Hi All, How to calculate the Inphase (I) and Quadrature (Q) components of signals, such as RF signals? I would like to shift the RF signals to a specific baseband frequency and then derive the I an Q components from signals. I sort of know I can use NCO megacore function to do these. But I would like to know the actual steps to achieve these and math theory behind it. Tutorial links or reference articles would be appeiciated. Many Thank, Lee

Hi Lee, I/Q demodulation is simply a direct implementation of the Fourier frequency shift theorem, i.e., multiplication by a complex-valued exponential in the time-domain results in a frequency shift in the frequency-domain. The complex-valued exponential can be split into cos + j*sin (Euler's rule), and that is what you implement in hardware. Take a look at these FPGA-DSP notes for more details ... http://www.ovro.caltech.edu/~dwh/correlator/pdf/esc-104paper_hawkins.pdf Cheers, Dave

Thanks a lot Dave. I will have a look.

Hi Dave, Thank you very much for the document. That is closely related to my project, DDC. I got two questions. Q1. Does the center frequency of Eq 37 mean the carrier frequency of signals, on page 63 of ESC-104? 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? Q2. Why Eq 37 used -j not +j? Does it matter? Many Thanks, Lee

--- 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

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

22 Replies

Altera_Forum
Honored Contributor
11 years ago
Hi Dave,

Thanks. Yes, I just re-read the NCO user guide and I can simulate the my NCO design vhdl file on ModelSim now. I used automatically generated tcl file to run the simulation. The instructions to follow is in page A-2 of the NCO MegaCore function User Guides.

I think Altera should remind users that the testbench file should not be used in Quartus but will be used by the tcl file to run simulation in Modelsim. In Xilinx, you can run the testbench file directly (recall from my memory).

Many Thanks,
Lee
Altera_Forum
Honored Contributor
11 years ago
Hi Lee,

--- Quote Start ---

Thanks. Yes, I just re-read the NCO user guide and I can simulate the my NCO design vhdl file on ModelSim now. I used automatically generated tcl file to run the simulation. The instructions to follow is in page A-2 of the NCO MegaCore function User Guides.

--- Quote End ---

Great! Glad to hear you got it working.

--- Quote Start ---

I think Altera should remind users that the testbench file should not be used in Quartus but will be used by the tcl file to run simulation in Modelsim. In Xilinx, you can run the testbench file directly (recall from my memory).

--- Quote End ---

I think Altera relies on the error messages to remind you :)

Cheers,
Dave

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

22 Replies

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