Reduction Definition and 472 Threads

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. P

    How Do You Solve a Second Order ODE Using Reduction of Order?

    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...
  2. 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...
  3. 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
  4. 1

    Having trouble understanding reduction of NADP+

    "Photosystem I transfers electrons to NADP+, reducing it to NADPH." This is mentioned many times in my textbook, in other examples besides photosynthesis. NADP+ reduced into NADPH. I agree that receiving an electron is a reduction. But how does receiving electrons turn NADP+ to NADPH? That...
  5. B

    Reduction Formulae: Defining I(n) & Establishing Reduction Formula

    Define I(n) by I(n) = integral of x^n / square root(1+x^2) dx. Evaluate I(0), I(1) and then establish the reduction formula I(n) = ((root2)-(n-1)I(n-2))/(n) for suitable values of n, which should be stated Here is my attempt I found I(0) first,and got the answer to be...
  6. A

    Pressure reduction and increased volume

    Hi. Can someone help me please. I have a steam generator which is designed to operate from natural gas with pressure of 2000 -4000 mmAq. It consumes a volume of 71 Nm3/h of the gas. I want to operate it on Liquid Petroleum Gas (LPG-Propane). The problem is that LPG is available in cylinders at...
  7. S

    Reduction of magnetic repulsion

    Hope I'm in the right spot, google searches lead me here. I am working with a couple N50 ring magnets which are axially magnetized, as an alternative to a coil spring. They are going around a steel rod which acts as the guide, and is an integral part of the complete assembly. My question...
  8. L

    LSZ reduction coeffs etc (Srednicki)

    In free field theory one particle states can be created as: |k\rangle =a^{\dag}(\vec{k})|0\rangle . Just as we can expand the field operator in terms of the creation and annihilation operators it is possible to obtain an expression for the creation operator in terms of the field, it turns out...
  9. K

    Simplifying a Boolean Function: Is This the Correct Solution?

    I have the following function to be reduced/simplified. F(A,B,C,D) = BC + (A + C'D') where ' denotes the complement Here's my solution: = BC + (A + C'D')' = BC + (A + (C+D) = BC + (A + C + D) = BC + C + A + D = C(B + 1) + A + D = C*1 + A + D = C + A + D Is this correct?
  10. M

    Matrix proof - augmented matrix - row reduction - column operation - proof

    Homework Statement If we let A be the augmented m x (n + 1) matrix of a system of m linear equations with n unknowns Let B be the m x n matrix obtained from A by removing the last column. Let C be the matrix in row reduced form obtained from A by elementary row operations...
  11. S

    Reduction in resonance magnitude for a motor/drive-axle model

    Hi all, I am conducting some tests on a simulated physical model of a motor/drive axle system. The goal of the experimentation is to come up with some suggestions to reduce the peak magnitude at the resonant frequency by 30%. Based on the analysis done, a few proposed changes are 1)...
  12. E

    Can Trigonometric Identities Simplify Row Reduction Problems?

    Homework Statement I am having trouble row reducing... 5cos(t) 5sin(t) | -cos(t) 2cos(t)+sin(t) 2sin(t)-cos(t) | sin(t) Homework Equations The Attempt at a Solution I know I am allowed to multiply a row by a constant but I...
  13. C

    How do you decide which operations to do in a matrix row reduction?

    How exactly do you decide which operations to do in doing a matrix row reduction? Every example I see just randomly multiplies the rows or does row operations and magically they get the answer. HOW do you know to do certain operations? I understand the reduced row echelon form but it still...
  14. B

    Rate of reduction of the volume of a raindrop

    I have trouble solving the following question, would someone offer some help? thanks. In very dry regions, the phenomenon called Virga is very important because it can endanger aeroplanes. [See Wikipedia] Virga is rain in air that is so dry that the raindrops evaporate before they can...
  15. M

    Integration with Reduction Formula

    Hello :smile: I was hoping someone could help me with this. I'm going round in circles and don't understand how to solve it. Homework Statement The integral I_m is defined as: I_m = \int^{\frac{\pi}{2}} _{0} (cos^m(x))dx where m is a positive integer. By representing cos^m(x)...
  16. Z

    Standard Reduction Potentials Question

    Homework Statement Which of the following statements is correct if Standard reduction potentials of Cu and Sn are 0.337V and -0.136V resp. (both from +2 charge) a) Cu2+ ions can be reduced by H2(g) b) Cu can be oxidised by H+ c) Sn2+ ions can be oxidised by H2(g) d) Cu can reduce Sn2+...
  17. S

    Integration by Reduction Formulae

    Can anyone help me out with a proof for the integral that's in the attached images, its driving me nuts :frown:
  18. A

    Can you do integral of sec^5(x)tan^2(x) without reduction formula?

    Homework Statement Can you do integral of sec^5(x)tan^2(x) without reduction formula? Homework Equations The Attempt at a Solution If so, would it be integration by parts? I tried splitting it up in way too many ways to post them on here. Thanks for any hints!
  19. O

    What are the steps for reducing sound intensity by 20 decibels?

    Homework Statement A man stands 3m from a siren. How far does he have to move to reduce the intensity level by 20 decibels? Homework Equations Intensity level = 10log(I/Io) the inverse square law The Attempt at a Solution i know the answer is 30m because 10 times the distance drops...
  20. Z

    Describing Massive Theories by Dimensional Reduction

    Hi, I know that massive field theories are not conformally invariant. However one can incorporate mass by adding an extra dimension, and setting its corresponding momentum to be equal to mass and thereby modifying the constraint equation for spin. The next step as I understand is to perform...
  21. P

    Reduction formula for ∫(lnx)^n dx

    Homework Statement derive a reduction formula for ∫(lnx)n dx and use it to evaluate ∫1e (lnx)3dx Homework Equations The Attempt at a Solution In other examples we've started by saying ∫(lnx)ndx = ∫(lnx)(lnx)n-1dx and using integration by parts. So let: f = (lnx)n-1 f' =...
  22. M

    Reduction of Order - Legendre Eqn

    Legendre's eq of order n>=0 is (1-x^2)y'' -2xy' +n(n+1)y = 0. You are given the soln y = P_n(x) for n=0,1,2,3 to be P_0(x)=1 ; P_1(x)=x ; P_2(x)=(3x^2-1)/2 ; P_3(x)=(5x^3 -3x)/2. Use reduction of order to find the second independent soln's Q_n(x) OK I've found Q_1(x) = ln(1-x)(1+x)...
  23. S

    Why does vasodilation in periphery lead to reduction in blood pressure?

    Hello everyone, Ok generally what do they mean when they say vasodilation in periphery lead to reduction in blood pressure? Do I have to think of this as expanding the size of a fluid filled container so less fluid splashes againts the walls reducing pressure. Or do I have to think of this...
  24. Z

    The Attempt at a SolutionReduce Ellipse: Centre & Eccentricity

    Homework Statement Reduce the given ellipse in standard form and find its centre and eccentricity. 4(x-2y+1)2 + 9(2x+y+2)2 = 25 Homework Equations Rotation of axes x=Xcosθ - Ysinθ y=Xsinθ + Ycosθ
  25. G

    Reduction of Order no independent or dependent variable

    Homework Statement y'' +(y')^2 = 6(y') -9 Homework Equations u = y' u' = y'' The Attempt at a Solution equation from 1 becomes u' + U^2 = 6u - 9 du/dx + u ^2 = 6u-9 du/dx = -u^2 + 6u -9 du/dx = -(u^2 +6u - 9) du/dx = -(u-3)^2 du/(u-3)^2 = - dx integrate...
  26. O

    Why and how are ketones reduced?

    found this on this page http://www.chemguide.co.uk/mechanisms/nucadd/reduce.html#top can someone explain why it is simplified? and how does it really happen?
  27. tom.stoer

    Spontaneous dimensional reduction of quantized spacetime

    Interesting paper: http://arxiv.org/abs/1009.1136v1 The Small Scale Structure of Spacetime Steven Carlip (Submitted on 6 Sep 2010) Abstract: Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such...
  28. atyy

    The Hidden Symmetries of the BKL Limit: From Cosmology to Quantum Gravity

    Carlip has argued that the dimensional reduction in many apprroaches to quantum gravity is related to the BKL limit where the dynamics becomes 1D, and the spectral dimension becomes 2D. http://arxiv.org/abs/0909.3329 Interestingly, another viewpoint about the (de)-emergence of space comes...
  29. D

    2nd ODE, Reduction of Order, Basis known

    I have a homework problem where I am to find y_2 for a 2nd ODE, with y_1=x. I'm familiar with the process of: let y_2 = ux y_2- = u'x u y_2'' = 2u' + u''x substituting these terms into the 2ODE, then letting u' = v. When integrating v and u' to solve for u, do I need to include...
  30. V

    Solve Reduction of Order: y" - 4y' + 4y = 0

    Homework Statement solve y"-4y'+4y=0 y1=e^(2x) using reduction of order The Attempt at a Solution y2=uy=ue^2x y2'=u'e^2x+2ue^2x y2"=u"e^2x+4u'e^2x+4ue^2x I then substitute that into the original equation to get u"e^2x+4u'e^2x+4ue^2x-4u'e^2x-8ue^2x+ue^2x=0 simplify to get...
  31. B

    Derivatives of First Solution in Reduction of Order

    Homework Statement find the first and second derivative of first solution. Homework Equations y(x)=m(x)y_1(x) y'(x)=m'(x)y_1(x)+m(x)y_1'(x) The Attempt at a Solution I have been given y_1=\frac{1}{x^n} Which part is the m(x) and which is y_1(x) I'm not sure how to do...
  32. M

    Reduction of benzophenone to diphenylethanol

    Hi When you are reducing benzophenone to diphenylethanol you use 4 moles of sodium borohydride. I don't know how you would write this as an equation because I don't know what the sodium borohydride becomes. It has lost 4 hydride ions and is just with a sodium and boron. Also, you haven't made...
  33. B

    More reduction of order DiffEq goodness

    Homework Statement Use the substitution y = (x^2 + 1)u to solve the differential equation (x^2 +1)y\prime\prime = 2y The Attempt at a Solution I was having some trouble with these earlier because I needed to brush up on my trigonometric substitution. Let's try this one... Making the...
  34. M

    Cold Rolling Reduction Calculation Troubleshooting: Negative Signs Explanation

    I have some difficulties on calculating the reduction on cold rolling process but mi signs is negative. Is that normal? Cheers
  35. r-soy

    Q in Oxidation and reduction I want chack my answer

    Hi 1 ) show how many electron are transferred in the following equation a ) Cu + Ag ----- > Cu^+ + Ag B) Zn + cl2 ----- > ZnCl2 my answer is : A) Cu ---- > Cu ^+ + ie- 1e + Ag^+ ----- > Ag then the electron which transfer is ( 1 ) B ) Zn + cl2 ---- zncl2 Zn...
  36. B

    Solve (cos x)y''-y'+y=0 Using Reduction Method

    find the general solution of (cos x)y''-y'+y = 0 L[y1] = 0 L[y2] = 0 L[y1] x y2 : (cos x)y1'' y2 - y1'y2 + y1y2 = 0 ...(i) L[y2] x y1 : (cos x)y2'' y1 - y2'y1 + y1y2 = 0 ...(ii) (i) -(ii) : (cos x)(y2''y1 - y1''y2) - (y2'y1 - y1'y2) = 0 W = | y1 y2 | = y1y2' - y2y1' | y1' y2'| W' =...
  37. D

    Exploring Dimensional Reduction in Star Systems and Galaxies

    Like entropy tends towards chaos, why do star systems or galaxies tend to reduce their movement through the 3rd "Z" dimension even though all particles can freely move in all 3 dimensions? Flattening out. Is there some sort of word or phrase which describes this behavior? Is it possible...
  38. T

    Reduction formula integration method help

    Homework Statement Well, I've been doing a lot of research about the reduction formula as a method for resolving integration problems. However, not much information on the topic is to be found about the topic. The only things i get to find are examples with the formulas already given, which is...
  39. T

    Reduction formula question (int by parts)

    Homework Statement Let I_{n} = \int^{2}_{0} x^{n}e^{x} dx where n is a positive integer. Use integration by parts to show that 2^{n}e^{2} - nI_{n-1} By first finding I_{1} = \int ^{2}_{0} xe^{x} dx find I2 and I3.Homework Equations I'm sure your all aware of the formula for Int by...
  40. M

    Solving a Reduction of Order ODE with Initial Conditions | Math Homework Help

    Homework Statement Solve: y'' -y' e^{y'^2-y^2} = 0 y(0) = 1 y'(0) = 0 Homework Equations The Attempt at a Solution No idea how to use it. If I use the substituion y' = p, and y'' = p'p I need to integrate e^{y^2} which is unintegratable. What should I do?
  41. C

    Calculating the Distance to Reach 7.5% Weight Reduction of a Uniform Sphere

    1. Homework Statement : It can be shown that for a uniform sphere the force of gravity at a point inside the sphere depends only on the mass closer to the center than that point. The net force of gravity due to points outside the radius of the point cancels. Question: How far would you have...
  42. T

    Verify Solution of Matrix Row Reduction Problem

    Homework Statement http://img708.imageshack.us/img708/7309/10324398.jpg The Attempt at a Solution First I row reduced the matrix into the RREF and got \left[ \begin{array}{cccc} 1 & 0 & -1 & -2 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 0 \end{array} \right] (0,1,2,3) is a linear...
  43. A

    Find the Ratio of Sound Intensity with 40 dB Reduction | DB Ear Plug Guide

    [b]1. When you buy earplugs at the store, they have a "dB rating". What it tells you is the reduction of SIL that the plugs will provide, if properly worn. Suppose you're helping some friends, working the stage at a rock concert wearing earplugs that provide a reduction of 40 dB. What is the...
  44. E

    Why Must Sodium Borohydride Be Added Slowly in Benzophenone Reduction?

    Why do you have to add sodium borohydride slowly to reduce benzophenone to benzhydrol? And why do we have to place the reaction in iced water?
  45. S

    Modulo Reduction Using Fermat's Little Theorem

    Homework Statement Reduce 34567 modulo 19. Homework Equations The Attempt at a Solution I approached by first reducing 4567 modulo 18. I got the following: 34567= 318*253+13=(318)253*313 congruent to 12531594323 congruent to 14 mod 19 Is this the correct approach? I am not...
  46. R

    Efficient Voltage Reduction for Solar Cell Arrays

    I plan on using two solar cells that can each generate 3 volts and ~80mA each and wiring them in series to get an array that generates 6 volts and ~80mA. However, I need ~4.5 volts from the array. What would be the best way to decrease the voltage to this level with the given array?
  47. K

    Fractional Reduction of Earth's Gravity at Halfway to Center

    You dig a hole half way to the center of the earth. You lower an object to the bottom of the hole. By what fraction has the force of the Earth’s gravity on the object been reduced relative to that at the surface? Assume that the Earth is a sphere and has uniform density
  48. M

    D’Alembert’s reduction principle

    Hey guys, I'm stuck on this problem! I have no idea how to even go about solving it. I tried searching the net for D'Alembert's principle but nothing was helpful. Any suggestions on how to go about solving it will be much appreciated! Find with the aid of D’Alembert’s reduction principle the...
  49. D

    Reducing Boolean Expressions: Axioms and Simplification Techniques

    I have been stumped by a simplification problem - well, I can solve it, but I'm not sure how to do it axiomatically! The expression is A(B+C)+B'D+C'D' I can see that the (B+C) is redundant in the first term - if A is true, the whole is true regardless of (B+C)'s value. So it reduces to...
  50. mheslep

    Reducing ZnO to Zn: Thermal vs. Electrowinning

    The two commercial methods of reducing ZnO to Zn appear to be Thermal, in the presence of C: 2 ZnO + C → 2 Zn + CO2 and electrowinning: ZnO + H2SO4 → ZnSO4 + H2O (followed by electrolysis on the ZnSO4) But what is the effect of straight electrolysis on ZnO in the presence of some electrolyte to...
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