In signal processing, overlap–save is the traditional name for an efficient way to evaluate the discrete convolution between a very long signal
x
[
n
]
{\displaystyle x[n]}
and a finite impulse response (FIR) filter
h
[
n
]
{\displaystyle h[n]}
:
where h[m] = 0 for m outside the region [1, M].
The concept is to compute short segments of y[n] of an arbitrary length L, and concatenate the segments together. Consider a segment that begins at n = kL + M, for any integer k, and define:
{\displaystyle y_{k}[n]\ \triangleq \ x_{k}[n]*h[n]=\sum _{m=1}^{M}h[m]\cdot x_{k}[n-m].}
Then, for kL + M ≤ n ≤ kL + L + M − 1, and equivalently M ≤ n − kL ≤ L + M − 1, we can write:
y
[
n
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=
∑
m
=
1
M
h
[
m
]
⋅
x
k
[
n
−
k
L
−
m
]
≜
y
k
[
n
−
k
L
]
.
{\displaystyle y[n]=\sum _{m=1}^{M}h[m]\cdot x_{k}[n-kL-m]\ \ \triangleq \ \ y_{k}[n-kL].}
With the substitution j ≜ n-kL, the task is reduced to computing yk(j), for M ≤ j ≤ L + M − 1. These steps are illustrated in the first 3 traces of Figure 1, except that the desired portion of the output (third trace) corresponds to 1 ≤ j ≤ L.
If we periodically extend xk[n] with period N ≥ L + M − 1, according to:
{\displaystyle x_{k}*h\,}
are equivalent in the region M ≤ n ≤ L + M − 1. It is therefore sufficient to compute the N-point circular (or cyclic) convolution of
x
k
[
n
]
{\displaystyle x_{k}[n]\,}
with
h
[
n
]
{\displaystyle h[n]\,}
in the region [1, N]. The subregion [M, L + M − 1] is appended to the output stream, and the other values are discarded. The advantage is that the circular convolution can be computed more efficiently than linear convolution, according to the circular convolution theorem:
where:
DFTN and IDFTN refer to the Discrete Fourier transform and its inverse, evaluated over N discrete points, and
L is customarily chosen such that N = L+M-1 is an integer power-of-2, and the transforms are implemented with the FFT algorithm, for efficiency.
The leading and trailing edge-effects of circular convolution are overlapped and added, and subsequently discarded.
For much of physics, its language is fundamentally math, but to a certain point, does philosophical thinking ever play an important part in creating or exploring physics?
It would seem, at least to me, that there is some significant overlap, given that much of understanding physics can't quite...
Hi! Some help with this problem would be much appreciated.
The overlap integral is defined as ##S = \int \phi_A (\mathbf{r}_A) \phi_B (\mathbf{r}_B) \,d\mathbf{r}##. For the two orbitals, I have that
$$\phi_A = \frac{1}{\sqrt{\pi}} \Big( \frac{1}{a_0} \Big)^{3/2} e^{-r_A / a_0}$$
for the 1s...
Now from physics I read that photons don't interact with one another normally, at higher energies they might through pair production but that is besides this point.
So this means that for example if we have multiple sources of EM radiation like say multiple sub pixels within a screen then each...
I have trouble understanding the solution to a homework problem.
Consider the interaction Lagragian ##\mathcal{L}_{\rm int} = -iqA_\mu \bar{\psi}\gamma^\mu \psi##, i.e. photon-electron/positron interaction. We want to focus on the Compton scattering
$$e^-(\vec p_1, \alpha) + \gamma(\vec p_2...
Hi
I study optics and many times i found a term called (Overlap integral ) as attached pictures .. I can't understand from where these expression comes (mathematically) and what these functions means in particular ( even from mathematical point of view)
I can't understand the nature of...
##\newcommand{\ket}[1]{|#1\rangle}##
##\newcommand{\bra}[1]{\langle#1|}##
I have a momentum-shifting operator ##e^{i\Delta p x/\hbar}## acting on the ground state ##\ket{0}## of the QHO, and I want to compute the overlap of this state with the n##^{th}## excited QHO state ##\ket{n}##. Given...
Homework Statement
Homework Equations
Since question says the current is always continous, so overlap is always there. So option B is incorrect.
Also since firing angle is increased from 0 to 45, the overlap angle will reduce. So it'll be less than 45. So option A is incorrect.
The Attempt...
When formatting a drawing canvas in Microsoft Word 2007, one box to click or unclick (by default, it is selected) when one goes to the Advanced settings of Layout is "allow overlap." Overlap of what?
Homework Statement
Question:
Drawn an orbital overlap diagram to represent the bonding in ammonia, NH3.
Homework Equations
[/B]
none
The Attempt at a Solution
I learned that bonding occurs with the outermost s and p orbitals.
For nitrogen:
1s2 , 2s2 , 2p3
For Hydrogren:
1s1 X 3.
This is...
That is to say, how does time behave in a region of space where multiple gravitational fields cancel out their accelerating effects?
I understand that time "slows down" in a gravitational field, but does this depend on the actual presence of the field, or instead the actual net acceleration...
Homework Statement
[/B]
I'm trying to solve the following problem. (a) was easy but I am stuck at (b).
Homework Equations
[/B]
Since we are told that the Hamiltonian is conserved, and the answer is in terms of the uncertainty of H, I assume I have to use the conservation of uncertainty...
What I am interested in doing, is considering the angular momentum eigenstate for a spin ##1## system: ##|J=1, M=1\rangle = \begin{bmatrix}
1 \\
0 \\
0
\end{bmatrix}##, forming the coherent state ##|CS \rangle = \begin{bmatrix}
0.5 \\
-\frac{i}{\sqrt{2}} \\
-0.5...
so I am finishing up my studies of intro to quantum mechanics, and this is not in my book and looking at previous exams i have to know this for single electron atoms/ions.
one of the problems was somethin like
"the wave function of an electron is the overlap of the orbitals:
Ψ=aΨ1s+i/√3Ψ2p+¾Ψ3s...
Hello.
I am trying to prove that the uncertainty in energy for a normalized state limits the speed at which the state can become orthogonal to itself.
The problem is number 2 on https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/assignments/MIT8_05F13_ps6.pdf
Having issues...
I was reading Peskin&Schroeder's QFT book, and there was some discussion about how ##\left|0\right>##, the ground state of a free field and ##\left|\Omega \right>##, the ground state of an interacting field differ from each other, and they outlined how the latter can be obtained by propagating...
Homework Statement
Homework Equations
none
This is how I was taught to draw orbital overlap diagrams in my lesson:
The Attempt at a Solution
[/B]
I have drawn four attempts for a possible orbital overlap diagram of NH3:
Attempt # 1:
For this one, are the atoms arranged correctly...
Homework Statement
Consider a spin state |n; +> where n is the unit vector defined by the polar and azimuthal angles θ and φ and the spin state |n'; +> where n' is the unit vector defined by the polar and azimuthal angles θ' and φ'. Let γ denote the angle between the vectors n and n':
n⋅n' =...
ummm, silly question I suppose(and one with likely no answer), and I don't know which Maths subforum to put it in. It's not a pressing thing, just a curiosity.
How do I find the equation of a section that is the overlap of two functions? Not the area of such a section(which would be using...
Hello.
It is said that if we exchange two electrons, we can't tell which is which. Identical mass, charge, etc. So if I hold two electrons, one in each hand, and someone switched them, I wouldn't be able to know. But one way to distinguish particles is their trajectory. If I have a very long 1D...
I am trying to find a way to calculate the overlap integral between atomic orbitals centred on two different atoms, A & B as a function of the separation distance. I hope someone in the forum can give a hint on how to do that.
Thanks,
ftft
hi,
I have four variables (x and y),(a and b). i want to find out number of state which these variables can attain.
Example :
1) x=2 ,y =5 , a= 0 , b=2 ( that is a and b is less than x and y)
2) x=2 ,y =5 , a= 0 , b=2 ( that is a is less than x and b equal to x)
3) x=2 ,y =5 , a= 0 , b=3 (...
http://oi58.tinypic.com/2d85aix.jpg
above is an url to the stats major program at my school. In red are the two classes that overlap. Is it likely that the overlap is intended, or a typo? Do universities ever allow such overlap (an emphasis class overlaps with a core class)?
They changed it a...
Homework Statement
Recall the definition of the overlap of wave functions Φ and Ψ:
[; (\Psi , \Phi ) = \int\limits_{-\infty}^\infty dx\: \Psi ^{*} (x)\Phi(x);]
Let ψ1(x) and ψ2(x) be unit-normalised wavefunctions representing sharp-energy states with different energies (and hence zero...
Hi
I have a waveguide that is rectangular and multimode that I but-couple to a standard telecom SMF28 fiber. I have imaged the output of the waveguide and the fiber with a 25X microscope objective onto the chip of an IR-camera. Usually the mode overlap is calculated by cross-correlation of the...
Is there a way to mathematically describe the space where wave functions overlap like with how wave functions describe the space a particle could exist. Then if that is possible can you determine the time period at which that overlap will occur.
I have a fun project I'm trying to do and it's been a good number of years since I did any math higher than algebra. As such, I don't know how to approach this and would like some pointers.
I am trying to understand how I can subtract one function from another ONLY where the two functions...
A chemist is becoming suspicious here:
So, for visual convenience, the so-called dxy, dxz, dyz, dz2, dx2-y2 orbitals are actually linear combination of eigenfunctions. But chemists have been using the geometric feature of these 'manmade' orbitals to make sense the chemical bonding successfully...
Hello,
If we let U and V be two single determinant wave functions built up of spin orbitlas ui and vj respectively, will the overlap between them be as follows:
<U|V> = Det{<ui|vi>}
Thank you
Hello,
I would like to implement SAB=<psiA|psiB>which is the overlap of two Kohn-Sham determinants (psiA and psiB are two matrices containing each the molecular orbitals coefficients). Can anybody help me with this calculation? For case of SAA and SBB it is required to get the value 1...
Hello,
I would like to implement SAB=<psiA|psiB>which is the overlap of two Kohn-Sham determinants (psiA and psiB are two matrices containing each the molecular orbitals coefficients). Can anybody help me with this calculation? For case of SAA and SBB it is required to get the value 1 (perfect...
i search all over the web but i cannot find the definition. Although I find all the literature saying that metal have valence band and conduction band overlapped, (and I cannot find a metal example with valence band and conduction band not being overlapped), I wonder if there is a...
Hi,
I am trying to understand the Overlap Ratio (OR) / axial contact ratio of a helical gear pair. Unlike transverse contact ratio, I am unable to understand OR so easily.
What does it mean if the OR is exactly 1? What will happen practically when it goes less than one? Thanks.
Homework Statement
Particle originally sits in ground state about x=0. Equilibrium is suddenly shifted to x=s. Find probability of particle being in new first excited state.
Homework Equations
The Attempt at a Solution
Shifted wavefunctions are for ground state: ##\phi'_0 =...
Hi
I have uploaded the problem in the two files 3 and 4. Basically I have to see if the two rectangles overlap each other given the x, y coordinates of the centre and the width and the height of them.
Here is my code in Java.
import java.util.Scanner;
public class problem3_28 {...
Hey guys.
When i was studying the molecular orbital diagram for HF, it was said to me that 1s od hydrogen CANNOT overlap with 2py or 2px of fluorine due to the assymetry of these two orbitals, so it overlaps exclusively with 2pz. (And cannot overlap with 2s of fluorine becouse of large energy...
How much overlap is there usually between a physics and math degree?
Is it 50%+? And does being good or interested in one usually translate into being good at or interested in the other?
Help I am really confused! Orbital overlap in Hcl.
Hi,
The orbital overlap in HCl is due to hybridization between one sp³ oribital from Cl and one s orbital from H.
So why does the following picture say that the orbital overlap is between one p orbital from Cl and one s orbital from H...
How much overlap is there between physical chemistry and chemical engineering with regards to thermodynamics, kinetics, and transport phenomena? Would it be beneficial for a chemical engineering student to take the physical chemistry courses that deal with these topics? Or would it be redundant...
I was working on my thesis when this question popped into my head, why can't there be overlap in FDM wihout ICI but you are allowed to overlap in OFDM without ICI?
Also why is the maximum overlap of subchannels 50% in OFDM before ICI occurs?
From math point of view as long as the carriers are...
I know that, for k an integer, the rose polar curve expressed by r=r(θ)= cos(kθ) has a period of π if k is odd and 2π if k is even (usually expressed as saying that there are k distinct petals if k is odd, and 2k petals if k is even). However, I have yet to pin down the reason for this...
The problem is kind of easy to understand.
Given is some points, say 10 points. (I am using numbering for understanding)
0 1 2 3 4 5 6 7 8 9
Now group these such that the group size is 5 and there is no overlap
so, there can be 2 groups. the groups are (0 1 2 3 4) & (5 6 7 8 9)
Now...
I'm taking a calculus-based introduction to physics this semester and I'm finding it fascinating so far. The idea that there is a reason and a method for everything really resonates with me and that has lead to me really enjoying this course.
I'm also really into programming. I've spent quite...
I am not an expert on cosmology, merely an interested layman, so I hope my question is not either too stupid or obvious.
As I understand it from reading books (currently Brian Greene's "Fabric of the Cosmos"), general relativity (GR) is used for analysing large massive objects whereas quantum...
will the same amount of charge present at higher concentration in the binding region(between two nuclei), give a stronger bond, compared to the same amount of charge present at a lower concentration in the binding region? if so, could it be explained. is this the reason why s-p overlap is...
Hi, I need some help to work out the electron-hole overlap integral Mnn' for a quantum well:
Knowing that M'nn'=\int\varphi*en'(z).\varphihn(z).dz
=> How can I show that Mnn' is unity if n=n' and zero otherwise (in a quantum well with infinite barriers) ?
=> How can I show that Mnn' is zero...
To find the probability of a particle being at position x we use
<\Psi|\Psi> where the complex conjugate ensures that the answer is real. This means that we're looking at the square of the wave function to determine the probability of finding the particle.
Now to determine the probability...
http://edu.ioffe.ru/register/?doc=galperin/l3pdf2.tex
I don't understand how do you get from equation 21 to 22? How did the summations of exponentials becomes cosine functins?