Digital mixer implementation for DDC/DUC

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atif javed
atif javed 2018-2-16
I am trying to implement digital up/down converter in which the implementation flow is
DUC
Interpolation->Digital mixer
DDC
Digital mixer->Decimation
In DUC(digital mixer) the input is I AND Q symbols then same I,Q are recovered at DDC digital mixer I want to find out complete equations of Mixer so that i can easily implement it
According to my understanding in DUC digital mixer the equation is Transmit_signal=I*Cos(wt)-Qsin(wt);
And in the receiver side the I and Q is recovered through following sequence
Reciver_I=Transmit_signal*Cos(wt); Reciver_Q=Transmit_signal*sin(wt);
Reciver_I_fil=lowpassfilter(Reciver_I); Reciver_Q_fil=lowpassfilter(Reciver_Q);
but i cannot be able to recover the exact I and Q symobls at the receiver side please help to find the exact equations

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