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Q: Why in fourier series constant is divided by two?
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How does the spring constant of two springs connected in a series compare with that of a single spring?

The spring constant of two springs connected in series is less than the spring constant of a single spring. When springs are connected in series, their effective spring constant is reduced, as the total force required to stretch or compress them increases compared to a single spring.


What is the history of fourier series?

Oh, the history of Fourier series is truly fascinating! It all began with Joseph Fourier, a brilliant mathematician in the 19th century. He discovered that you could represent complex periodic functions as a sum of simpler trigonometric functions. This insight revolutionized mathematics and has had a profound impact on fields like signal processing, physics, and engineering. Just imagine, breaking down intricate patterns into beautiful harmonious components - it's like creating a masterpiece on canvas with just a few brushstrokes.


Is the Harry Potter series divided in two parts?

No, but the last movie is.


Difference between fourier series and z-transform?

Laplace = analogue signal Fourier = digital signal Notes on comparisons between Fourier and Laplace transforms: The Laplace transform of a function is just like the Fourier transform of the same function, except for two things. The term in the exponential of a Laplace transform is a complex number instead of just an imaginary number and the lower limit of integration doesn't need to start at -∞. The exponential factor has the effect of forcing the signals to converge. That is why the Laplace transform can be applied to a broader class of signals than the Fourier transform, including exponentially growing signals. In a Fourier transform, both the signal in time domain and its spectrum in frequency domain are a one-dimensional, complex function. However, the Laplace transform of the 1D signal is a complex function defined over a two-dimensional complex plane, called the s-plane, spanned by two variables, one for the horizontal real axis and one for the vertical imaginary axis. If this 2D function is evaluated along the imaginary axis, the Laplace transform simply becomes the Fourier transform.


Cross-power spectrum of two fourier transform images?

It's (I1./I2*)/(|I1./I2*|), where I2* is the complex conjugate of the Fourier transformed Image 2


What is the term for A sequence of numbers in which the ratio between two consecutive numbers is a constant?

A geometric series.


Some two-way roads are divided into three lanes?

Two-way roads are divided into there lanes throughout the country. This occurs in big cities, because there is constant traffic throughout the day.


Is the figure that is multiplied by the product of the masses of two objects divided by the square of the distance between them to give the gravitational force between the two objects?

The "figure" is the gravitational constant.


Will 'Harry Potter and the Deathly Hallows' be the last movie in the series?

The Deathly Hallows is being divided into two movies. After the Deathly Hallows Part II, the series will be over.


What does a constant slope mean?

It means that the rise divided by the run for a curve has the same value. If A and B are any two points on the curve, with coordinates (Xa, Ya) and (Xb, Yb), then (Yb - Ya)/(Xb - Xa) is a constant.


Difference between fourier transform and first fourier transform?

The question almost certainly intends "fast" instead of "first". The difference between a Fourier Transform and a Fast Fourier Transform is only the amount of effort required to generate the result. Both have the same the result. The original Fourier Transform requires an amount of effort which is proportional to the square of the amount of data being used. So if the amount of data doubles, the amount of effort to calculate the result quadruples. In contrast, the subsequently discovered Fast Fourier Transform requires an amount of effort proportional to the product of the amount of data and the base-two logarithm of the amount of data. Thus, if the amount of data doubles, the amount of effort increases but by less than a quadruple. With each doubling of the data size, the amount of effort increases by a diminishing factor which slowly drops toward but never reaches two.


What is a word using the root word ortho?

Three of them are "orthogonal", "orthodontist", and "orthopedic", and "orthogonal" is a very important word in mathematics. For one example, two vectors are orthogonal whenever their dot product is zero. "Orthogonal" also comes into play in calculus, such as in Fourier Series.