Developing the Basic Building Blocks of Mathematics to be employed in Practical Embedded Systems

Mathematics is vitally important as it is used in many areas of science and engineering, in particular are functions such as sine, cosine and the exponent in addition to being to able to carry out such tasks as decimal division. The sine wave is vitally important in physics and communications due to its ability to retain its waveshape when added to another sine wave of the same frequency and arbitrary phase. It is the only periodic waveform that has this property and leads to techniques such as Fourier analysis. Unfortunately these blocks are not included in the standard DSP Builder blockset in Simulink and so a method of creating these operations must be created if this methodology is to be employed in real world tasks such as power relay protection and stereo vision systems. Shown here is a method of performing these calculations using the limited blocks provided for a 50-bit based embedded system with a discussion about the accuracy when compared to traditional digital system counterparts. The order of the equations used and the scaling factors of the blocks are investigated to provide evidence of why certain values need to be changed depending upon the calculation being performed.