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On wikipedia there are only 2 lines about ESPRIT: Estimation of signal parameters via rotational invariant techniques (ESPRIT)... MUSIC doesnt have an entry in the music disambiguation page, other than something for neural networks.

I have read that they are more advanced than FFT. What are their advantages and disadvantages?

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The prime thing such algorithms aim to do is to make use of more information that you may have about the signal. In this case, the extra information is that you know the number of signals (sinusoids) present in your measurements.

One pro for both is, therefore, when your measurements match the assumption, you get a more accurate representation of the spectrum: it has the right number of lines. The FFT does not guarantee this.

A con is that, if your assumption is wrong (there are three lines instead of two), then these algorithms perform worse.

These algorithms do not give better resolution than the FFT. Only more data can give more resolution.

There is a good exposition here comparing the two to each other.

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  • $\begingroup$ In the presentation you reference they say that MUSIC and ESPRIT are high resolution methods - better than conventional beamforming. Could you explain what you mean by not having better resolution? Do they mean estimation accuracy? $\endgroup$ – David Apr 23 '16 at 2:27
  • $\begingroup$ No. The presentation says "known as high resolution estimates". There is a subtle difference. I will find the references later this weekend. Have too much to do today. $\endgroup$ – Peter K. Apr 23 '16 at 9:43
  • $\begingroup$ @DanBoschen Ooops! Looks like I didn't follow up. The best reference I know of for these sorts of problems is Barry Quinn's and Ted Hannan's (RIP) "The Estimation and Tracking of Frequency" but I'm not sure it explicitly deals with this issue. $\endgroup$ – Peter K. Nov 30 '18 at 19:17
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    $\begingroup$ @PeterK. I was confused by your Ooops but now follow and please I hope you did not think I was being sarcastic!!! I was referring to the reference in your post specifically that you linked in your last sentence and didn't even see your last comment. $\endgroup$ – Dan Boschen Nov 30 '18 at 19:34
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    $\begingroup$ @DanBoschen No worries! That's what I thought you meant. I just noticed my comment, too, and my lack of follow-up! :( $\endgroup$ – Peter K. Nov 30 '18 at 20:10

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