Delay Effects and Circular Buffers

Before we can start looking at some finite impulse response (FIR) algorithms, we need to deal with the concept of long delay lines or circular buffers. Not only are they used for the delay effects, but also they are needed to make long FIR filters. In this chapter we'll take a break from the DSP filter algorithms and develop some digital delays. If you think back to the infinite impulse response (IIR) filters you've worked on so far you will remember that after implementing the difference equation, you need to shuffle the z−1 delay element values. You do this by overwriting the delays backwards, like this:

Suppose you had a filter that was higher than a second-order one and you had to implement

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