Why is a Time Shift also a Phase Rotation in Frequency?

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Iain Explains Signals, Systems, and Digital Comms

11 ай бұрын

Explains the Fourier Transform property that relates the time-shift of a signal (in the time domain) to the frequency-rotation that occurs in the frequency domain - using graphical waveform examples.
* Note that there is a minor "typo" in the equation. The exponential should include the complex variable "i".
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Related videos: (see iaincollings.com)
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Пікірлер: 19

@Embarking-on-a-new-adventure 11 ай бұрын

I am glad those formula's were not asked during my Ham exam 😁

@iain_explains 11 ай бұрын

I haven't heard of a Ham Exam before. I'm guessing you're not a butcher assessing the quality of a farmer's pigs. (... that's a 'dad joke', I know). But I might check what's asked on such an exam, and see if there are any topics I could cover on my channel. Thanks for the idea.

@elijahsmith7552 11 ай бұрын

@@iain_explains it would be great to see a video explaining some of the more popular digital modes in amateur radio, e.g. VARA or FT8. I found your channel through ham radio topics. Thanks for all the info.

@iain_explains 10 ай бұрын

Thanks for the suggestion. I've put it on my "to do" list.

@stephensu4371 11 ай бұрын

nice work, i like those transform (L, F, Z) video

@iain_explains 11 ай бұрын

Glad you like them!

@payman_azari 11 ай бұрын

Thanks Professor, very informative. can you also consider explaining about minimum-phase and excess-phase characteristics of a signal (I see no decent tutorial) I am currently using it to calculate the time delay between signals, and I get good results, but I think there can be a deeper understanding of these concepts.

@iain_explains 11 ай бұрын

Thanks for the suggestion. I've put it on my "to do" list.

@payman_azari 11 ай бұрын

@@iain_explains Great! 😊

@_SeaH0rse 11 ай бұрын

Beautiful videos Iain. Are we assuming that time is linear, in this context?

@iain_explains 11 ай бұрын

Glad you like the videos. Not sure what you mean by "assuming that time is linear". I'm not a physicist, but time is a dimension, it's neither linear nor non-linear. Or as Einstein said, "time is an illusion", from a relativity point of view.

@_SeaH0rse 11 ай бұрын

@@iain_explainsthe reason i asked was that i wanted to be sure that rotations are “frequency versions” of time shifts, that is, if time were a linear step in “time domain”, in “frequency domain” it would be a rotation.

@_SeaH0rse 11 ай бұрын

Presuming, again, that frequency is 2-dimensional by definition, while time is unidimensional.

@iain_explains 10 ай бұрын

No, that's not true. Frequency is not 2-dimensional. Perhaps this video might help: "What is Negative Frequency?" kzfaq.info/get/bejne/neBmdK6Ikriaaac.html

@kunleiyu3925 11 ай бұрын

Thank you vary much for making such a wonderful video! But I am not sure about the phase shifting term. An imaginary number seems to be missing there.

@iain_explains 11 ай бұрын

Sorry, yes you're right. It's a "typo". Thanks for letting me know. I'll add a comment to the description below the video.