My question is very fundamental: adding two sinusoids in phase results in a sinusoid with twice the total energy of both sinusoids combined according to how we calculate power as A^2/2 with A being the amplitude. None of this answers the extremely fundamental question of how is energy conserved??!
The energy (or power really) at the point of interference is twice the total energy/power of the two waves. How does that work in light of conservation of energy?
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...
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...
Also another question. You said: "The FFT of 101 data points is doing the FFT of the periodic time series
1, [99 points defining the cosine wave], 1, 1, [99 points repeated], 1, 1, etc"
But doesnt taking a larger point FFT mean padding the input with trailing zeros? Your input seems padded...
Thanks alpha zero. That cleared up many things. Can you tell me what it mathematically means to use an FFT with a length more than the time domain signal length?
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...
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...
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...
I do not understand how <ek , er> results in a delta function. Isnt the integrand going to be e^(2pi i k) * e^(-2pi i r). While this is equal to 1 if k = r, it isnt necessarily 0 if r isnt equal to k. How did u interpret it as delta? please clarify.
"For functions defined on the interval from n-1/2 to n + 1/2 with n some arbitrary integer, we define the inner product:
LaTeX Code: \\langle f,g\\rangle = \\int_{n - 1/2}^{n +1/2} f(x)g^{*}(x)dx
Then we see that:
LaTeX Code: \\langle e_k, e_r\\rangle = \\delta_{k,r}
where LaTeX Code...
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...
Ok, after playing with it, I see what you're saying, the larger the range of t, the closer it is to the real thing (although I dont see why). but, how to relate the values on the x axis to frequency?
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...
still doesnt help. thats like the unit step function. im looking for a function thats 0 everywhere and 1 at 0. is it hard to manually code such a thing?
i cant use the dirac function that comes with matlab because I need a modified diract function that is 0 everywhere and ONE at 0. the one that comes with matlab is INF at 0.
how to, please a sample code pelase im not proficient with matlab and the way it works but im trying my best. I just wana see a sample code to get the hang of it...
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...
thanks. i've been thinking about it also I arrived at this: since the electron orbits the nucleus VERY fast one could say the average position of the electron in time is right where the nucleus is so effectively the electron cancels the effect of the positive charge and the electric field...
born2bwire, from ur first paragraph, wat do u mean by local 'net charge'? and does answering this question strictly reuires knowledge of modern phsyics (quantum theory)?
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?