tailieunhanh - Understanding digital signal processing - Chapter 3

Tài liệu tham khảo giáo trình tìm hiểu xử lý tín hiệu số bằng tiếng anh ( Understanding digital signal processing ) Chương 3. Chuyển đổi Fourier rời rạc | CHAPTER THREE The Discrete Fourier Transform The discrete Fourier transform DFT is one of the two most common and powerful procedures encountered in the field of digital signal processing. Digital filtering is the other. The DFT enables us to analyze manipulate and synthesize signals in ways not possible with continuous analog signal processing. Even though it s now used in almost every field of engineering we ll see applications for DFT continue to flourish as its utility becomes more widely understood. Because of this a solid understanding of the DFT is mandatory for anyone working in the field of digital signal processing. The DFT is a mathematical procedure used to determine the harmonic or frequency content of a discrete signal sequence. Although for our purposes a discrete signal sequence is a set of values obtained by periodic sampling of a continuous signal in the time domain we ll find that the DFT is useful in analyzing any discrete sequence regardless of what that sequence actually represents. The DFT s origin of course is the continuous Fourier transform X defined as X f j x t e 2 dt 3-1 where x t is some continuous time-domain signal In the field of continuous signal processing Eq. 3-1 is used to transform an expression of a continuous tune-domain function x t into a continuous frequency-domain function X f . Subsequent evaluation of the X expression enables US to determine the frequency content of any practical signal of interest and opens up a wide array of signal analysis and processing Fourier is pronounced for-yã. In engineering school we called Eq. 3-1 the four-year transform because it took about four years to do one homework problem. 49 50 The Discrete Fourier Transform Ị i possibilities in the fields of engineering and physics. One could argue that the Fourier transform is the most dominant and widespread mathematical mechanism available for the analysis of physical systems. A prominent quote from Lord Kelvin better states this sentiment .