Using fft and ifft for carrier modulation/demodulation In practice, such parallel data modulation and coherent demodulation can be simply done by using inverse fast Fourier transfer(IFft) and fast Fourier transfer (FFt) The basic orthogonal function is 2丌 g(k)=expl j k=0, 1,N-1,n=0,1,N-1 2 2 丌 >expl j pn expl -j kn=N,k=p N 2丌 2丌 exp pn expl-j3Mn=0,k≠p =0
Using FFT and IFFT for carrier modulation/demodulation In practice, such parallel data modulation and coherent demodulation can be simply done by using inverse fast Fourier transfer (IFFT) and fast Fourier transfer (FFT) The basic orthogonal function is , 0,1,... 1, 0,1,... 1 2 ( ) exp = − = − = k n k N n N N g k j = − = = − − = − = 1 0 1 0 0, 2 exp 2 exp , 2 exp 2 exp N n N n k n k p N pn j N j k n N k p N pn j N j
Signal representations The transmitted discrete time domain signal x(n) is x(n)=∑X(k)exp 2丌 0≤n≤N-1 After inserting guard interval, the signal becomes x'(n)with length N+G Assume the lowpass filter has rectangular shape 60)=:- T 2r or, b(t)=sinc 0;,f|≥ T 2T
− = = 1 0 2 ( ) ( ) exp N k nk N x n X k j Signal representations 0 n N −1 The transmitted discrete time domain signal x(n) is After inserting guard interval, the signal becomes x’(n) with length N+G ( ) = T N f T N f N T B f 2 0; 2 ; Assume the lowpass filter has rectangular shape = t T N b(t) sinc or