Random Signals: Average And Effective Values

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{3}A_{32} Base Sequence = 12735 String Sequence = 12735 -3 - 32 **

Expressions Of Pj Problems

Random Signals: Average And Effective Values

Math

Pj Problems - Overview

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7 Spaces Of Interest - Overview

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The signal *v(t)* from a voltage source is a binary waveform: it is either 0.5 V or -0.5 V.

The sign change has a 50-50 chance of occurrence within the interval of 1 μs. In other words, *v(t)* has an equal chance for positive or negative values within this interval.

What is the average and effective values of *v(t)* over a period of 5 secs?

**The string**:

S_{7}P_{3}A_{32} (Force - Push) .
**The math**:

Pj Problem of interest is of type *force*. Voltage problems are *force problems*.

The binary waveform is an example of a *non-noise random signal*. *Random signals* are probabilistics. That is, they are specified only partly through their time averages (their mean, rms value, and frequency range). Some examples of *random signals* are signals picked up by a radio or TV station antenna; the voltage recorded at the terminals of a microphone due to speech utterance; binary waveforms in digital computers; image intensities over the area of a picture; and the speech or music which modulates the amplitude of carrier waves in an AM system.

There are 5(10^{6}) intervals during the 5 secs period.

So, average value of v(t), v_{avg} = [0.5(1/2)5(10^{6}) - 0.5(1/2)5(10^{6})]/5(10^{6}) = 0

Effective value, (v_{eff})^{2} = [0.5^{2}(1/2)5(10^{6}) + (-0.5)^{2}(1/2)5(10^{6})]/5(10^{6}) = (0.5)^{2}

So, v_{eff} = 0.5

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Single Variable Functions

Conics

Ordinary Differential Equations (ODEs)

Vector Spaces

Real Numbers

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

More Pj Problem Strings