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Anatomy of a Robot Part 6

Tham khảo tài liệu 'anatomy of a robot part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 86 CHAPTER THREE plus a remainder. This formula provides a standard way to approximate and compute functions like sine and cosine. It s the way compilers set up the computation. It involves several multiply and accumulate steps. Each term in the equation is another MAC. Generally the remainder can be made arbitrarily small by carrying out more terms making n larger . A tutorial on the Taylor series can be found at www.wikipedia.com wiki Taylors_theorem. Finite Impulse Response FIR filters These are generally used for filtering a continuous stream of information that represents audio or video. Consider the reception of an audio signal in the presence of a strong 1 kHz interfering noise source. We would like to remove the 1 kHz noise from our signal as best we can . If the audio signal is digitized it can be fed into a FIR filter specifically designed to filter out 1 kHz signals. The FIR filter method gives us a way to do this in as precise a manner as required governed only by cost. Suppose we want to filter the signal x t to produce signal y t . The generalized formula for an n-stage FIR filter is given by y1t2 h0 X x t2 hl X x 1t 12 h2 X x t 22 . hn X x t n2 where hl . bl are the coefficients of the fiIter. We ll explain ahe meh in a later chapter but we can see that this formula is also a series of MACs. A web site on FIR filters can be found at www.wwc.edu troaro qea sidebnr.html. Fourier Transforms Fourier Transforms were developed as we might guess by Joseph Fourier see Figure 3-7 in the early 1800s. The transforms are a way of representing any function within certain bounds as the superposition of a series of pure sine waves. In this way a function is broken down into a series of pure fre- FIGURE 3-7 Joseph Fourier COMPUTER HARDWARE 87 quencies multiplied by coefficients . A good drawing of superimposed sine waves can be found at www.yorvic.york.ac.uk cowtan fourier ftheory.html. The Fourier Transform has many variants including the Fast Fourier Transform FFT