# Waves: Part 4 - Complex Numbers

In this part we look at the most elegant way of finding and defining a sine wave.

Fig.1 a) Real numbers live in one dimension, b) Complex numbers are two dimensional and the real axis lies across the center. The imaginary axis is vertical and has units of i. A complex number can by specified by a and b, c) A complex number can also be specified by the Modulus, which is the radius and the Argument which is an angle.

Figure 2 - Various powers of i shown in the complex plane.

Fig.3 The graph shown has the characteristic that the slope is equal to y.

Fig.4 Euler’s equation links the exponential form of a complex rotation with the sine and cosine representation.

Fig.5 a) a pair of contra rotations. The vertical motion is coherent and adds. The horizontal motion cancels, b) The contra rotation requires a sine wave to have equal amounts of positive and negative frequency, hence the pair of sidebands obtained in modulation.

# Waves: Part 9 - Propagation Inversion

As a child I came under two powerful influences. The first of these was electricity. My father was the chief electrician at a chemical works and he would bring home any broken or redundant electrical parts for me to tinker…

# BEITC Session Report - Using TV For GPS Backup In The USA

China and Russia have back-up GPS systems. The USA has no GPS backup, although politicians have been talking about the need for 20 years. ATSC 3.0 stations have the hardware in place to provide nationwide backup. The US Department of Transportation is…

# Waves: Part 8 - Shock Waves

Shock waves are interesting phenomena that take place in a number of different media. For an arcane physical process, they have done quite well to be adopted by the mainstream media as one of their clichés, along with Mae …

# TV RF At 2023 NAB Show - New Technology For NextGen TV Transmission

Ned Soseman presents his highlights of the transmission technology that will be at the 2023 NAB Show.

# Waves: Part 7 - Reflection And Refraction

Here we look at reflection and refraction, which figure highly in the cameras and lighting equipment used by broadcasters, to say nothing of the real word in which images are captured.