In an OFDM signal, if the symbol window (of N samples) is misaligned at the input to the FFT, the constellation points on each tone are rotated by a certain amount. To undo this effect we use the Fourier shift theorem which allows us multiply by a complex exponential on each tone. I am using a Wavelet Packet Transform instead of an FFT. My question is, is there an equivalent time/scale shift theorem for wavelets as there is time/frequency shift theorem for Fourier sinusoids? If so, what should I do to my received constellation points to recover them. Note: the FFT basis is complex valued while the waelet basis is real valued. So there are complex QAM constellation points on the tones in OFDM but only real valued PAM constellation points on the wavelet packet modulated signal. I know this is a pretty difficult question, but even a pointer would be appreciated. Much appreciated... DD

# shift theorem for wavelets (with application to OFDM)

Started by ●November 3, 2003

Reply by ●November 5, 20032003-11-05

I found a partial answer to my own question in "Effects of a Carrier Frequency Offset on Wavelet Transceivers" by Bianchi and Argenti... excellent paper presented at Baiano, Sept. 2003. However, I am more interested in the effect of symbol misalignment than in the effect of carrier frequency offset (which doesnt happen in baseband). All I can see is that my constellations are 'messed up'. Is there any underlying structure to this... DD