Digital Signal Processing (4)

　　1965年出现的计算傅里叶变换的高效算法，进一步加速了数字信号处理的一种新观点的发展。这种算法后来称作快速傅里叶变换(或简写成FFT)。从很多方面来看，快速傅里叶变换含有重要的意义。许多以前在数字计算机上实现的信号处理算法，需要的处理时间要比实时多几个数量级。这常常是与这样的事实联系在一起的，即谱分析是信号处理的一个重要组成部分，而以前还没有一种行之有效的办法去实现它。而快速傅里叶变换算法把计算傅里叶变换需要的时间减少了几个数量级，这就有可能实现日益复杂的信号处理算法,使其具有能与系统互相作用的处理时间。此外，由于用专用数字硬件也可以实现快速傅里叶变换算法已成为现实，许多过去认为不切实际的信号处理算法，看来也有可能用专用数字硬件实现了。

　　快速傅里叶变换算法的另一个重要含意是和它离散时域概念联系着的。它可以直接计算离散时间信号或序列的傅里叶变换，并且包含有一整套在离散时间域中精确成立的特性和数字关系，它已经不单纯是连续时域傅里叶变换的近似了。其重要作用是促使人们利用离散时域数学重新建立许多信号处理概念和算法，于是这些技术在离散时域中形成了一套严格的关系式。从而使人们摆脱了那种认为用数字计算机处理信号仅是模拟信号处理技术之近似的观点。由于这种观点上的改变，人们对于新兴的数字信号处理学科出现了强烈的兴趣。 (未完待续)

　　The evolution of a new point of view toward digital signal processing was further accelerated by the disclosure in 1965 of an efficient algorithm for computation of Fourier transforms.This class of algorithms has come to be known as the fast Fourier transform or FFT.The implications of the FFT were significant from a number of points of view.Many signal processing algorithms which had been developed on digital computers required processing times several orders of magnitude greater than real-time.Often this was tied to the facts that spectrum analysis was an important component of the signal processing and that no efficient means had been known for implementing it.The fast Fourier transform algorithm reduced the computation time of the Fourier transform by orders of magnitued.This permitted the implementation of increasingly sophisticated signal processing algorithms with processing times that allowed interaction with the system.Furthermore,with the realization that the fast Fourier transform algorithm might,in fact,be implementable in special purpose digital hardware,many signal processing algorithms which previously had appeared to be impractical began to appear to have practical implementations with special purpose digital hardware.

　　Another important implication of the fast Fourier transform algorithm was tied to the fact that it was an inherently discrete-time concept.It was directed toward the computation of the Fourier transform of a discretetime signal or sequence and involved a set of properities and mathematics that were exact in the discrete-time domain it was not simply an approximation to a continuous-time Fourier transform.The importance of this was that it had the effect of stimulating a reformulation of many signal processing concepts and algorithms in terms of discrete-time mathematics and these techniques then formed an exact set of relationships in the discrete-time domain.This represented a shift away from the notion that signal processing on a digital computer was merely an approximation to analog signal processing techniques.With this shift in point of view there emerged a strong interest in the new or reborn field of digital signal processing.（游米儿）