Software Listing of Author : "H. Lohninger"

In data acquisition experimenters are often confronted with the unfavourable situation of detecting a signal too small to be recognizable - the signal is embedded into noise which is almost as high as the signal itself, or even higher than it.

In order to cope with this situation one has to increase the signal to noise ratio (SNR) to a minimum level of 3. In principle, this can be accomplished by reducing the noise (using better equipment, or a different experimental set-up). However, the reduction of noise has principal limits which are given by physical laws (i.e. the thermal noise cannot be removed without cooling the entire measuring device to absolute zero).

Another approach to increase the SNR is to repeat a measurement many times and add all measurements. Given that the signal is stable enough over a longer...

  • Platform: WinOther

The central limit theorem is considered to be one of the most important results in statistical theory. It states that means of an arbitrary finite distribution are always distributed according to a normal distribution, provided that the number of observations for calculating the mean is large enough. Usually 10 observations are sufficient to result in a approxomate normal distribution. The central limit theorem is the reason why normal distributions are so frequent in nature.

The program CenLimit shows the effects of the central limit theorem. The user may select from various distributions to draw different numbers of observations for calculating the means. The distribution of the means is plotted. You may use this program to find out the relationship between the number of observations and the resulting standard deviation...

  • Platform: WinOther

When performing statistical tests, one needs to check whether the test statistic is greater or less than the critical value. While most statistical programms automatically create a default table of critical values, it is sometime necessary to look into distribution tables. However, retrieving a critical value from a distribution table is prone to mistakes due to the symmetry considerations which have been taken into account to reduce the volume of the printed tables.

In such cases the Distribution Calculator offers a reliable solution. The user simply enters the degrees of freedom, the test statistic or the level of signifance, and the program calculates the probability or the test statistic, respectively. The Distribution Calculator offers calculations for the normal distribution, the t distribution, the chi-square...

  • Platform: WinOther
  • LinConG
  • License: Freeware
  • Price: 0.00

Computer languages usually offer a command to create random numbers. The generation of random numbers, however, is not an easy task for a computer, since the computer is a deterministic machine with no built-in randomness. Thus it is impossible to create true random numbers without any additional hardware.

What can be done, is to create pseudo random numbers which behave almost like random numbers but which are repeated after a fixed (mostly quite long) period. These pseudo random numbers are generated by linear congruential generators (LCG). The principle of an LCG is quite simple: a new pseudo random number is generated on the basis of the previous random number by adding a certain offset and wrapping the result if it exceeds a certain limit.

The program Linear Congruential Generator allows to experiment with...

  • Platform: WinOther

Potential energy is stored energy showing various forms of appearance, i.e. gravitational potential energy, elastic, chemical, or electrical potential energy. The energy is stored by doing work against a force such as gravity or the spring in a clockwork motor.

Gravitational potential energy is an important form of energy, having much impact on our daily lives (think of the increased gas consumption when driving a car up a mountain road, or think of power utilities storing energy in water reservoirs).

The gravitational potential energy Ug of an object is equal to the work that would have to be done by a constant gravitational force F = mg on the object to move it against the force by a distance h, and is equal to

Ug = mgh

where m is the mass of the object, and g the acceleration due to...

  • Platform: WinOther

In mathematics, a Riemann sum is a method for approximating the values of integrals. It may also be used to define the integration operation. The sums are named after Bernhard Riemann. There are four different kinds of Riemann sums, called left, right, middle and trapzeoidal sum. Any Riemman sum on a given partition is contained between the lower and the upper Riemman sums. A function is defined to be Riemann integrable if the lower and upper Riemman sums get ever closer as the partition gets finer and finer. This fact can also be used for numerical integration. More on Riemann sums can be found in the free eBook Elementary Calculus by H.J. Keisler.

The program RiemannSum allows to calculate the Riemann Sums for various functions. The user may adjust the width of the slices to see the convergence of the Riemann sum towards...

  • Platform: WinOther
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