Inphase (I) and Quadrature (Q) components of signals

--- Quote Start ---

Q1. Does the center frequency of Eq 37 mean the carrier frequency of signals, on page 63 of ESC-104?

--- Quote End ---

Yes.

--- Quote Start ---

For example, for 20MHz carrier frequency signals with bandwidth of 1 MHz and sampling frequency 40 MHz, the normalized frequency, fo, will be 20/40. Is it correct?

--- Quote End ---

That is a special case. Since the carrier is at Nyquist/2 (the center of the sampled band) you do not need an NCO, you can simply use a phasor that rotates 1, -j, -1, j, etc., see slide 117

http://www.ovro.caltech.edu/~dwh/correlator/pdf/esc-104slides_hawkins.pdf

The input data to this phase should use a signed-symmetric format, so that the products with -1 or -j do not cause a positive-valued over-flow (or cause 1-bit of bit-growth).

--- Quote Start ---

Q2. Why Eq 37 used -j not +j? Does it matter?

--- Quote End ---

Inside an FPGA there are two data streams, the real-part Y_I[n] and the imaginary-part Y_Q[n], that complex-valued pair can be represented as (Y_I[n], Y_Q[n]) or equivalently Y_I[n] + j*Y_Q[n]. The quadrature component Y_Q[n] = -sin(2*pi*f0*n), i.e., the negative sign is absorbed into the component, rather than the higher-level representation of the two data streams inside the FPGA.

Cheers,

Dave