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IIR filters, causality, and stability. It can be covered quickly as most of this material is assumed known from a prerequisite linear systems course. Chapter 4 focuses on FIR filters and its purpose is to introduce two basic signal processing methods: block-by-block processing and sample-by-sample processing. In the block processing part, we discuss convolution and several ways of thinking about it, transient and steady-state behavior, and real-time processing on a block-by-block basis using the overlap-add method and its software implementation. This is further discussed in Section 9.9 using the FFT. In the sample processing part, we introduce the basic building blocks of filters: adders, multipliers, and delays. We discuss block diagrams for FIR filters and their time-domain operation on a sample by sample basis. We put a lot of emphasis on the concept of sample processing algorithm, which is the repetitive series of computations that must be carried out on each input sample. We discuss the concept of circular buffers and their use in implementing delays and FIR filters. We present a systematic treatment of the subject and carry it on to the remainder of the book. The use of circular delay-line buffers is old, dating back at least 25 years with its application to computer music. However, it has not been treated systematically in DSP texts. It has acquired a new relevance because all modern DSP chips use it to minimize the number of hardware instructions. Chapter 5 covers the basics of z-transforms. We emphasize the z-domain view of causality, stability, and frequency spec
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