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How is sample rate frequency related to audio frequency?

For example, say I have an audio file with a sample rate of 44100 Hz, 1 byte per sample (256 different values), and, for simplicity, a single channel.

I know that human hearing can perceive frequencies from 20Hz to 20kHz. Consider for example, 1 second of sound: it consists of 44100 values which can be from 0 to 256.

How can I detect how to divide 44100 (sample rate) by 20Hz and 62Hz, 125Hz .... 16khz (for example 10 band eq). In other words how to define if the specified sample refers to 20Hz or 62Hz or 16kHz, etc.?

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I think you haven't quite understood what the frequency domain actually is and how it relates to pulse-code modulation (PCM is what you mean by "it consists of 44100 values"). –  leftaroundabout Nov 29 '12 at 17:41
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2 Answers

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The Nyquist-Shannon theorem indicates that the highest frequency that can be sampled is 1/2 of the sampling frequency. However, it does not follow that you can simply adjust your sample rate to extract lower frequencies.

The reason for this is aliasing: when a signal is sampled at a rate less than twice the greatest frequency that occurs in the signal, the frequencies above half the sample rate will appear as lower frequency signals in the final output. These lower frequency samples weren't part of the original signal - they are an artifact of the interaction between the sampling rate and the high frequency content in the original signal.

To address this issue, a signal should be low-pass filtered at a frequency that is 1/2 the sample rate in order to avoid aliasing.

If you are looking for an algorithm for filtering digital signals, check on http://dsp.stackexchange.com.

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The two are not directly related. Sample rate frequency relates to the number of audio samples per second, whereas audio frequency is to do with the number of vibrations per second caused by the actual sound (which gives you the pitch).

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How to define is specified sample refers to 20 hz or 62hz or .... 16khz. –  testCoder Nov 29 '12 at 9:13
Do you mean you want to know the audio frequency of a specified sample? –  Robert Nov 29 '12 at 11:30
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