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1. Energy of the summation of two sinusoidal waves

Suppose we have two laser diodes that are made to transmit light at the same wavelength and intensity. Also, suppose that we place them in an open space and separate them by a distance such that when their generated beams intersect at one point in space and one point only. Further suppose that...

Theorem: For every Hermitian operator, there exists at least one basis consisting of its orthonormal eigen vectors. It is diagonal in this basis and has its eigenvalues as its diagonal entries. The theory is apparently making an assumption that every Hermitian operator must have eigen...
3. OFDM frequency sensitivity (MATLAB related)

Hello everyone, I am trying to simulate an OFDM system and part of what I want to do is investigate the Bit Error Rate with respect to frequency offset. I understand how the offset vs BER curve should be looking like the curve obtained in the code in this link...
4. FFT question (MATLAB)

Hello, I have a very basic FFT question. Correct me if I am wrong, but the FFT is a fast implementation of the DFT (which is essentially the same as Discrete Time fourier series). The DFT is periodic in time and frequency. Thus if you input a time domain made of 4 times samples for example to...
5. Fundamental OFDM question (MATLAB related)

Upon feeding the IFFT block with the mapped date elements, shouldn't the binary data be upsampled by a sampling frequency that is equal to twice the highest subcarrier frequency (nyquist criterion)? I have written a code for a complete OFDM trasceiver system and I have not upsampled my binary...
6. Simulating OFDM system performance under different frequency offsets using MATLAB

Homework Statement I am simulating an OFDM transceiver using MATLAB. I am trying to investigate the effect of frequency offsets on the system performance by measuring different offsets against their respective bit error rate with a SNR of 10 dB. Homework Equations All equations and...
7. Poisson's summation formula

I am trying to understand the derivation of the Poisson's sum formula. Wikipedia's article is like crosswords to me. I checked mathworld's take on it. It looked simple, but it stated that the equation is derived from a more general result without stating or proving that general result. Here's...
8. Basic question on the FFT in matlab

Homework Statement From what I understand, the array output of the FFT of a function in time represents the frequency contributions of different frequencies with the first output coming from 0 freqeuncy, 2nf from the 1st fundamental frequency and so on.. if so, then why does this code(which...
9. How to manually write the code for a matlab delta function

that is 0 everywhere and 1 at 0. the code I wrote was this: n = -20:1:20; if n==0 imp = 1 else imp = 0; end >> stem (n, imp) ??? Error using ==> stem at 40 X must be same length as Y. but i got that error. Using vectors and matrices is useless cause the delta...
10. Distribution of charge within a CONDUCTOR

Can someone please tell me how charge (electrons is distributed inside a conductor with a circular cross section for example? how can charge be UNIformly distributed within it and why is it that the E field inside a conductor should always be zero? what dictates that?
11. MATLAB question I dont think I got it right

Homework Statement evaluate and plot this convolution: y[n] = 2^n u[n+4] * u[n-3] Homework Equations The Attempt at a Solution This is my code: n0 = 20; n = -n0:n0; u1 = (n+4)>=0; f1 = 2.^n; x = f1 .*u1; h = (n-3)>0; y = conv (x,h); l = length(x)+length(h)-1; k2 = linspace(-n0,n0...
12. Convolution in matlab

Homework Statement Sketch this function in matlab g = 3cos (10pi t) convolved with delta(t+1/10) Homework Equations The Attempt at a Solution I just need the full code to do it as an example so that I can follow up easily. thanks
13. Signal average power (complex signal)

Homework Statement Evaluate the average signal power of the complex signal x(t) = e ^ jwt Homework Equations The Attempt at a Solution I know how to solve this but I have a couple of questions on why we have the take the magnitude of the complex signal in the integral? Besides, does a...
14. MATLAB errors

Homework Statement plot using matlab: g = 3 cos (10pi t) convolved with 4 impulse (t +0.1) Homework Equations The Attempt at a Solution x = -10:0.1:10; u = 3*cos (10*pi*x); v = 4*dirac(x + 1./10); y = conv (u,v); plot (x,y); but i keep getting this error: Error using ==>...
15. Characteristic function in prbability

I was reading about it here: http://mathworld.wolfram.com/CharacteristicFunction.html very neat. But then I tried out of boredom integrating the expression by parts where u = the exponential term and v = f (x) (or P(x)). The integral came out nicely as I got a term similar to the left hand...
16. Normal distribution

Hello again So we are studying the gaussian normal distribution and what I understand about it is that it helps picture many of the natural phenomena where the basica idea is probabilities are equally distributed around the average. I understand that the e^-x^2 term in the formula ensures the...
17. Cumulative distribution function to probability density function how

Hello! I'm taking a mathematics course in probability and stochastic processes and we started covering the CDF (cumulative distribution function) which i understand perfectly and then the PDF (probability density function). The PDF was defined to be the derivative of the CDF. Now, the CDF is...
18. SOlving power flow using gauss seidel and matlab, HELP

Homework Statement We were asked to do a course project using to solve a powerflow system usign gauss seidel and newton raphson methods. after writing down the equations at each bus and double checking them this is the final code 2. The attempt at a solution c=1 V1=1 P2=-8 Q2=-2.8 V3=1.05...
19. Simple intuitive/graphical interpretation of the Gauss-Seidel method

Hi, I am currently studying the application of Gauss Seidel iterative method for solving systems of linear equations and am having trouble understanding the principle behind it. Can some1 provide any graphical or intuitive interpretation?? thank you
20. AC to DC conversion voltage regulators and zener diodes question

I am at the last stage of AC-DC conversion. I understood filtering all right. but when the filtered signal arrives at the regulator, isnt the regulator supposed to change that 'ripple' signal into a straight line?? Also, is there a derivation for the diode IV equation somewhere?
21. A conceptual question about current

Hello! We know that current flows in a circuit due to an electric field set up from the terminals which resembles that of a dipole, right? Now because it resembles the dipole's field, the electric field is NOT constant everywhere along the wire, and therefore, the electrons experience a...
22. Laplace initial value problem HELP! PLEASE!

Laplace initial value problem.... HELP! PLEASE! Hello all! I'm stuck on this question: y' + y = t sin t y(0) = 0 solve it using laplace transform,... my final is tomorrow, and its 2 am, i would appreciate a quick respone thanks in advance!
23. Proof of the convolution theorem for laplace transform

My textbook provides a proof but there's one thing about the proof i do not understand it starts assuming L{f(t)} = the laplace integral with the f(t) changed to f(a) same goes with L{g(t)} as it changes it to g(b) i understand the big picture>>starting from a product of 2 L transforms...
24. Understanding the core idea behind determinants

I'm really putting some effort into understanding the core idea behind determinants. For a 2x2 matrix, I obviously saw how to derive the formula for the determinant (using AA^-1=I). The question is, how did they define the |A| for higher order matrices? I'm reading a textbook on linear algebra...
25. Product of two integrals

Product of two integrals.... In proving a theorem, my DE textbook uses an unfamiliar approach by stating that the product of two integrals = double integral sign - the product of two functions - dx dy i hope my statement is descriptive enough. My question is, what's the proof to this?
26. Laplace transform

Laplace transform.... I cant help but keep asserting how me textbook of differential equations just keeps stating new ideas without any background on WHY and HOW they were created. I've just started Laplace transform and the first thing i see is a blue DEFINITION box that just states the...
27. Something about homogenous DE with constant co-efficients:

I know the solution to them is done by taking it for granted that the solution MUST be of the exponential form e^mx. But in the special case where we get two REPEATED roots in which case we multiply one of the solution by x to get an independent solution of the form x e^mx. This is what's...
28. Theorem of the uniqueness and existence of a solution of ODE

Could you please explain the theory intuitively and provide a proof to it. I understand how to apply it but i want to understand the logic behind it.
29. Existence and Uniqueness of a solution for ordinary DE

I just dont understand the idea behind it. I hate it when they throw these theories at us without proofs or elaborate explanations and just ask us to accept and applym mthem. Anyone care to enlighten me?
30. Base conversion - the LOGIC and INTUITION behind it

Base conversion -- the LOGIC and INTUITION behind it... for example, converting from base 10 to 2, a systematic way is to divide the number by 2's successively and keep track of the remainder. the remainder coefficients represent the binary number. Now why does this work is beyond me but I...