applications of Transistor

    O wait i meant the signal is input into the base not emitter.. i mean common emitter mode. I am still just a student so i dont realy actively use these things i am just trying to peice this together and figure out where my understaning is wrong.
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    Applications of Transistor

    Thank you or your reply. They way i understand how a transistor amplifier (BJT) works is that you input a small signal into the emitter then based on the change in the base emitter voltage the current Ic changes. Is this not correct? Then i was under the impression that the only reason...
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    Applications of Transistor

    So does this mean that the small signal analysis holds if we have a big enough diode? Even if we dont have a "small signal" per se.
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    Applications of Transistor

    I have a question along the same lines too. I am studying transistors as amplifier circuits at the moment and it seems to be that they can only be used to amplify small signals is that true? And if they can only be used to amplifier small signals what is that point of that? Do most of the...
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    Error progrigation

    Thank you sir
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    Error progrigation

    Error propagation 1. Homework Statement Calculate: \frac{ - \frac{R_{2}}{R_{1}}}{1 + \frac{1}{A} + \frac{R_{2}}{A R_{1}}} 2. Homework Equations R_{1} = 10000 \pm 5 \% R_{2} = 10000 \pm 5 \% A = 1000 3. The Attempt at a Solution I try to follow the example of at the website...
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    Opamp common mode rejection and virtual short

    ahh i should have read that before i posted... but i do have another quetion about what i dont understand about CMR: Is the only reason why we want common mode rejection is because of feedback and gain stabilizaiton? meaning that if the common mode gain A_{s} was high that there would be some...
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    Opamp common mode rejection and virtual short

    I have a few questions concerning opamps. First what is the big deal about infinite common mode rejection? It seems to me by looking at the open-loop gain equation A(V2 – V1) = V0 it is obvious that when V2 = V1 the output is zero (common mode rejection). This may be where I am confused …...
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