4.6 Java1490-2d fourier transforms using java, part 1  (Page 4/15)

Where people live

Your town has a small business district at the intersection of the two highways. Beyond that, most of the people who live in your town (and who will listen to your radio station ) live along the two highways. Thus most of the population lives in the directions of northeast, southwest, northwest, andsoutheast from the center of town. There are very few people living in the directions of north, south, east, and west. That real estate is mostly populatedby cows and cotton fields.

A limit on the transmitting power

Your new FCC license places a limit on the amount of power that you will be allowed to transmit. You would like to use that available powerto reach a many human listeners as possible. If you simply construct an omnidirectionaltransmitting antenna and start broadcasting, approximately half of the power that you transmit will be available mostly to cows and cotton plants. As aresult, the amount of power, and hence the reach of the power that you transmit to human listeners will be less than you would like for it to be.

A directional transmitting antenna

While the FCC won't allow you to increase the amount of power that you transmit, they will allow you to control the directions in which you choose totransmit that power. You will probably hire an expert in the transmission of radio signals to design a directional transmitting antenna system, which willbroadcast most of the available power in the directions where the people live. Ideally, the antenna system will transmit very little of the available power inthe directions of the cows and the cotton fields.

The design of the antenna system

The antenna designer will have many tools at her disposal. Whether or not she uses wavenumber terminology, many of the calculations that she performs willdepend on wavenumber concepts. She will be concerned about the reciprocal wavenumber (wavelength) of the radio signals that will be broadcast. She will be concerned with the lengths of the active elements in the antenna system, andthe distance between active elements if she chooses to use an array of active elements.

Basic concepts

I will leave the radio station scenario at this point and discuss some more basic concepts. I will return to the radio station scenario later. We will needto start with simpler things and work our way up to the radio station scenario.

Much of this discussion will be couched in terms of receiving signals rather than transmitting signals. (For most people, receiving is easier to understand than transmitting.) However, most of the conclusions that we reach regarding antenna systems used for receiving signals are also applicable to antennasystems used for transmitting signals.

A one-dimensional space

Just to get us started down the right path, we will temporarily constrain space to have only one dimension. We will discuss the propagation of waves alonga taut wire, as well as the measurement of the waves propagating along that wire.

Assume that a wire is fastened at both ends, is fairly taut, and is suspended between two walls so that it is free to move up and down only. Assume that weattach two sensors to the wire, one meter apart, and that each of these sensors is capable of generating an electrical signal that is proportional to thevertical displacement of the wire at the point where the sensor is attached. If the wire goes up, the sensor generates a positive signal. If the wire goes down,the sensor generates a negative signal.