[PD] audio signal distinguishing

[sebfumaster at aol.com]

By having them appropriately low-passed and sampled. Digital audio is sampled. If you sample a real-world signal without putting a lowpass filter on it first, you will getthese frequencies of over pi radians. Notice how the higher frequency (3pi/2) gets sampled less than twice in one period, and the highest frequency thatcould be sampled twice a period is pi radians/sample. So, before sampling we need to put a lowpass filter on the signal in order to filter out everythinghigher in frequency than pi radians/sample. Otherwise, the higher-frequency real signals will "go past" the 2 sampling points and you will get 2 different sine waves that could be represented by the same samples. Therefore in practice, digital audio assumes that the samples represent sine waves lower than pi radiansin frequency. so if you did sample without low passing first, you would get these weird lower-frequency sine waves in your digital signal that correspond to air pressure waves (sounds) higher than the range of human hearing, assuming a normal sample-rate
Also notice that if you have a real sampled cosine wave w/ higher frequency than pi radians/sample it can be represented as the frequency (frequency in radians - 2pi) which will be negative. This negative frequency will be the same as the positive frequency it will be confused for when sampled.If you have a sine wave that's higher than pi radians/sample, it will also be confused for the same corresponding negative frequency, but negative (shifted by 1/2 aperiod).
Since all sinusoids are linear combinations of sine and cosine, this means that any sampled sinusoid of frequency higher than pi radians will be confused for thecorresponding frequency of radians if the higher frequency on the unit circle were flipped over the x axis from the negative to the positive-y part. (with thelower-frequency sine portion being multiplied by -1)
and obviously if the signal to be sampled is higher than 2pi radians/sample in frequency it will be confused for the corresponding lower frequency on the unit circle,in radians/sample
Hope this helps,    -Seb

-----Original Message-----
From: Billy Stiltner <billy.stiltner at gmail.com>
To: pd-list at lists.iem.at <pd-list at mail.iem.at>
Sent: Thu, May 23, 2019 10:14 am
Subject: [PD] audio signal distinguishing

from chapter 3 of theory and techniques of electronic music"Figure 3.1: Two real sinusoids, with angular frequencies π/2 and 3π/2, showingthat they coincide at integers. A digital audio signal can’t distinguish betweenthe two."
How does an audio signal distinguish 2 waveforms?_______________________________________________
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