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  1. perplexabot

    12VDC/2A power adapter to power two systems?

    Hey! So I have a raspberry pi that uses 5V/1.2A and a LCD monitor that uses 12v/0.2A. I would like to power both using a single wall power outlet. I found a power adapter that converts 100-240VAC/50-60Hz/1.2A to 12VDC/2A. I was wondering if it is as easy as cutting off the connector on the...
  2. perplexabot

    MATLAB Solve Riccati (DARE) with MATLAB

    Hey all, I was wondering if you can help me define the arguments for the dare() function of matlab. Here is the DARE form I have: \begin{equation} \begin{split} \Phi(p_\infty) &= \Phi_\infty = \Phi_{33}-\Phi_{32}(\Phi_\infty+\Phi_{R})^{-1}\Phi_{23}\\...
  3. perplexabot

    A Derivative of log of normal distribution

    Hey all, I've had this point of confusion for a bit and I have thought that with time I may be able to clear it out myself. Nope, hasn't happened. I think I need help. Let us say we have the following \phi_{k+1}=\phi_{k}+v_k where, v_k\overset{iid}{\sim}\mathcal{N}(0,\sigma^2) and...
  4. perplexabot

    A Hessian of f(x)^T*Q*y

    Hey all. Let me just get right to it! Assume you have a function f:\mathbb{R}^n\rightarrow\mathbb{R}^m and we know nothing else except the following equation: \triangledown_x\triangledown_x^Tf(x)^TQy=0 where \triangledown_x is the gradient with respect to vector x (outer product of two gradient...
  5. perplexabot

    A Conditional expectation and covariance of function of RVs

    Hey all, I have been doing some math lately where I need to find the conditional expectation of a function of random variables. I also at some point need to find a derivative with respect to the variable that has been conditioned. I am not sure of my work and would appreciate it if you guys can...
  6. perplexabot

    I Gradient of ||f(x)||^2

    Hey, I have been trying to figure out how to solve \triangledown_x ||f(x)||^2_2. I have used the chain rule (hopefully correctly) to get the following: \triangledown_x ||f(x)||^2_2=2\triangledown_xf(x)^T \frac{f(x)^T}{||f(x)||_2} Is this correct? The reason I doubt my answer is because I know...
  7. perplexabot

    A What is the identity?

    Hey all. So I think I've been trying to figure this out longer than I should, that is why I am here now. I was reading an ieee paper and have been pondering a missing proof (the paper deems this proof too easy to show, literally... I must be really stupid or something). It is a simple question...
  8. perplexabot

    When is the gram matrix positive definite?

    Hey all. I know that A^TA is positive semidefinite. Is it possible to achieve a positive definite matrix from such a matrix multiplication (taking into account that A is NOT necessarily a square matrix)?
  9. perplexabot

    Constraint on M to keep M^T * A * M positive semidefinite?

    Hey all! Let me get right to it! It is given that $$A \succeq 0$$ I need the following to hold for M: $$M^TAM\succeq 0$$ What are the constraints or conditions on M for M^TAM\succeq 0 to hold? Anything would help at this point... I am open to discussion. Note: It may be worth mentioning that...
  10. perplexabot

    Changing to SDP (optimization)

    Hey all. Let me get right to it! I have the following objective function: \mathbf{minimize} \ \ trace((G^TG)^{-1}) I am trying to minimize it with CVX. I used schur complement to do the following: \begin{equation*} \begin{aligned} & \underset{G}{\text{minimize}} & &...
  11. perplexabot

    Linear algebra and choosing training vector

    Hey all. So I have been reading this article and have a question I would like to ask. I will be referring to this article extensively so it would be kind of you to open it: http://www.ee.ucr.edu/~yhua/MILCOM_2013_Reprint.pdf I believe reading the article is not required to answer my questions...
  12. perplexabot

    Independent elements of matrices?

    Hey all. I am currently reading an article and there is a paragraph that I am having a hard time understand. This is what the paragraph says: "Since Ar = Arτ and Ai = -Aiτ, we know that only the lower triangular (including the diagonal) elements of Ar are independent and only the strictly lower...
  13. perplexabot

    How to find transfer function of real world system?

    Hey all! I am trying to figure out how one goes about to try and find the transfer function (impulse response) of a real life system. Assuming the system is LTI. This "system" I speak of is a channel that is comprised of components such as linear amps, a mixer (can we even assume a mixer is...
  14. perplexabot

    Engineering Differential Mode Gain and 1/2 circuit

    Hey all! I have been trying this problem for a while and can't seem to get the same answer as the solution. If someone can tell me where I am going wrong, that would be much appreciated. I am very close to the solution, but I am missing a term in the denominator. Everything is shown below! Thank...
  15. perplexabot

    Input Resistance of Common Gate question...

    Hey all. I have been trying to calculate the input resistance of a common gate amplifier, but seem to have problems doing so. I know I have to set a test voltage (or test current) at the input, and I've been told, to ground the output. So using the Hybrid pi model for a mosfet, I did the...
  16. perplexabot

    Entropy question for 2 input 1 output system

    Hey all. I have a question regarding the solution to a question, both shown below (only part of the solution is shown). Specifically the line that states: H(Y|X) = H(Z|X). Why does this equality hold? Expanding and using the definition of entropy, I can see that for the above equality to hold...
  17. perplexabot

    Double sum of same variable simplification help

    Hello all, I have been meditating on this for a while, but can't seem to understand how this simplification came to be. Any help will be greatly appreciated. So, here is what we start with: ##\mathop{\sum_{k=0}^m\sum_{l=0}^n}_{m{\geq}n} x(k,l)## We also know that: l (lower case L) = n-m+k and...
  18. perplexabot

    Op-Amp convex optimization question

    Hey all. I have a question regarding an equation in a document I am reading about convex optimization of OP-AMPs. The document is attached, the equation is of section 3.4 and the equation number is (9). Can you please explain how it came to be? I understand that i3 = i4 = i5/2 but I don't...
  19. perplexabot

    C/++/# C++ and pthread simple program help

    Hey all. I am currently trying to brush up on my multithreading "skills" (I dare say) that I learned in my undergrad class. I have the following code that I am trying to run: #include <pthread.h> #include <iostream> using namespace std; void* func1(void*); int main(int argc, char** argv){...
  20. perplexabot

    Is this a convex set?

    Homework Statement Show if the set is convex or not! S2 = Homework Equations I know that to show a set is convex you can either use the definition or show that the set can be obtained from known convex sets under operations that preserve convexity. Convex definition: x1*Theta + (1 -...
  21. perplexabot

    Matrix derivative of quadratic form?

    Homework Statement Find the derivative of f(X). f(X) = transpose(a) * X * b where: X is nxn a and b are n x 1 ai is the i'th element of a Xnm is the element in row n and column m let transpose(a) = aT let transpose(b) = bT Homework Equations I tried using the product rule...
  22. perplexabot

    Operator change of basis

    Homework Statement Homework Equations \check{T} = BTB^{-1} (eq1) The Attempt at a Solution Ok, so I have a couple of questions here if I may ask... First, I want to be sure I understand the wording of (a) and (b) correctly. Is the following true?: (a) Write the matrix T...
  23. perplexabot

    Dual gate mixer help

    Hello all. So i have been trying to simulate a ndg transistor mixer in LTSpice. Here is what I have so far, but I am missing something and I can't figure what it is... Here is the schematic along with the waveforms. For some reason the output will not go over 0.3V (do I have to bias it?)...
  24. perplexabot

    IF amps for a superhet AM receiver

    Hey all. So I am now trying to work on IF amps for a superhet AM receiver (medium wave) and found the following figure in the ARRL handbook: I have a couple of questions regarding these schematics. First and most importantly, do these work for IF signals (of 455KHz with BW of 18KHz)...
  25. perplexabot

    DBM: Ring Diode Topology

    Hi all. I started a thread a while back about RF mixer design. I didn't know what to do or what design to choose. You guys laid some options for me and after some research and time I have finally decided that I will go for a double balanced, ring diode topology. Here is a schematic from google...
  26. perplexabot

    Cascode Amp questions

    Hello all. I have been looking into RF amps. I have come across the following cascode amp (from ARRL handbook 2014, p 12.10, FIG. 12.11. Thanks to Baluncore for the great reference). Here is a simplified version made with Qucs: My questions are regarding the capacitors, C1 and C2. Why are...
  27. perplexabot

    Controls VS. Communications (EE)

    Hey all. I will get straight to the point. I am about to get into graduate school and I have the option to choose between Controls & Robotics OR Communication & Signal Processing. I am kind of not sure what to pursue, the reason is because I feel if I choose one I will unfortunately lose the...
  28. perplexabot

    RF Mixer circuit help

    Hello all. So I have been trying to build a mixer lately, I have done my research on google but I am still kind of lost. I know now many mixers exist; single diode, multiple diodes, single balanced, double balanced, unbalanced and so on. I don't want to build a circuit blindly, so I am trying to...
  29. perplexabot

    High power switching circuit problem.

    Hello all. I am trying to use a mosfet as a high power switch. I have an arduino nano pin controlling the gate of the fet. I am using an NTE2374 mosfet. I am using a typical circuit: I also have the gate connected to the source (ground) so that when the gate is not HIGH, it isn't floating...
  30. perplexabot

    Power spectral density math

    Homework Statement For now I am trying to find the power spectral density only. The Attempt at a Solution From the given graph, I got g(t) = -1 + 2rect(t/2), with a perdiod of 4s PSD = Sg(f) = lim(T \rightarrow\infty ) \frac{1}{2T} || G(f) || ^{2} My fourier transform of g(t), G(f), I...
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