44 KHz (CD) not enough !? (Nyquist etc.)
Reply #7 – 2003-05-12 14:16:15
... Just try this: Create a sine signal (using e.g. Cool Edit) at 11024 Hz (with a few seconds duration, using a sampling frequency of 44.1 KHz). ... I've done this already. [EDIT] The following can't be the reason for "amplitude modulation" of 11024 Hz signal. The (hopefully) correct explanation is given in maths part (*). ___________________________ The following is true for a test tone near to Nyquist limit, e.g. a 22049Hz tone at 44100Hz sampling frequency: [/EDIT] The reason for the "amplitude modulation" visible in waveform view is the limited number of samples ("window") used for calculating the waveform. Try this: Create silence with Cool Edit and change one single sample in the middle to e.g. +30000. Now zoom in that you can see the waveform between the samples and zoom in vertically. You'll see that the changed sample causes a changed waveform in a range of 42 samples. In reallity this range is (should be) not 42, of course, but infinite. 42 is chosen, probably because it's a compromise between exactness of the result and computation power needed. So if more samples e.g. 420 or 4200 arround a gap between two sample values are taken into account to compute the shape of the waveform in this gap, there won't be an "amplitude modulation" left. Of cours you could choose a "test frequency" of 22049.99 Hz and you'll see "amplitude modulation" again, but I hope you get the point ... ______________ * OK. Finally some maths: I've created the 11024 signal as you suggested and zoomed in at the max. and min. positions of so called "amplitude modulation" to get the sample values: max.: 0 10361 0 -10361 0 10361 0 -10361 ... min.: 7326 7326 -7326 -7326 7326 7326 -7326 ... This corresponds to y=a*sin(alpha) with alpha values: max: 0° 90° 180° 270° 360° ...; a = 10361/sin(90°) = 10361 min: 45° 135° 225° 315° 405° ...; a = 7326/sin(45°) = 7326*2^(1/2)= 10361 Result: at both positions the amplitude is identical, the reason for the visible "amplitude modulation" must be something cool Edit related.