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Understanding digital signal processing - Chapter 9

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Tài liệu tham khảo giáo trình tìm hiểu xử lý tín hiệu số bằng tiếng anh ( Understanding digital signal processing ) Chương 9. Các định dạng dữ liệu kỹ thuật số và hiệu ứng của họ | CHAPTER NINE Digital Data Formats and Their Effects In digital signal processing there are many ways to represent numerical data in computing hardware. These representations known as data formats have a profound effect on the accuracy and ease of implementation of any given signal processing algorithm. The simpler data formats enable uncomplicated hardware designs to be used at the expense of a restricted range of number representation and susceptibility to arithmetic errors. The more elaborate data formats are somewhat difficult to implement in hardware but they allow us to manipulate very large and very small numbers while providing immunity to many problems associated with digital arithmetic. The data format chosen for any given application can mean the difference between processing success and failure it s where our algorithmic rubber meets the road. In this chapter we ll introduce the most common types of fixed-point digital data formats and show why and when they re used. Next we ll use analog-to-digital A D converter operation to establish the precision and dynamic range afforded by these fixed-point formats along with the inherent errors encountered with their use. Finally we ll cover the interesting subject of floating-point binary formats. 9.1 Fixed-Point Binary Formats Within digital hardware numbers are represented by binary digits known as bits in fact the term bit originated from the words Binary 349 350 Digital Data Formats and Their Effects digIT. A single bit can be in only one of two possible states either a one or a zero A six-bit binary number could for example take the form 101101 with the leftmost bit known as the most significant bit msb while the rightmost bit is called the least significant bit Isb . The number of bits in a binary number is known as the word length hence 101101 has a word length of six. Like the decimal number system so familiar to US the binary number system assumes a weight associated with each digit in the number. That .