I'v been doing an investigation about detection of a specific signal and I need to determine that how a received signal resembles the reference signal. A primary approach to this problem is done simply by taking cross correlation of signals, but I need to know about more accurate methods. References would be also appreciated.
Hi Alireza,
actually there are many ways to determine the similarity of signals (or the distance between them). Here some cues:
Using cross correlation (or correlation coefficient as normalized measure) surely is a widely applied method. As alternative correlation approach you could consider rank based correlation (Spearman's rho) (cross correlation e.g. assumes a linear dependency which might not be true).
Similarity of signals also can be accessed in the frequency domain, you could have a look for "coherence" to find more information.
Even by using measures of information theory similarity can be qunatified. Have e.g. a look to "entropy".
Apart from that, there are many distance metrics which can be applied similarly (the smaller the distance the bigger the similarity). The most often used metric is the euclidean distance (or a normalized version), but you'll find other metrics when searching for "distance measures".
Now, what's best suited strongly depends on your signals and what you regard to be similar (which can be problem specific). Hope this helps.
Greetings, Sebastian
Hi Alireza,
actually there are many ways to determine the similarity of signals (or the distance between them). Here some cues:
Using cross correlation (or correlation coefficient as normalized measure) surely is a widely applied method. As alternative correlation approach you could consider rank based correlation (Spearman's rho) (cross correlation e.g. assumes a linear dependency which might not be true).
Similarity of signals also can be accessed in the frequency domain, you could have a look for "coherence" to find more information.
Even by using measures of information theory similarity can be qunatified. Have e.g. a look to "entropy".
Apart from that, there are many distance metrics which can be applied similarly (the smaller the distance the bigger the similarity). The most often used metric is the euclidean distance (or a normalized version), but you'll find other metrics when searching for "distance measures".
Now, what's best suited strongly depends on your signals and what you regard to be similar (which can be problem specific). Hope this helps.
Greetings, Sebastian
Dear Alireza,
You can use the new Statistical Measure of Signal Similarity introduced in the paper at the link: Conference Paper A New Statistical Measure of Signal Similarity
Best wishes
Sebastian Zaunseder already said this, but I repeat. Start with cross-correlation.
The structural similarity (SSIM) index has become a dominant method of measuring video quality in broadcast and post-production houses throughout the television industry. And SSIM has been repeatedly shown to significantly outperform MSE and its derivates in accuracy, including research by its own authors and others.
http://ieeexplore.ieee.org/document/4775883/
https://it.mathworks.com/help/signal/examples/measuring-signal-similarities.html
Check out this article:
Chapter Mutual Information: A Similarity Measure for Intensity Based...
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