ETTC'2003 - SEE

e depicted in Eq.11~13, where f0 is the local oscillator frequency and supposes to be same with
the carrier. I (nT), Q (nT) and their complex spectrum are figured in fig.7.
− j2πf
0nT r(
nT ) ⋅ e = r(
nT ) cos( 2πf
0nT
) − j ⋅ r(
nT ) sin( 2πf
0nT
) = I(
nT ) + jQ(
nT )
I( nT ) = r(
nT ) cos( 2πf
0nT ) (12)
Q( nT ) = −r(
nT ) sin( 2πf
0nT ) (13)
Fig.7 I (nT), Q (nT) and their complex spectrum
because the data rate of both I (nT) and Q (nT) are relatively high compared with their
bandwidth, therefor it is necessary to further reduce the data rate to an extent that succeeded Dsp
units could handle in real time. Herein that is implemented with a multistage filtering structure
consisting of a CIC and a FIR filter. The CIC filter is put at the first stage, and constructed with
two cascaded fourth order CIC filters, it reduces data rate of I (nT) and Q (nT) from 64Msps to
16Msps with a decimate factor of 4.
The FIR filter is put at the second stage and it has two functions, one is to counter the
passband droop generated by the CIC filter and the other is to shape the required frequency
response, the passband is from 0 to 1.5MHz and the stopband is from 2MHz to 8MHz with
rejection of –60dB. It further decimates two times of outputs of the CIC filter, so the output rate of
I’ (nT1) and Q’ (nT1) is 8Msps, T1 is the sample period of 8Msps. fig 8 plots the impulse and
frequency responses of these two filters respectively. I’ (nT1) and Q’ (nT1) and their complex
spectrum is plotted in fig.9.
Fig.8 The impulse and frequency response of the CIC and FIR filter
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