Click on the image to download the 33 megabyte "zip" file. Consider your proposal as a "blueprint" for creating an online interactive professional portfolio "eFolio". A cognitive map is included.

Then numerical derivative can be written in general form as As we said before, is anti-symmetric filter of Type III. Its frequency response is: Our goal is to select coefficients such that will be as close as possible to the response of an ideal differentiator in low frequency region and smoothly tend to zero towards highest frequency.

The most intuitive way of doing this is to force to have high tangency order with at as well as high tangency order with axis at. This leads us to the system of linear equations against: In the same way we can obtain differentiators for any. As it can be clearly seen tangency of with response of ideal differentiator at is equivalent to exactness on monomials up to corresponding degree: Thus this condition reformulates exactness on polynomials in terms of frequency domain.

Results Below we present coefficients for the case when and are chosen to make quantity of unknowns to be equal to the quantity of equations. Differentiator of any filter length can be written as: Frequency-domain characteristics for the differentiators are drawn below.

Red dashed line is the response of ideal differentiator. Besides guaranteed noise suppression smooth differentiators have efficient computational structure. Costly floating-point division can be completely avoided. As a consequence smooth differentiators are not only computationally efficient but also capable to give more accurate results comparing to other methods Savitzky-Golay filters, etc.

Also smooth differentiators can be effectively implemented using fixed point e. If we will require tangency of 4th order at with which is equivalent to exactness on polynomials up to 4th degree following filters are obtained: These filters also show smooth noise suppression with extended passband.

As filter length grows it smoothly zeroing frequencies starting from the highest towards the lowest. Proposed method can be easily extended to calculate numerical derivative for irregular spaced data. Another extension is filters using only past data or forward differentiators.

Please check this report for more information: One Sided Noise Robust Differentiators. Here I present only second order smooth differentiators with their properties. I will post other extensions upon request. Coefficients of these filters can be computed by simple recursive procedure for any.

Also they can be easily extended for irregular spaced data as well as for one-sided derivative estimation when only past data are available.

Contact me by e-mail if you are interested in more specific cases. In case of higher approximating order we get following estimation.

These filters can be used to approximate second derivative for irregular spaced data as are coefficients from the formulas for uniform spaced data derived above.Write an equation of a line in slope-intercept form with a slope of 4 3 and which passes through the point (8, -4). 2. Write an equation of a line in Standard Form with a slope of -1 and which passes through the point (4, 6) 3.

Write an equation of a line in slope-. Section Graphing Linear Equations in Slope-Intercept Form 63 Equation Description of Graph Slope of Section Graphing Linear Equations in Slope-Intercept Form 67 Solve the equation for y.

y − 2x = 3 4x + 5y = 13 Write an equation that represents the height y (in feet) of the. Practice for slope, y-intertcept, and writing equations Write the slope-intercept form of the equation of each line given the slope and y-intercept.

1) Slope = −1, y-intercept = −5 2) Slope = −1, y-intercept = −1. graphing linear equations, when the equation is given in the slope-intercept form (y = mx + b)graphing linear equations, when the equation is given in the normal form (Ax + By + C = 0); graphing lines, when the slope and one point on it are given.

One type of linear equation is the point slope form, which gives the slope of a line and the coordinates of a point on it. The point slope form of a linear equation is written as. In this equation, m is the slope and (x 1, y 1) are the coordinates of a point.

Here x 0 = 1/T-j ∑ t=j+1 T x t is the sample mean of x t, t=j+1,,T, and x j = 1/T-j ∑ t=j+1 T x t-j is the sample mean of x t-j, so that r ̂ j * corresponds to a correlation coefficient proper.. Note the difference with the definition of the sample autocorrelations {r ̂ j} in grupobittia.com difference tends to be small, and vanishes asymptotically, provided the series are stationary.

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