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To be able to work properly, robots, mobile phones, 3D, and GPS devices are all dependent upon quick, complex mathematical calculations. Erik Hertz, a researcher at Halmstad University, has developed a method that can facilitate this. Recently, he defended his thesis in the multidisciplinary research field of mathematics and electronics.
Mobile phones are just one example among many products that are constantly improving.
– People who develop and sell the various products have had it easy as technology was both constantly improving and becoming quicker. They didn´t even have to think or worry about the mathematical side of things. However, technology development has now come to a stop, says Erik Hertz.
This is where his model comes into use. It is a mixture of mathematics and electronics – he calls it hardware mathematics – and he uses mathematical calculations, that are both simple and efficient, to be implemented in hardware.
For example, power consumption is an important factor considering the high expectations we all have today:
– Many of the technological gadgets we use today are battery powered and place great demands on high speed and low power consumption. Furthermore, much higher precision is required nowadays compared to before.
Erik Hertz has a background in telecommunications specialising in mobile telephony; therefore his research has mainly concerned this area. Today, electronics have been scaled down so much that it is possible to put in action the ideas he has had for some time.
– In future systems within mobile telephony, we will see a huge development of the amount of calculations where a large part of this will be approximations of unary functions, i.e. functions with only one variable, such as root functions, says Erik Hertz.
– And, instead of having to use huge long tables with different values, mobile phones will work with the aid of different algorithms.
Another important application area with very high demands on performance is image processing, where 3D is required. Erik Hertz´s method named Parabolic Synthesis can meet the increasing demands concerning speed and accuracy. The calculations are done faster and the method can also reduce the effect of the errors that quite often occur.
And in comparison with the algorithm that is common today i.e. CORDIC, his new method is much more effective, subject to certain requirements.
Erik Hetz says:
– To give an example, calculations can be done 12-13 times faster while at the same time the chips have become smaller and power consumption is less.
The big companies have already invested heavily in the existing method where the telecom industry is somewhat hesitant to embrace something new. However, Erik Hertz´s dissertation has been well received.
– My method is both cheaper and better; however, I am aware that if someone has already invested heavily in one method, it takes time before they invest in something new and different, says Erik. I am now talking about collaboration with smaller GPS companies, where they will see a direct benefit by using my method.
Warehouses where GPS-guided forklift trucks require millimeter precision to get around is an area that will benefit from quick calculations, as well as robots that can move faster and more accurately.
Text: KRISTINA RÖRSTRÖM
Photo: ERIK HERTZ, KRISTINA RÖRSTRÖM