Section 6

Hiding a Transmitted Signal

Refer to figure - Signals, for the following discussion.

There are two main instruments used to visually measure electrical energy, the Oscilloscope and the Spectrum Analyzer.

Oscilloscopes

The Oscilloscope is used to look at the voltage between any two points at a specific moment in time.

The basic scope measurement is to measure a voltage at a given point in an electrical circuit relative to the 0 volt reference ( ground, no charge ) point. As electrons pass by the positive probe the strength of the electric field moves a small white dot ( it could be any color ) vertically. The vertical scale determines how much voltage must be present to move the dot vertically a given distance. If the scale is 1 volt for ever vertical mark, then if the dot moves up two marks, then the voltage at the positive probe must be 2 volts. The horizontal scale is usually calibrated in time ( measured in seconds or fractions of a second ).

The oscilloscope graph shows a scope measurement of an electrical signal, hitting it's peak voltage at horizontal positions 1 and 5. This distance in time determines the period of the signal. There are 1000 milliseconds in a second. Most electrical measurements made in time are calculated in frequency rather than period. Frequency is the inverse of period.

Frequency = 1 / period

4 ms = .004 seconds

Frequency = 1 cycle / .004 sec

or

Frequency = 1000 cycles / 4 sec

**Frequency = 250 cycles per second or 250 Hertz ( 250 Hz )**

This states that the voltage level at the point being measured hits it's peak 250 times every second.

Wavelength is th physical distance between wave peaks.

For electrical signals the wavelength is calculated by the equation:

Wavelength = Velocity of Light / Frequency

The velocity of light is ( all values are approximate ):

299,792,452 meters/second

or

186,235 miles / second

or

983,319,242 feet / second

Wavelength = 186,235 / 250

Wavelength = 745 miles

Spectrum Analyzers

The Spectrum Analyzer looks at the voltage of each signal it sees in a given bandwidth. The voltage is measured on the vertical axis and the frequencies are measured on the horizontal axis. The spectrum analyzer usually displays the amplitude as power rather than voltage. The power is expressed in dB ( decibels relative to a given power level ) or dBm ( decibels relative to a 1 milliwatt power level ).

The spectrum analyzer graph shows the spectrum analyzer's measurement of the same signal that the oscilloscope is measuring. The sample rate indicates that the analyzer is taking a measurement 1000 times a second and so it is seeing 4 points of the signal every cycle. The absolute minimum number of samples an instrument can take to be able to determine what a signal is, is twice per cycle. A spectrum analyzer uses either a large number of filters to look at each signal or it takes a lot of measurements and mathematically computes what frequencies are present and what the amplitudes are. Modern Spectrum Analyzer use many filters in parallel, fast switching filters and a lot of math to produce precision results.

Complex signals are composed of many simple signals. Figure - Square Wave, shows a few of the signals that when combined make a simple square wave signal on an oscilloscope.

Light, Introduction, An Encryption Process

Last updated: Mar 4, 2011