Re-create missing negative frequencies?

[fleem]

I am being given complex frequency domain data from a measuring instrument. The data does not include negative frequencies. I have some existing software to process this data, but that software currently expects the spectrum data to also include negative frequencies. I want to continue using that software for now without change. So my question is, can I fill in the missing negative frequency data with the complex conjugate values of the corresponding positive frequency data? For example, if the positive frequency for 2GHz is 3+4j, then can I assume the value for -2GHz is 3-4j. (Note that I realize this may be wasteful of CPU because redundant data will be processed, but that's not an issue at the moment--it might be later). Also, I don't care if absolute magnitudes are not preserved, as long as any scaling is constant. Any help, ramblings, guesses will be appreciated.

 

[fleem]

NVM. i just stumbled upon this thread: https://www.physicsforums.com/showthread.php?t=294925

So I guess the answer is "yes, I can just set the missing negative frequencies to the complex conjugate of the positives".

 

[DrGreg]

Provided the original time-domain signal is real, not complex (which it probably is in a real-world measuring instrument), then yes you can.

(Find the words "reality condition" in the Wikipedia article Fourier transform.)

 

[fleem]

Provided the original time-domain signal is real, not complex (which it probably is in a real-world measuring instrument), then yes you can.

(Find the words "reality condition" in the Wikipedia article Fourier transform.)

Great. Thanks for the help!