3 ms·
You are right, let me rephrase it: You would loose half of the remaining potential to encode entropy. Of course, if you start with a real valued signal, then y
by Lichtso 5y ago
You are right, let me rephrase it: You would loose half of the remaining potential to encode entropy.
Of course, if you start with a real valued signal, then you already lost that before even getting to the transform part. Or in other words you have to transform a signal twice as long as it needs to be, because half of it is mirrored and then discarded (I assume).
- omegalulw 5y agoThe goal is to produce real valued noise - you won't get that if the spectrum is not mirrored.
- ssfrr 5y agoThe goal is to generate a random spectrum that corresponds to a real-valued signal. If the positive and negative frequencies aren’t conjugate-symmetric then the resulting signal after the IDFT will be complex-valued. You can think of it in terms of degrees of freedom. A real-valued length-N signal has N degrees of freedom. A length-N spectrum is complex-valued, meaning 2 degrees of freedom per frequency bin. When you constrain it to be conjugate-symmetric you bring the degrees of freedom back to N, which matches the real-valued signal.