Відео

Plotted on the complex plane for fun and the process is as follows 1) 7777 random numbers generated 2) DFT 3) Fourier Series in exponential form 4) Animating(auto scale)

@@IcebergProject9 I see, but putting random number to DFT just yields randomness with no interesting distribution. You might as well have skipped the DFT step and we wouldn't even be able to notice

@@h.i.sentertainments8580 Thanks for your another valuable question. If you input real numbers, DFT gives you complex conjugate pairs. Plz find [DFT4] in this channel

@@IcebergProject9 your input is actually already complex. ℝ⊂ℂ, rela number is part of complex number

@@IcebergProject9 so you are essentially just generating random complex numbers below certain radius

1) random numbers genrated 2) DFT 3) Fourier Series in exponential form 4) Animating(auto scale)

You are right in the real domain, but you have N roots in the complex domain. This animation shows the roots for N=2, 3, 4, 6, 12, 24 in the complex domain. And it is used in the Discrete Fourier Transform.

@@IcebergProject9 thanks for explaining 😊🙏🤠

I'm really happy if you got something from my video. Thank you for the message.

I feel great that it was helpful. Thank you for leaving a precious message. Good luck.

PPT, GeoGebra, and Pixabay. Thank you for question.

Good point. It would be better to say that 'Time sets below have different FFTs, but they are from the same PSD'

First of all thanks for the reply :) But when you say "different FFT" do you mean real part, imaginary part or module of the FFT? I think they should definitely have the same modulus of FFT (since the PSD is derived from the squared modulus of the FFT divided by N)

Thank you for another valuable question. The FFTs differ not only in phase but also in amplitude because the number of data we compute in practice is finite as you already know. PSD is just expected value. Please review the free reference, MIL-STD-810H(Annex F in Method 514.8).

Glad you enjoyed it. Plz find 'sinusoidal and circular motion on complex plane' in this channel.

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The DFT series is now all 5 videos. I'll upload one or two more in the second half of this year. There is no membership and there never will be. Thanks for your interest.

Palmgren-Miner's rule has been widely used for its simplicity but has many drawbacks, one of which you have pointed out. Thanks for your valuable comment.

Thanks for your positive feedback.

Glad it's informative to you. Enjoy other videos too.

Thanks for your valuable question in advance. Since fn is the natural frequency of the virtual specimen, which is a simple mass spring damper system, no modal analysis is required. And please note that the damper is not drawn for simplicity.

Thanks for your valuable comment!

Thanks for your feedback

This one is for quick grasp of the concept. You would find great explanations by others. Good luck!

@@IcebergProject9 can you make it 360 seconds video, to cover the basics/requirements for the concept? I studied Signals&Systems, and trying to cover DSP now. I need PSD for biosignals - EMG etc.

Thanks for your encouragement.

Thanks for your valuable advice.

Thanks for your encouragement.