• ### Frequency 44101hz = 1hz ?

If the sample rate is 44100hz, I found out 44101hz becomes same as 1hz.

So, if I make [osc~ 440], it sounded exactly like [osc~ 44540] (44100hz + 440hz).

and I also found out [osc~ 44099] is equal as a 1hz sine wave which is inverted [osc~].

I don't understand why this happens.

Is there any difference in quality of sound between 440hz and 44540hz?

Can some one please explain this to me?

• Posts 3 | Views 2773
• I'm still learning this, but here's what I know...

Beyond Nyquist, strange stuff happens.

Nyquist frequency is 1/2 of the sample rate. In theory, you can't do ANYTHING in the digital realm above Nyquist, because it is the maximum frequency you can reproduce at a given sample rate, i.e., when each sample is +1,-1,+1,-1..., it takes 44.1K samples to represent a 22.05K frequency.

Also consider the possibility of a 22.05K frequency, where the sample just happens to land on every 0 crossing. In this case, the sound is perfectly 'invisible' to the digital realm. And in truth, you are just as likely to experience this as you are to get a perfect +1,-1,+1,-1... series. Thus, very strange things happen even as you approach Nyquist. So a 44.1K sampling rate is actually fairly useless at representing signals above 20K. Fortunately, 20K is beyond the range we can hear.

So what happens when you try to represent a high frequency signal that CANNOT be represented digitally because there aren't enough "plotting points"? Harmonics at best, noise at worst.

As to how this can make 1K look like 44101K, take a peek at the first chart under "Sampling Sinusoidal Functions" at the following link (two different sinusoids that fit the same set of samples):

http://en.wikipedia.org/wiki/Aliasing

• yep, to further embellish: always picture frequencies as a circle when dealing with discrete time values. This is what's called the z plane. let's say you are trying to get a cosine wave at 440 hz. In order to get a sine wave you go around a circle (not the z plane) and increment the angle every sample. You go around this circle 440 times every second, and take the cosine value of whatever point you are at every sample. so if we were to visualize this frequency on the "z plane" we may as well visualize it as the angle that is incremented every sample (well I like to visualize it like this anyway). at a sampling rate of 44100 hz this would be incrementing the angle 440 / 44100 times the total amount of the circle at every sample

so what happens when we go up to the nyquist frequency? as shawnb mentioned, since nyquist is half the sampling rate, at every sample the phase of our angle that we're using to get the cosine value is incremented exactly half a rotation (pi radians) and so we get the series that shawnb mentioned. (because cosine of 0 radians is 1, cosine of pi radians is negative 1)

ok, so now going past nyquist: we are now incrementing more than pi radians every sample, lets call the angle theta, and taking the cosine of this value. this is exactly the same thing as incrementing by negative theta (the angle that we get when we reflect theta over the x axis) and taking the cosine value, and that is why you cannot accurately get frequencies above nyquist. the same thing happens with sine waves and the y axis. (also sine waves are just cosine waves with shifted phase)

now taking this past the sample rate: we want to increment the angle so that it goes around the circle 44101 times every second in your example. so every sample we increment the angle by 44101/44100 of the total circle. well, because it is on a circle this is the same angle we would get if we incremented the angle by 1/44100 of the total circle every sample. thus we visualize the frequency the same way on the "z plane"

I hope this helped with the conceptual side of things

I simplified the concept of the z plane: really you should visualize a real cosine wave as that angle and itself reflected around the real axis, both with an amplitude of half of the original, but then you would need to get into complex numbers.

Posts 3 | Views 2773
Internal error.

Oops! Looks like something went wrong!