Hi All,
I am currently working on mp3 encoder project. After the polyphase filtering and before the MDCT calculation frequency inversion is done in the encoder right? ie every even indexed sample of every even indexed subbands are multiplied by -1. I dont understand why this is being done. In all the documents they have told that this is done to avoid the natural frequency inversion in polyphase filtering operation. Where does this frequency inversion happens in polyphase filtering stage? Can you please elaborate why this is done?

Thanks
Abhijit

This is due to the filterbank being critically sampled. The extended nyquist theorem states that you can reconstruct a sampled signal if the signal's bandwidth (it doesn't have to start at 0 Hz!!) is half the sampling rate. If you sample -- for example -- a signal at 22 kHz which only has content bewteen 11-22 kHz you can reconstruct it. Note, however that frequencies are mirrored into the lower base band which is where the frequency inversion comes from. So, a 13 kHz sine sampled at 22 kHz appears to be a 9 kHz sine, a 14 kHz sine appears to be a 8 kHz sine ... and so on. You still can reconstruct it under the assumption your original signal has no content below 11 kHz. This is true for the PQF filterbank because it makes sure of that by bandpass filtering. The PQF filterbank is no exception (QMF / Wavelet type filterbanks also share this frequency inversion effect).

The "natural" frequency inversion is accounted for by multiplying every 2nd sample of every 2nd subband my -1 so that after the MDCT stage and alias reductiuon butterflies your i-th transform coefficients correspond to the i-th subband for 0<=i<576.

HTH,
SG