数字信号处理是将信号以数字方式表示并处理的理论和技术。其目的是对连续模拟信号进行测量式滤波，具有灵活、精确、抗干扰性能、尺寸小、造价低、速度快等优点。

　　在上面所有用数字计算机处理信号的例子中,计算机的杰出优点都表现在它的灵活性上。但这种处理常常不能实时完成。因此，当时流行的作法是利用计算机逼近和仿真一个模拟信号处理系统。数字滤波器的早期工作就是属于这种方式的，在这里，一个滤波器可以在数字计算机上用程序来实现，先把信号作模-数转换变成数字信号，然后在计算机上用程序实现数字滤波，再接着作数-模转换，整个系统近似于一个完善的模拟滤波器。想把数字系统付诸实际应用，去作语音通信或雷达信号处理或者任何其他各种应用的想法，即使是最乐观时，看来还是不切实际的。因为从速度、价格和尺寸等三个重要因素来考虑，使用模拟部件是有利的。

　　由于信号是用数字计算机处理的，自然而然有一种趋势，以愈来愈巧妙的信号处理算法去作试验。有一些算法是从计算机的灵活性发展起来的，并且未见到用模拟设备实现过。于是很多算法在当时被认为很有趣,但却是有点不切实际的想法。例如有关谱分析和同态滤波的技术趋势就是这种算法中的一类。在数字计算机上已经清楚地证明，应用这些技术可以改进语音带宽压缩系统、解褶积和消除回声。在实现这些技术时，要求直接计算输入的傅里叶变换之对数的傅里叶反变换。而利用模拟的谱分析仪实现不了所要求的傅里叶变换精度和分辨率。因此这种信号处理算法的发展，使实现全数字化的信号处理系统的想法更具有吸引力。人们抱着这些系统将付诸实现的信念，积极地开始了数字化声码器、数字化谱分析仪及以其他数字系统的研究工作。 (未完待续)

　　In all of the above examples of signal processing using digital computers, the computer offered tremendous advantages in flexibility. However, the processing could not always be done in real-time. Consequently, a prevalent attitude at that time was that the digital computer was being used to approximate, or simulate, an analog signal processing system. In keeping with that style, early work on digital filtering was very much concerned with ways in which a filter could be programmed on a digital computer so that with analog-to-digital conversion of the signal, followed by the digital filtering, followed by digital-to-analog conversion, the overall system approximated a good analog filter. The notion that digital systems might, in fact, be practical for the actual implementation of signal processing in speech communication or radar processing or any of the variety of other applications seemed at the most optimistic times to be highly speculative. Speed, cost, and size were, of course, three of the important factors in favor of the use of analog components.

　　As signals were being processed on digital computers, there was a natural tendency to experiment with increasingly sophisticated signal processing algorithms. Some of these algorithms grew out of the flexibility of the digital computer and had no apparent implementation in analog equipment. Thus, many of these algorithms were treated as interesting, but somewhat impractical, ideas. An example of a class of algorithms of this type was the set of techniques referred to as spectrum analysis and homomorphic filtering. It had been clearly demonstrated on digital computers that these techniques could be applied to advantage in speech bandwidth compression systems, deconvolution, and echo removal. Implementation of these techniques requires the explicit evaluation of the inverse Fourier transform of the logarithm of the Fourier transform of the input. The required accuracy and resolution of the Fourier transform were such that analog spectrum analyzers were not practical. The development of such signal processing algorithms made the notion of all-digital implementation of signal processing systems even more tempting. Active work began on the investigation of digital vocoders, digital spectrum analyzers, and other all digital systems, with the hope that eventually such systems would become practical.（游米儿）