What is Reduction: Definition and 469 Discussions

Noise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree.
All signal processing devices, both analog and digital, have traits that make them susceptible to noise. Noise can be random or white noise with an even frequency distribution, or frequency-dependent noise introduced by a device's mechanism or signal processing algorithms.
In electronic recording devices, a major type of noise is hiss created by random electron motion due to thermal agitation at all temperatures above absolute zero. These agitated electrons rapidly add and subtract from the voltage of the output signal and thus create detectable noise.
In the case of photographic film and magnetic tape, noise (both visible and audible) is introduced due to the grain structure of the medium. In photographic film, the size of the grains in the film determines the film's sensitivity, more sensitive film having larger sized grains. In magnetic tape, the larger the grains of the magnetic particles (usually ferric oxide or magnetite), the more prone the medium is to noise. To compensate for this, larger areas of film or magnetic tape may be used to lower the noise to an acceptable level.

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  1. I

    Using integration by parts to prove reduction fomula

    Use integration by parts to prove the reduction formula: int(sec^n)x dx = (tan(x)*sec^(n-2)*x)/(n-1) + [(n-2)/(n-1)]int(sec^(n-2)*x dx n /= 1 (n does not equal 1) I used "int" in place of the integral sign. This was a problem on the corresponding test from the cal A class I am from...
  2. E

    Proving Reduction Formula

    If I n =integral sin (nx) dx/sinx,prove that In =2sin((n-1)x)/n-1 +In-2 for all integers n>(egual) . I don't know how to start...
  3. R

    Guyan Reduction for Modal/Eigen Analysis of Buildings

    Hi all, Before posting here I've read couple of articles, some books and through google search for this topic. I've basic perception of what's the reduction, what's the main goal and how we achieve it. But still got a dangling questions in my mind. For sake of simplicity let's assume...
  4. P

    Nonlinear 2nd order ode reduction solutions

    hey guys i've been trying to work out this ode reduction question, http://img204.imageshack.us/img204/8198/asdawt.jpg after i use the hint and end up with a seperable equation then integrate to get \begin{align} & p=\pm \frac{1}{\sqrt{{{y}^{2}}-2c}} \\ &...
  5. S

    MHB Repeated roots, non homogeneous - second order, reduction of order method

    I semi understand the reduction of order method, and i understand the general solution for a 2nd order with repeated roots. however, i can't seem to form up the correct thing to solve this question, and research again proves futile. Any assistance will be appreciated. Use the method of...
  6. C

    Second-order ODE, reduction of order?

    Homework Statement Find the specified particular solution: (x^2+2y')y'' + 2xy' = 0, y(0)=1, y'(0)=0 Homework Equations The Attempt at a Solution The equation seems amenable to the substitution p=y', so it can be transformed into (x^2 + 2p)p' + 2xp=0, or (x^2 + 2p)dp + 2xpdp=0. Since...
  7. J

    Having trouble understanding a dimension reduction step in a matrix.

    This is dealing with computer vision, but the only part I'm having trouble understanding is a step in the matrix math. So it seems appropriate it should go here. The paper/chapter I'm reading takes one of those steps saying "from this we can easily derive this" and I'm not quite sure what...
  8. D

    Understanding Gear Reduction: How to Achieve Lower Angular Velocity in Gears

    hi everyone! i was wondering how gear reduction is done besides connecting a small gear to a larger gear (radius speaking)? In my problem i have a gear - radius:5cm, angular velocity: 1000rpm I have a second gear - radius:5 cm, anguler velocity required: 1 rpm How do i make this...
  9. I

    Help with Matrix Reduction: Q1 & Q2 Answers

    Hi everyone! I'm in need for some help with Matrix Reduction! I have two questions: Question 1 Find the inverse of Matrix A by reducing the array (A|I), where A= 2 4 6 4 5 5 3 1 -3 Question 2 Find all solutions of the following system: 2x1 + 4x2 + x3 - 3x4 - 3x5 = -5 x1 + 2x2 - x3 + 3x4 -...
  10. P

    Differential Equations - Reduction of order

    General Question. How would I recognize when to do a full reduction of order versus using the formula y2=y1 integral(e^integral(P(x)dx)/y1^2) So far I only know by when the homework problem set, specifies to use the formula or the reduction of order. However I want to know if I can tell...
  11. S

    Stuck on the reduction of order step for solving this differential equation

    Homework Statement Find the general solution for the equation (x - 1)y'' - xy' + y = sin(x), x > 1 Given that y_1(x) = e^x satisfies the associated homogeneous equation. Homework Equations y_2 = v_2(x) * y_1 The Attempt at a Solution I read...
  12. A

    Equation distance reduction factor ERG

    Homework Statement Hello, I'm searching for the formula for the 2 pictures in attachment. The first is de reduction factor day and the other is the reduction factor night. As example for the factor day: on X I put the distance 10 Km, then I choose the value off L = 3 then I have as...
  13. F

    Strength reduction factors for welded edge joints

    I've looked everywhere and can't seem to find any information. Would someone be kind enough to point me to some literature?
  14. F

    Using reduction of order (conceptual) problems

    Homework Statement I have a nonhomogeneous 2nd order DE and I am given one solution to it and told to use variation of parameters? to get the general solution. First i need to get the 2nd solution though. Should I use reduction of order to get the 2nd solution? If so, then in what form should...
  15. S

    Integration using the reduction formula

    Read the math in the image below Is it possible to integrate the rational function using that reduction formula. If yes, how do I go about doing it? Keep it simple, I'm new to this (And I missed a lesson) Thanks!
  16. L

    Reduction formulas for integral of sin and cos

    Integrate sin2(x)cos4(x)dx using reduction formulas? My book says integral sin2(x)cos4(x)dx= integral cos4(x)-integral cos6x dx Now the reduction formula for n=6 for integral cos6(x)dx= (1/6)cos5(x)sinx+(5/6) integral cos4(x)dx Here is the part I don't get: It then says ...
  17. U

    Row Reduction over indicated field

    Hi- I am taking linear algebra and the teacher threw some problems at us that I cannot seem to figure out or find examples for online. Also, the textbook doesn't even cover the material. The problem states: Using Gauss-Jordan elimination, solve the following system with coefficients in...
  18. V

    Function Smoothing/ Noise Reduction

    Hi, my problem involves a laser sensor as a bin level sensor. what i want to do is get rid of the noise from the signal obtained. the spikes in the picture below are because the location of the laser sensor has to be where it is and when large rocks move down into the chute they pass infront...
  19. H

    Need help in deriving this reduction formula

    It might be difficult for you to read this integral in non latex form, but i'll try my best. As i don't know how to write this in latex form, assume "for this problem" that I(n) is pronounced as "I subscript n" or nth term of I. Homework Statement I(n)=∫ (sinx)^n dx [with...
  20. N

    Calculate Compound Reduction: % Reduction Every Second at Any Frame Rate

    hello everyone. I need a little help with something probably simple, for a game engine I'm writing. I want to reduce a number n by a certain percentage each second, p. But i want to do this with higher granularity, depending on the framerate my game is running at. So for example, if i...
  21. Y

    Impact of Bond length on Reduction of coordination complex

    Homework Statement The complex [Mn(CO)5Cl]+ is reduced by one electron and then by a second electron afterwards. How would the first reduction affect the C-O bond length in carbon monoxide? How would the second reduction affect the C-O bond length? Homework Equations The Attempt at...
  22. O

    Dc Voltage reduction LiPo battery

    Hi I have what seems to be a untractable problem On a racing motorcycle I am using a total loss ingition/datalogging and water pump system. To power this I am using a 5000Ma 30C LiPo battery (used because of it light weight and small size). The measured battery output is 15.2 Volts. Both the...
  23. C

    Legendre differential equation and reduction of order

    Homework Statement Question is to find a general solution, using reduction of order to: (1-x^2)y" - 2xy' +2y = 0 (Legendre's differential equation for n=1) Information is given that the Legendre polynomials for the relevant n are solutions, and for n=1 this means 'x' is a solution...
  24. S

    Guyan reduction for dynamic analysis

    Please cana nyone physically explain the meaning of Guyan reduction for dynamic analysis? I have an ide that it relates to the erduction in the degreeso f freedom of the structure for FE analsysis such that the model is still accurate but performs (in relation to the time required for completing...
  25. A

    A problem about reduction of the order of a linear ODE

    Homework Statement Show that if y1 is a solution to the ODE y'''+a2y''+a1y'+a0y=0 then the substitution y=uy1 reduces the order of the equation to a 2nd order linear ODE. The Attempt at a Solution well, I calculated first, second and third derivatives of y and plugged them in the equation and...
  26. L

    Solving A Non-Homogenous DE Using Reduction Order

    Given y''-4y=2 and that one solution is y_{1}=e^{-2x} I need to find a second solution of the homogeneous equation, and then a particular solution of the homogeneous equation. Here's how I solved the homogeneous equation: y=ue^{-2x}, y'=u'e^{-2x}-2ue^{-2x}...
  27. L

    Finding A Second Solution For A DE Via Reduction Of Order

    I'm given y''-4y'+4y=0 and there is a solution y_{1}=e^{2x} Using this I need to find a second solution. Starting with the assumption: y_{2}=u(x)*y_{1} Then: y=ue^{2x} y'=2ue^{2x}+u'e^{2x} y''=4ue^{2x}+2u'e^{2x}+u''e^{2x}+2u'e^{2x} When I substitute back into the original equation, after doing...
  28. A

    Reduction by solvated electron

    [隱藏] When sodium metal is added to ammonia, some of the sodium dissolves. Each of the dissolving sodium atoms loses an electron and becomes a cation. Both the cation and the free electron are solvated by ammonia molecules. Na(s) + (x+y) NH3(l) → Na(NH3)x+(aq) + e-(NH3)y(aq) (blue) At this...
  29. S

    Variable reduction on constrained optimization techniques

    Hi all, I have this kind of optimization problem: Variable to control: A=A=[a1;a2;...;am] objective function to minimize: L=A*TL where L is a scalar T is a matrix [1,m] TL is a matrix [m,1] constrain: Dt>Dtv where: Dt=[dt1;dt2;...;dtn] Dtv=[dtv1;dtv2;...;dtvn] is a...
  30. P

    Second order DE, reduction of order method?

    Homework Statement find general solution of x2y''-xy'-3y=0 Homework Equations two solutions are given, y1=1/x and y2=x3 The Attempt at a Solution i think this is a reduction of order question? the only theory i can find in my text for second order DE relates to constant...
  31. K

    Reduction of order from 2nd to 1st

    I have been given the equation: y'' + y' - 2y = 0 and asked: " Express the equation as a 1st-order system. Solve the system using matrix methods." I thought in order to reduce an equation you needed one solution to it already. I tried using the general solution but it got messy...
  32. S

    Linear Algebra Row Reduction: Solving a System of Equations with Row Operations

    Linear Algebra Row Reduction? Homework Statement This question is frustrating me, and I might be missing the obvious, I tend to make algebraic mistakes, but I don't know what I'm doing wrong here! I'm trying to solve this system using row reduction: x-5y+4z=-3 2x-7y+3z=-2...
  33. S

    Solving a Reduction of Order Homework Problem

    Homework Statement Hi, i was reviewing some of the material covered this week and I'm wondering if someone can explain a brief step that I'm not quite understanding. The step is once you differentiate your given solution for example twice, then plug it back into the original equation, one of...
  34. I

    Vector Triple Production Reduction

    \nablax (A x B) I'm trying to reduce this triple product down so nabla is only operating on either A or B, not the product of the two vectors. I've been playing with this for a while now but can't really seem to make a dent in it. Any suggestions would be well appreciated.
  35. Jadaav

    Reduction of metal oxides by Carbon

    Can Carbon displace Aluminium, Silver and Gold from their oxides ? Also where is Carbon found in the reactivity series ? Edit : Got confirmation of Carbon's position in the reactivity series. But I still have a doubt about Silver and Gold because they are unreactive.
  36. J

    Relativistic Momentum Help With Equation Reduction

    Hi, so basically have been looking at http://en.wikibooks.org/wiki/Special_Relativity:_Dynamics#Momentum" and working my way through the maths for myself. However I have hit this point and can't get past it: \begin{align} u = \frac{v - u}{1-\frac{uv}{c^2}} \end{align} Which should be...
  37. N

    More reduction formulae troubles

    Homework Statement \intx^{n}2^{x}dx = \frac{2}{ln 2} - \frac{n}{ln 2} \intx^{n-1}2^{x}dx For n is greater or equal to 1, find \intx^{3}2^{x}dx This is a definite integral from 0 to 1 The Attempt at a Solution My first question is, after reducing this once, you are left with...
  38. N

    Evaluation of a reduction formula

    Homework Statement \int (1 - x^2)^n dx = \frac{2n}{2n+1} \int (1 - x^2)^n-1 dx for n greater or equal to 1, find \int (1 - x^2)^4 dx The integrals go from 0 to 1 Homework Equations The Attempt at a Solution Well what I did was to keep doing n - 1 whilst pulling a fraction...
  39. J

    Gear mechanism and wheel arrangement for reduction of fuel consumption

    Hi everyone, I hope I have posted in the right place. I'm a commerce student and have absolutely no idea about mechanical stuffs. My father has an idea in mind which he would love to implement. He too is a commerce student. Hence, I need some help from you'll to see if this is really practical...
  40. U

    Unit reduction is not making sense, what's going on?

    I am using an equation that states that critical sonic velocity is: a_{cr}=\sqrt{\frac{2\gamma}{\gamma+1}gR_{gas}T'} The units should result in velocity (\frac{m}{s}) Yet, when I do the unit reduction I do not get that answer. Here is what I get: Lets ignore the square root for now. Also...
  41. E

    Computing Copper Loss: Examples & Reduction Strategies

    Good day. just want to ask anyone about copper loss. How is it computed for example in a manufacturing plant or in a dept mall.Could anyone give an illustration/example? Also , is it true that copper loss can be reduced by using big wires?What if the wire is big enough? thank you. hope...
  42. L

    Comparing Mass Reduction from Fusion of Nuclei

    1. Rank from greatest to least the reduction of mass per nucleon that accompanies the fusion of the following pairs of nuclei: a. Two hydrogen nuclei b. Two carbon nuclei c. Two aluminum nuclei d. Two iron nuclei 2. n/a 3. I know fusion is when two elements are combined and...
  43. C

    Block Diagram Reduction: Steps to Find Closed Loop Transfer Function

    1. Homework Statement 2. Homework Equations I need to reduce the above block diagram to find the closed loop transfer function This is my solution to the reduction part of the problem: i) Add the feed forward paths; (10 + 10) ii) cascade G(s)2 x G(s)3 , {G(s)2 = 1/1+12, G(s)3= 20/s}...
  44. J

    Reduction of Order ODE - Stuck on question

    Reduction of Order ODE - Stuck on question! Help Please! The question says that y1= x is a solution to: x^3 y'' + x y' - y = 0 It then says to use y2 = y1 f(x) So I can do it this far and then I just get lost and my notes don't seem to clear anything! I'm just going to say y(2) = y2...
  45. B

    Def. of (mod2) reduction of w in H_2(M,Z)

    Hi, All: Just curious as to the definition of the "mod2 reduction of a homology class". The context is that an element w in H<sub>2</sub>(M<sup>4</sup>,Z) is called characteristic if "its mod reduction [w]<sub>2</sub> is Poincare-dual to the Stiefel-Whitney class...
  46. T

    Friction as a reduction of power

    Hi. I was wondering if someone could help me out. I am trying to work out what a value of friction will do to the power of a motor. For example, if I know the power output of the motor is 1W, and I introduce X amount of friction, what will the resulting output in power be. Could someone...
  47. E

    LSZ reduction and Renormalization constants

    Hey folks, i have a question about LSZ and how to take into account the renormalization constants of the theory in question. In the derivation, only the field strength renormalization enters as a factor of Z (or square root thereof) but some mates said that also the vertex renormalization...
  48. P

    Reduction of Order Problem

    Hey, guys. I'm having a hard time with a 2nd ODE reduction of order problem. The DE is t2y'' - 4ty' + 6y = 0, with y1 = t2. So I set up my y = t2v(t); y' = t2v' + 2tv; y'' = t2v'' + 4tv' + 2v. I then substituted back in and got: t4v'' = 0 This is where I'm getting stuck. The book...
  49. P

    2nd order ODE reduction of order method

    Homework Statement x^2 y''+2xy'-12y=0,y_1=x^3 y''+(2y')/x-12y/x^2 =0 Homework Equations The Attempt at a Solution y=uy_1=ux y'=u' x+u y''=u'' x+2u' subbing that in instead of y,y',y'' u'' x+2u'+2(u'x+u)/x+12(ux)/x^2 =0 now my book says to reduce the...
  50. E

    HELP Control Systems Engineering: Block Diagram Reduction Problem

    Help! I'm a third-year chick in engineering, stuck on a block diagram reduction problem for my control systems engineering course. Please email me and I'll send you a screenshot of the problem! kati@sidwall.com Thanks a mill. K xo
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