Shannon Nyquist Sampling Theorem 

The equality holds only for even functions, e.g., a cosine.

This is actually the reason I came to look at this video and it answered that. Thanks!

@Leland Hugh seriously? Is this the place for this? 😂

4:20 It's a little bit nit picky, perhaps, but f is in Hertz or cycles per second. Omega is angular frequency and measured in radians per second. Omega=2*pi*f where the units on pi are radians per cycle and the units on f are cycles per second. The cycles part, being in the denominator and numerator respectively, cancel out leaving radians per second.

Wow, I was just thinking about this having finished the video. Thank you for all the info!

Thank you so much 😀. Who knew art was so important for math!

Thank you!

cool! thank you!!

How many people study signal processing??

Thanks -- I appreciate it!

actually in average around 1 million views for all videos per year for the last 4-5 years

@@raghavinder2161 compared to the total population they are likely sparse LOL

Glad you liked it!

Awesome, thanks!

That's why Nyquist frequency upper border is not included in what it is possible to be measured without aliasing.

How much higher than twice? Is it appropriate to do 2.5X or something? Must it an integer multiple?

​@@ericyip947no, it doesn't need to be an integer multiple. even just a couple hz would most likely suffice

Actually 22khz is pushing it. The range is from 20hz to 20khz but by the time we are adults most of us lose those highest highs. 14khz is considered normal for adults over 30. The actual reason for 44.1khz is to allow for filtering at the high end. A low pass filter is put onto the signal starting at 20khz and sloping down to null at 22khz. This is needed to prevent aliasing.

Awesome, I'm so glad!

Awesome, thanks so much!

Whittaker-Nyquist-Kotelnikov-Shannon!

I’m not sure how oscilloscopes do it, but you can also highpass signal in the analog domain and compute it’s power spectral density. If there is a lot of energy - you have severe aliasing. Another sign of aliasing is if changing the sampling phase slightly, you get different frequency power.

oh, didn't know he'd say that at the end...lol

if i have a really short (duration) signal i am trying to catch, i go all the way to 10x if its a highly unpredictable signal (noise issues tho). If it is a predictable short duration signal, i like 5x.

Thanks David, great catch!

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Ok, cool, it wasn't just me that thought that was crazy. Although now that I think about I'm pretty sure he didn't, but instead just flipped the video after recording it. The gig is up Steve, looks like I just caught you left handed!

That seemed like a bad explanation from my understanding... You only get mirroring across the y axis (and only for real signals), aliasing causes shifts by multiples of the sampling rate: 1.5-1=0.5 (note that there'd be two peaks being summed there actually if the signal was real, the other being from -1.5+2) *Edit: they would be square rooted, summed, and squared since you're dealing with power in this case I believe.

Also, if you're familiar with fourier transforms, a useful way to think about sampling is as multiplying your signal by an impulse train, where each impulse is spaced by the sampling period. That then turns into convolving with an impulse train spaced by your sampling frequency in the frequency domain, which in turn explains the whole shifting and adding process. Then you can think of aliasing as having spectrum components that will overlap when shifted (such that after adding you can't tell whether it's part of the original or a copy), so to not have aliasing your signal has to be band limited to half the sampling frequency. Edit: explaining the conclusion a little better: if you're signal is properly band limited to f_s/2 (a.k.a you're sampling at twice the maximum frequency component of the signal), your original signal will be centered around 0 between -0.5f_s (from reflection (ish, potentially different phase but same magnitude if we're talking straight fourier transform) across y axis for real signal) and 0.5f_s, a copy will be at f_s between 0.5 and 1.5, a copy will be at -f_s between -1.5 and -0.5, etc. No overlap, no aliasing!

Yes the video gets mirrored/flipped to show the notes correctly to the audience.