# Active noise cancelling headphones - How fast does a digital signal processor have to be to perfectly cancel out noise with an inverted signal?

How fast does a digital signal processor have to be to perfectly cancel out noise with an inverted signal? Is it possible for a digital signal processor react so fast?

• I'm asking about active noise control specifically Sep 6 at 22:35
• You might want to say "inaudible" rather than "perfect" because nothing is perfect. I think you are asking about the clock speed of the DSP but that isn't the proper thing to ask. The proper thing to ask is the maximum latency between input and output since the actual execution cycles is going to vary depending on the DSP and the code. Sep 6 at 23:01
• Which leads you to this: physics.stackexchange.com/questions/60614/… Sep 6 at 23:05
• Perfectly? Then infinite speed… Sep 7 at 5:03
• How many lines of code does your algorithm have (per delivered audio sample)? If it has infinite number of lines, then you know the answer to your question. I would say the upper limit for your application would be around 20-30ms for adequate cancellation quality. Run as many or as few lines of code in that time frame.
– Syed
Sep 7 at 7:45

There's a "rule of thumb" for any phase-sensitive control loop that the processing phase lag has to be less than $$\frac{\pi}{4}$$ at the frequencies of interest to be stable.