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#1




Sampling Theorem/Nyquist
Hi,
I know this is random, but I am taking online courses for my bachelors in music production. Since I am online, reaching my teachers on weekends isn't the easiest achievement, so I figured I would post on here to see if anyone would be able to help me with my question, since google and wiki hasn't been much help. My question is regarding the sampling/Nyquist theorem. Our teacher had us take 2 files with the same bit depth (16b) and same sample rate (44.1kHz) (file 1 is 2.6MB/ 11 seconds and file 2 is 2.1 MB/ 14 seconds) and reduce both to 16 bit 22.05 kHz (file 1 reduced to 1.3 MB and file 2 is reduced to 1.1 MB) and we have to explain, based on what we have been taught about the sampling theorem, which file is less adversely affected. Well from what I have been taught I know that the sample rate is twice the frequency and if there is a frequency above the Nyquist frequency, that is called the alias. So I'm not understanding what it is that I am looking for to explain why one was more affected than the other, besides the fact of my opinion of the sound quality. Is it based on the file size reduction or the file duration? Any info on this or a point in the right direction would be VERY helpful! Nate 
#2




Re: Sampling Theorem/Nyquist
Quote:
First off, there's something fishy about the file sizes. If they are both 44.1/16, then the 14 sec file should be bigger. After samplerate converting to 22.05 kHz., the new Nyquist is 11.025 kHz. The antialiasing filter should have removed any content above that so the file that originally had more content above 11.025 kHz is the one that is more adversely affected. So, what tones or content is in the two files?
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James Cadwallader Hackintosh  Gigabyte Z77XUP5TH, Intel Core i73770K, 32GB 1600Mhz DDR3, 2x SATA 6Gb/s 240GB SSD, 3x SATA 6Gb/s 1TB HDD, 1x Glyph 2TB USB3 HDD, Mojave 10.14.6. Pro Tools Ultimate 2021.3, HD Native, Focusrite Red 8Pre (Mac) Pro Tools 2020.12, Mbox3 (Win) Presonus Faderport, Pro Tools  Control 
#3




Re: Sampling Theorem/Nyquist
You've probably seen this comment all over these forums before but we need a lot more information to help people out e.g. see Help us Help You  READ THIS Before Posting!. In this case we would settle for your school, student number, and lecturer/instructor email address.
 Seriously while you should really do this yourself I hope this question actually came with a bit more explanation including file encoding assumptions etc... Darryl 
#4




Re: Sampling Theorem/Nyquist
@Jimmy
So it has nothing to do with the numbers per say, it's the loss of the distinct sound? See that's what I'm not getting, I can hear the difference and which one has lost it's quality worse than the other, but how does the theory prove it if both files were exported to the same bit depth and sample rate? @Daryl Sorry but I am not handing out my student number, I go to full sail university if that helps. Here is a bit more depth: 1) he gave us 2 test files (both 16 bit depth @ 44.1 kHz) File 1 is 2.6 MB, file 2 is 2.1MB 2) import them into pro tools 3) 1st export: file 1 to 16 bit depth @ 22.05 kHz (rain, 2 birds chirping) (file 1 becomes 1.3 MB and 2 becomes 1.1 MB) 3a) describe the size and quality compared to original 4) 2nd export: file 1 to 16 bit depth @ 11.025 kHz (file 1 is 643 KB, 2 is 532 KB) 4a) describe file compared to original 5) Do previous steps to file 2 (bass, kick, snare beat) 6) "Which file was less adversely affected by sample rate reduction, 01_Test.wav or 02_Test.wav?" 7) "Based on what you know of the sampling theorem, why should this be so?" 8)Then we repeat this process but changing the bit depth to 8 instead of 16 So based on the theorem, from my understanding, quality is determined from the bit depth and sample rate, alais, alias filter, and Nyquist frequency. So how do I prove why one is better than the other when they are set at the same depth and frequency? I'm sorry if it seems like I am trying to have this all spoon fed to me, but I have been reading on this theorem for 3 days now and I just can't pull this solution from anything I have read. Nate 
#5




Re: Sampling Theorem/Nyquist
If I play this game can I get course credits? (not sure if you will however for crowd sourcing your assignment questions). But anyhow...
Can you post the files online _exactly_ as they were originally given to you. Don't convert or reencode them on a music file sharing service. Drop them on dropbox or similar. I want to see how the files were encoded since you are not telling us  and they can't both be PCM or any other uncompressed data. Can you post the exact text of the question i.e. exactly verbatim with any and all other information you were given about the files. Darryl 
#6




Re: Sampling Theorem/Nyquist
Quote:
He also described what's in the files. One is rain and birds twittering. The other is bass, kick and snare. The answer is obvious. Which one of those sources will lose more in a rate conversion to 22.05 and why? This kid already has enough information. He needs to step out and intuit the answer.
__________________
James Cadwallader Hackintosh  Gigabyte Z77XUP5TH, Intel Core i73770K, 32GB 1600Mhz DDR3, 2x SATA 6Gb/s 240GB SSD, 3x SATA 6Gb/s 1TB HDD, 1x Glyph 2TB USB3 HDD, Mojave 10.14.6. Pro Tools Ultimate 2021.3, HD Native, Focusrite Red 8Pre (Mac) Pro Tools 2020.12, Mbox3 (Win) Presonus Faderport, Pro Tools  Control 
#7




Re: Sampling Theorem/Nyquist
How do I have the answer that is what I don't get. Am I reading too much into this? Is it because of the file size reduction? You have to realize I am only into this degree by 3 months and the second week into this class. Before Friday I have never heard of this theorem.

#8




Re: Sampling Theorem/Nyquist
The file with the most top end will suffer the most from sample rate reduction. The file with the most dynamic range will suffer most from bit rate reduction.
(Simplified explanation) 
#9




Re: Sampling Theorem/Nyquist
Quote:
Darryl 
#10




Re: Sampling Theorem/Nyquist
Yes!
This has absolutely nothing to do with file size and length of time. This has everything to do with sampling rate and Nyquist frequency. If you listen to the files after sample rate converting, which one is more adversely affected and why? I flat out gave you the answer in my first post. At a sampling rate of 44.1, the Nyquist is 22.05. At a sampling rate of 22.05, the Nyquist is 11.025. At a sampling rate of 11.025, the Nyquist is 5.5125. What is the Nyquist frequency? A practical answer would be the frequency above which nothing can be sampled at that particular rate. So at a Nyquist frequency of 11.025 kHz, which is more affected? Rain and tweets, or bass, kick and snare.
__________________
James Cadwallader Hackintosh  Gigabyte Z77XUP5TH, Intel Core i73770K, 32GB 1600Mhz DDR3, 2x SATA 6Gb/s 240GB SSD, 3x SATA 6Gb/s 1TB HDD, 1x Glyph 2TB USB3 HDD, Mojave 10.14.6. Pro Tools Ultimate 2021.3, HD Native, Focusrite Red 8Pre (Mac) Pro Tools 2020.12, Mbox3 (Win) Presonus Faderport, Pro Tools  Control 
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