Periodic Signals

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{2}A_{21} Base Sequence = 12735 String Sequence = 12735 - 2 - 21 **

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Periodic Signals

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Signaling is a ubiquitious phenomenon in the societies of cognitive beings.

(a) What is a signal?

(b) What is a periodic signal?

(c) Identify the following periodic waveforms:

(i)

(ii)

(iii)

**The string**:

S_{7}P_{1}A_{17} (Containership -Location)

S_{7}P_{2}A_{21} (Identity - Physical Properties).
**The math**:

Pj Problem of interest is of type *identity*.

(a) *Signals* are essentially indicators of *presence* (the *being* in a location). Thereafter, one is interested in the *identity*, analyses and possible uses of the *presence*. In electric circuits, the voltage and current signals indicate the *presence* of voltage and current sources. The identities of voltage and current signals are expressed as *waveforms* (graphical representations of functions).

(b) *Periodic Signals* are *time-dependent cyclic signals*. In other words, there is an interval called the *period* of the signal during which the signal repeats the same waveform pattern.

Mathematically, an arbitrary signal x(t) is periodic if it can be expressed as follows:

x(t) = x(t + nT)-------(1)

Where n = 1, 2, 3 ...; and T is the *period* (the time it takes to complete 1 cycle) of x(t).

The *frequency* (f) of *x(t)* in cycles/sec (Hertz) is:

*f = 1/T*-------(2)

(ci) The waveforms in c(i) are cosine and sine periodic signals (sinusoids).

The red waveform is a cosine function. Its general form is:

v(t) = V_{max}cosω----(3)

Where the radian frequency (angular velocity), ω = 2πf.

The signal expressed in (3) is often the reference sinusoid.

A sinusiodal signal has the general form:

v(t) = V_{max}cos(ωt + θ)-----(4)

The sinusiodal signal expressed in equation (4) is said to *lead* the sinusiodal signal expressed in equation (3) by *phase angle, θ*.

The *phase angle θ* = *ωτ*

Where τ is the *time shift*

The *Blue* waveform is a sine function. Its general form is:
*v(t) = V _{max}sinωt*----(5)

The relationship between the cosine signal and the sine signal is:

V

Since the cosine signal

The relationship can also be expressed as follows:

V

Since the sine signal

(cii) The waveforms in c(ii) is a periodic pulse signal.

(ciii) The waveform in c(iii) is a periodic sawtooth signal.

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

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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

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