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Topic: Step function

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	Heaviside step function - Wikipedia, the free encyclopedia
		The function is used in the mathematics of control theory and signal processing to represent a signal that switches on at a specified time and stays switched on indefinitely.
		The Heaviside function is an antiderivative of the Dirac delta function, H' = δ.
		This function is the cumulative summation of the Kronecker delta:
	en.wikipedia.org /wiki/Heaviside_step_function (388 words)

	PlanetMath: signum function (Site not responding. Last check: 2007-10-13)
		In applications, such as the Laplace transform, this definition is adequate since the value of a function at a single point does not change the analysis.
		A related function is the Heaviside step function defined as
		This is version 4 of signum function, born on 2003-05-05, modified 2003-07-18.
	planetmath.org /encyclopedia/SignumFunction.html (192 words)

	step function
		Another function that is sometimes called the step function, is the entier function int(x) or [x].
		The function describes the velocity of an object as result of a sudden force, during a infinitely small time interval.
		The Fourier transform of the function is the sinc function.
	www.2dcurves.com /line/linestp.html (287 words)

	PlanetMath: Heaviside step function
		However, the function was already used by Cauchy[2], who defined the function as
		Cross-references: delta function, Fourier transform, Laplace transform, signum function, function
		This is version 4 of Heaviside step function, born on 2003-07-18, modified 2005-07-28.
	planetmath.org /encyclopedia/HeavisideStepFunction.html (141 words)

	Means or Step Plus Function Limitation
		Thus, while a finding of non-equivalence prevents a prior art element from anticipating a means or step plus function limitation in a claim, it does not prevent the prior art element from rendering the claim limitation obvious to one of ordinary skill in the art.
		Avoid confusion with the doctrine of equivalents An "equivalent" for the purposes of 112, 6th paragraph, should not be confused with the doctrine of equivalents.
		Section 112, 6th paragraph limits the scope of the broad language of "means or step plus function" limitations, in a claim to a combination, to the structures, materials and acts described in the specification and equivalents thereof.
	www.uspto.gov /web/offices/com/sol/og/con/files/cons089.htm (2050 words)

	Design and Analysis of Queue Control Functions for Explicit Rate Switch Schemes
		Since the step function has discontinuities, it is very sensitive to the queue length value near the thresholds and the steady state might not be reached if the parameters are not set properly.
		The step function never converges: the values are fluctuating near the target values, so the standard deviation after one second is lower than the standard deviation in the first second.
		When the step function (figure 4 (a)) is used, the oscillations are more compared to the oscillations when other functions are used.
	www.cs.wustl.edu /~jain/papers/ftp/qctrl_bv/index.html (3518 words)

	-Basics 5- (Site not responding. Last check: 2007-10-13)
		This section is focused on the mechanics of transforming a function of time into a function of ‘s’, and the inverse transform operation.
		Step 3: Use this result as the coefficient of the Unit step function and
		The next step would be to determine the values of A, B, C,..., F so that the recombination of the partial fractions on the right hand side would have a numerator equivalent to the original numerator N(s).
	www.eduscape2000.com /DiffEq/basics5.html (566 words)

	www.batmath.it di maddalena falanga e luciano battaia
		The function f(x)=signum(x), in the interval [-1,1] is a step function.
		This is a step function on every interval [a,b] and is called the characteristic function or the integral part function.
		Given two step functions, s and t, and the corresponding two dissections D and E of their common domain [a,b], it's a useful exercise to prove that the two functions s+t and s·t are step functions and a possible dissection of [a,b] is simply D
	www.batmath.it /eng/a_riemann/step.htm (379 words)

	heavy-side step function
		r(t) is the integral of the step function u(t).
		It's graph is a ramp whose slope matches the amplitude of the step function (in this case, 2r(t-2), 2r tells you the amplitude of the original step function was 2.
		The idea of step functions is that you draw how you want the output signal (or function) to look on a piece of graph paper, then come up with an equation to describe that.
	www.physicsforums.com /showthread.php?t=84701 (1412 words)

	CTM: Step Response in Matlab
		Given a system that can be described by either a transfer function or a set of state-space equations, the response to a step input can immediately be plotted.
		You wish to see what the system response to unit step disturbance is. The unit step disturbance will be a change of the force acting on the system from zero Newtons one Newton at time t= 0.
		Because a transfer function can only have one input, all of the outputs (represented by the number of rows in the numerator of the transfer function) will be plotted on one set of axes.
	www.engin.umich.edu /group/ctm/extras/step.html (1033 words)

	Evaluating COTS Using Function Fit Analysis
		Function point analysis is the decomposition of an existing or planned system based on the user's perspective of functional requirements.
		During this step, a function point count is completed based on documented functional requirements or by analyzing the functions of an existing system to be replaced.
		The function point data from the previous steps is used to develop the project estimates in Step 4.
	www.qpmg.com /evaluating_cots.htm (3289 words)

	Guide to the Marine Biology Case Study (1)
		While it’s true that the Fish object’s Move function is invoked by the Step function, it is clear that the actual moving is performed by the Fish object.
		Despite the fact that the Environment object’s use of an apmatrix of Fish objects to represent the environment is transparent to the Step function, the function is able to perform its task.
		Since the number of steps required to eliminate the simulated population is usually far less than 999, it would be useful to find a way to terminate the program when the population level hits zero.
	mysite.verizon.net /vze4hzs6/mcx1/MBCS.htm (3061 words)

	CTMS: Step Response in MATLAB
		A step input can be described as a change in the input from zero to a finite value at time t = 0.
		You wish to see what the system response to unit step input is (an applied force of 1N).
		Both the step response for a set of state space equations or for a transfer function can be plotted with a user-supplied time vector.
	www.library.cmu.edu /ctms/ctms/extras/step.htm (670 words)

	Math 447 - rdavis2
		To accomplish this a function was created that would accept T and return a value in the form of x^2 + y^2 - p1^2.
		This was done by finding the "zeros" of the function (defined by T) and then using the bisection method on several ranges.
		The accuracy of both methods was characterized by observing the affect of varying values of N (iterations) and H (step size) on the error of both methods.
	mason.gmu.edu /~rdavis2/math447 (1175 words)

	Bode Step MATLAB Toolbox Function Listings
		function [gain1,phase1] = bonyqas(u,g,lslope,hslope,nml); % function [gain1,phase1] = bonyqas(u,g,lslope,hslope,bnm); % BONYQAS Asymptotic Bode and Nyquist diagrams corresponding in minimum % phase manner to a piece-linear gain response in dB specified by the % gain g(h) at k corner frequencies u(h) in rad/sec.
		% function [wd,wc,width,numc,denc,numl,denl] = bostep(x,y,n,bnc,zetaz,zetap,typ) % Defaults: [wd,wc,width,numc,denc,numl,denl] = bostep(10,0.1667,3,0.1,0.6,0.4,2), % x is gain stability margin in dB, default x = 10; % y is phase stability margin y*pi rad, default y = 0.1667; % n defines asymptotic slope -6n dB/oct, default n = 3; % bnc (0 to 1) is n.p.
		% The function numc(s)/denc(s) is the normalized compensator obtained % with function bostep for the nominal plant (1/s)(-s+wc/bnc)/(s+wc/bnc).
	www.luriecontrol.com /FunctionListings.htm (1690 words)

	E12
		Note that the area of the bottom function is equal to one, independent of the value of T. As T goes to zero the top function becomes the unit step.
		Both the impulse response and the step response are zero-state responses (i.e., the initial conditions are equal to zero).
		Note that because there is a discontinuity in the step response, there is an impulse in the impulse response (the step response of the first example had no discontinuity).
	www.swarthmore.edu /NatSci/echeeve1/Class/e12/Lecture/L03/L3.html (824 words)

	Step function - Wikipedia, the free encyclopedia
		In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of half-open intervals.
		A particular step function, the unit step function or Heaviside step function H(x), is obtained by setting n=1, α
		It is the mathematical concept behind some test signals, as those used to determine the step response of a dynamical system.
	en.wikipedia.org /wiki/Step_function (170 words)

	Lesson 4
		Mathematically, we proceed by assigning (as usual) the x-axis to the variable to be chosen from a normalized probability distribution function f(x) over a range (a,b) and the y-axis to the pseudo-random number supplied by the computer.
		Note that the mapping function must be unique both in the x->y mapping and the y->x direction, so it must be a non-decreasing function.
		Once again, we make this a sum of functions that are 0 except within a single region.
	web.utk.edu /~rpevey/NE582/lesson4.htm (1015 words)

	Math Help - Calculus - Derivatives - Technical Tutoring
		This function is zero for x values less than zero and 1 for all x greater than or equal to zero.
		This function fails the first condition (that the right and left limits are the same), so it fails to be continuous at 0, and so is not a continuous function.
		Since this point is arbitrary and the function value (and limit) is defined, the function passes both tests everywhere and so is continuous everywhere.
	www.hyper-ad.com /tutoring/math/calculus/Derivatives.html (1904 words)

	Function Points Step by Step
		An function point auditor should be independent, but an auditor can be still be inside your company, perhaps part of your metrics team, or they can be an independent third party.
		Of course the function point count itself can be used as evidence, but using the function point count alone would be severely inadequate.
		At the end of this article is a 20 step procedure that should assist anyone with developing their own guidelines or with auditing a function point count.
	www.softwaremetrics.com /fpsteps.htm (2250 words)

	BLOCK DIAGRAM CONSTRUCTION (Site not responding. Last check: 2007-10-13)
		To do this, you would "drag" a step function icon from the Sources window, a transfer function icon from the Linear window, two to workspace icons from the Sinks window, and a clock icon from the Source window to the blank block diagram window.
		The next step is to connect these icons together by drawing lines connecting the icons using the left-most mouse button (hold the button down and drag the mouse to draw a line).
		Connect the step function icon to the input of the transfer function icon, then connect the output of the transfer function icon to first to workspace icon.
	www.rpi.edu /dept/chem-eng/WWW/faculty/bequette/lou/simtut/node3.html (389 words)

	Laplace Transforms - 1a. The Unit Step Function (Heaviside Function)
		The switching process can be described mathematically by the function called the UNIT STEP FUNCTION (otherwise known as the Heaviside function after Oliver Heaviside).
		That is, u is a function of time t, and u has value zero when its argument is negative; and 1 when its argument is positive.
		Such a function may be described using the SHIFTED (or "DELAYED") UNIT STEP FUNCTION.
	www.intmath.com /Laplace/1a_lap_unitstepfns.php (417 words)

	XL2000: How to Display a Custom Function in Step 2 of the Function Wizard
		By default, this custom function appears in the Function Wizard under the function category called "User Defined." You can call custom functions with the Function Wizard in Excel just as you call built-in functions.
		However, there may be times when you want to use a Visual Basic for Applications macro to bypass step 1 of the Function Wizard and display a particular custom function in step 2 of the wizard.
		Microsoft support professionals can help explain the functionality of a particular procedure, but they will not modify these examples to provide added functionality or construct procedures to meet your specific needs.
	support.microsoft.com /?kbid=213183 (620 words)

	Jones on Stepping Motor Midlevel Control
		Depending on how the state is encoded, the create-vector function may be trivial; for certain applications, the next-state function is also trivial, but in the general case, next-state becomes an up-down counter while create-vector becomes a ROM holding the sequence of state vectors needed to form the control trajectories.
		Amature astronomers frequently need very slow motors to turn their telescopes, and in recent years, stepping motors have taken the place of synchronous motors and gear trains for many applications, particularly for barn-door or Scotch mounts, a class of extremely simple camera mounts used in astrophotography.
		Each flip-flop presents both inverted and non-inverted outputs to the world; this allows an equivalent circuit to be made by substituting a double-pole double-throw switch for the exclusive-or gates, and another equivalent circuit can be derived from this by substituting a pair of 2-input 1-output multiplexors for the switch.
	www.cs.uiowa.edu /~jones/step/midlevel.html (2148 words)

	Fold - MLton Standard ML Compiler (SML Compiler) (Site not responding. Last check: 2007-10-13)
		Unlike the usual list fold in which the same function is used to step over each element in the list, this fold allows the step functions to be different from each other, and even to be of different types.
		, that is, equationally speaking, equivalent to the identity function on a step function.
		The result type of the step is completely left open to be filled in by type inference, as it is an arrow type that is capable of consuming the rest of the arguments to the fold.
	mlton.org /Fold (3148 words)

	Fourier Series
		Any periodic function of interest in physics can be expressed as a series in sines and cosines—we have already seen that the quantum wave function of a particle in a box is precisely of this form.
		The first step is a trivial one: we need to generalize from real functions to complex functions, to include wave functions having nonvanishing current.
		The function is linearly divergent at the origin, and has finite oscillatory behavior everywhere else.
	galileo.phys.virginia.edu /classes/751.mf1i.fall02/FourierSeries.htm (1996 words)

	Four Function Calculator Step By Step
		Repeat the wiring technique of Step 6 for the lower switch, and the last free input dot on the left side of the AND gate.
		Repeat the wiring technique of Step 6 for the single dot on the right side of the AND gate to the dot on the left side of the LED.
		Steps H1 through H4 should produce the naming scheme for the Receivers as shown in Figure 1.
	www.dst-corp.com /james/CalculatorStepByStep (2608 words)

	Data Structures and Program Execution (Real-Time Workshop Embedded Coder)
		By default, Generate reusable code is off, and the model entry point functions access model data via statically allocated global data structures.
		Therefore when Generate reusable code is on, the argument lists generated for the entry point functions vary according to the requirements of the model.
		is called, blocks that have a terminate function execute their terminate code.
	www.weizmann.ac.il /matlab/toolbox/ecoder/ecode11c.html (405 words)

	Transforms of Derivatives and Integrals, Differential Equations
		Without the unit step function, it must be written in three separate lines, one for each definition range.
		Shifting means to substitute the variable "t" inside of the function with a new variable that is equal to "t-a".
		This will shift the graph of the function backwards along the t-axis by a step of the size "a".
	www.math.fsu.edu /~fusaro/EngMath/Ch5/TUSFSSTDDF.html (724 words)

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