4.6 Java1490-2d fourier transforms using java, part 1  (Page 9/15)

Could continue adding elements tothe array

Although I won't demonstrate it, I can tell you that if I were to continue adding elements in this manner to increase the length of the array, the centralpeak and the peaks at the folding wavenumbers would continue getting narrower, and the trough between the peaks would continue getting deeper and probablyflatter.

A more selective wavenumber filter

In other words, when viewed as a wavenumber filter, a long array with more elements is a moreselective wavenumber filter than a short array with fewer elements. By properly designing an array to act as a wavenumber filter, it is possible to cause that filter to be veryselective.

When we use a properly designed array to produce a directional antenna, it is possible to produce a highly directional antenna (and avoid wasting our valuable radio frequency energy by sending it to cows and cotton plants).

A weighted three-element array

Continuing with our three-element array scenario, let's take a look at the center pair of images in Figure 3 and compare them with the leftmost images in Figure 3 .

For this case, the array still contains three elements with the same spacing as before. However, the electrical output from the center element is amplifiedto make it twice as strong as the outputs from the other two elements before the three electrical signals are added together.

Note that the array elements are no longer shown as being white against a black background in the very top of the top-center image. Instead, thecenter element is white but the other two elements are greenish indicating different weights.

It is a little hard to tell what this does to the central peak in the wavenumber response, but it definitely changes the shape of the response in thetrough between the peaks. Whether or not this would be a beneficial change would depend on the problem being addressed.

A three-element array with negative weighting

Finally, take a look at the rightmost pair of images in Figure 3 . Once again, the array contains three elements and the center element is weighted twice asheavily as the other two. In addition, the sign of the electrical signals from the two outer elements is inverted before the three are added together.

Note that the black color represents the smallest algebraic value. Negative values are smaller than positive values. Therefore, the background(which represents a weigh of zero) has changed from black to something between green and blue. The two elements withthe negative weights are shown as black and the element with the positive weight is shown as white.

The wavenumber response

This has a major impact on the wavenumber response of the three-element array.

There is no longer a peak at a wavenumber value of zero. Rather, there is now a null point at zero wavenumber as indicated by the black and blue colors at thecenter of the plot. There is now a peak on each side of zero (as indicated by the white and red colors) , half way between zero and the folding wavenumber.