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Digital Signal Processing Basics

A 256-tap FIR filter runs in real time at a sampling frequency of 44.1 kHz. Which of the following is the number of multiply-accumulate (MAC) operations needed per second?

  1. AAbout 44,000
  2. BAbout 11.3 million
  3. CAbout 22.6 million
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Answer: B. About 11.3 million

An FIR filter performs as many multiply-accumulates per output sample as it has taps, here 256. There are 44,100 outputs per second, so 256 × 44,100 = 11,289,600, about 11.3 million MACs are needed. Even a processor that performs one MAC per cycle needs a clock of at least about 11.3 MHz, and in practice work such as reading and writing data is added.

  • A. This is the number of outputs per second (the sampling frequency) itself. Each output needs 256 MACs.
  • B. Correct. 256 × 44,100 ≈ 11.3 million.
  • C. This counts multiplications and additions separately (2 × 256 × 44,100). Counting a MAC as one operation gives half of it.
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  1. An FIR filter output is computed for every sample at a sampling frequency of 48 kHz on a processor clocked at 200 MHz that performs one multiply-accumulate per cycle. Ignoring the time for other processing, which of the following is closest to the maximum number of taps that can be processed in real time?
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