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I have been working on Active Noise Cancellation in real time for Air vent in kitchen.
Initially for the demonstration purpose, I am using sinusoidal sound ( 40k Hz Fs,1000 samples, 2 kHz frequency, 1 Amplitude). I am using simple LMS Algorithm initially to test this, I could produce the anti noise with the same frequency and amplitude but because it is a real time application, I could be able to produce the sine wave with 30-31 samples per each cycle of sine wave.

The problem is the sound coming through the noise cancelling speakers is not good compared to the source noise, there is some buzz noise coming in addition (kind of background noise). This could mainly be because of distortions in speaker, I don't have any idea how to control this !!
But I am thinking this may be could be because of very less number of samples that I am using for Cancelling speaker.May be the reproduction of the noise is not so good because of less number of samples.

So my question is how many samples per cycle are ideally required for good reproduction of sine wave sound??

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It depends on how good your interpolation between samples is. If you have really good interpolation, anything more than 2 samples per cycle will suffice. This is not just a theoretical fact, it is my experience in practice using polyphase interpolation that combines 64 adjacent table-lookup samples.

If you're using linear interpolation (which combines 2 adjacent table-lookup samples in the interpolation), I would use no less than 1024 samples per cycle for a high-quality sine wave (about 120 dB S/N).

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  • $\begingroup$ Thank you. The point I missed is sampling rate. I guess my platform NI myRIO 1900 is sampling the output audio @172.5 kHz. How does this affect the audio quality ? I found here the higher sampling rates will introduce non linear distortion as sound cards will have non linear response for high frequencies. $\endgroup$
    – charansai
    Commented Dec 28, 2015 at 12:28
  • $\begingroup$ And one more help, How many samples are good enough for good interpolation of Fan noise.? Any insight regarding this would be appreciated, I am out of thoughts as to how to approach this number (number of samples) $\endgroup$
    – charansai
    Commented Dec 28, 2015 at 12:28
  • $\begingroup$ first of all, the Sampling theorem actually tells you, independently of the sample rate, that at a very minimum you need something more than two samples per sinusoidal period. if your sample rate is 172.5 kHz, you can conceptually output a sinusoid of 86 kHz with that. but that is pushing the edges. $\endgroup$
    – robert bristow-johnson
    Commented Dec 28, 2015 at 20:11
  • $\begingroup$ and i have no idea what this has to do with Fan noise. $\endgroup$
    – robert bristow-johnson
    Commented Dec 28, 2015 at 20:12
  • $\begingroup$ Eventually I will be working on Fan noise after sinusoidal noise so I was asking. Thanks for your time :))) $\endgroup$
    – charansai
    Commented Dec 28, 2015 at 20:23
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You could analyse if the disturbing frequencies are higher than your main signal. That occours, if your signal is not smooth enough. If so, you can use a simple lowpass filter - analog or digital. Regarding the threory about reconstruction of sine waves (as elements of signals in frquency domain) check Nyquist Frequency.

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