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Here is a real-life application on adaptive filtering on real signals. And watchout! We used 1-tap complex filters, filters with only one modulus/phase coefficient, which we called "unary filters". It was patented in Method of adaptive filtering of multiple seismic reflections, published in a limited form in Geophysics: Adaptive multiple ...


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All the other responses are excellent, especially Envidia's, so not to take away from those but I want to add this very intuitive view that bottom lines it quickly: Consider the spectrums below that start with a real signal (positive and negative frequencies are complex conjugate symmetric). This is what we could measure with a single scope probe (one stream ...


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Absolutely! Conjugates are mentioned in textbooks because conjugation has no effect on real signals, but it does on complex ones. This way, formulations are more general and apply to both real and complex valued signals. Complex numbers don't exist themselves, they are a mathematical construct. Having said that, their mathematical properties can be ...


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You should explore how are these complex time-domain symbols transmitted over channel (atmosphere or wire) using modulated waveforms. Also, a good starting point would be to figure out that complex numbers are nothing but 2 orthogonal/perpendicular dimensions. When we say $x = 3 + 3i$, we are basically saying we have a pair of numbers which lie in ...


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Software-defined radio (SDR) models real band-pass signals as complex baseband signals. All signals and filters operate on complex numbers.


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This sounded as an odd concept to me, until I saw the recent Matlab code contest at MatlabCentral on this issue: Problem 2554. Sum the real and imaginary parts of a complex number (Last Solution submitted on May 12, 2020). On SE Maths, there is a question on Standard notation for sum of vector elements?. So, complex numbers can be interpreted as vectors (...


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