Why are analytical wavelets said to have no negative frequency?

Question

I have been reading about analytical wavelets and came across this definition:

An analytic wavelet is a complex wavelet such that its Fourier transform is null for negative frequency.

If it is a complex signal and if that is the reason it doesn't have any negative frequency components then why is it saying:

Fourier transform of a complex signal can produce both positive and negative frequency components. The positive frequencies correspond to the original frequencies present in the signal, while the negative frequencies represent their complex conjugates

Kindly help me with this doubt. Any more insights about Analytical wavelets will also help a lot.

Answer 1

If it is a complex signal and if that is the reason it doesn't have any negative frequency

"Analytic" is the reason why it doesn't have any negative frequencies. That's the very definition of an analytic signal: https://en.wikipedia.org/wiki/Analytic_signal

All analytic signals are complex but not all complex signals are analytic.

Fourier transform of a complex signal can produce both positive and negative frequency components.

That's poorly worded (at best). The Fourier Transform ALWAYS produces values for positive and negative frequencies.

The positive frequencies correspond to the original frequencies present in the signal, while the negative frequencies represent their complex conjugates

Incorrect. That is true ONLY for real signals. For complex signals positive and negative frequencies are generally independent. Also the term "original" seems questionable here.

I'm not sure what you are reading, but there may be better options.