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From: | Roee Bar |
Subject: | Re: [Discuss-gnuradio] USRP Complex Demodulation |
Date: | Tue, 17 Nov 2015 00:46:03 -0800 |
Yes, the images came ok. Using your original example of transmitting I(t)=cos(wm*t), Q(t)=sin(wm*t), let’s take I(t)=cos(wm*t) and Q(t)=0: sout(t) = cos(wm*t)*cos(wo*t) - 0*sin(wo*t) = 1/2 * [ cos(wm*t-wo*t) + cos(wm*t+wo*t) ] At the receiver (sorry if the derivation is too explicit): I(t) = sout(t) * cos(wo*t) = 1/2 * [ cos(wm*t-wo*t) + cos(wm*t+wo*t) ] * cos(wo*t) = 1/4 * [ cos(wm*t) + cos(wm*t - 2*w0) + cos(wm*t + wo*t) + cos(wm*t) ] = 1/2 * cos(wm*t) + 1/4 * [cos(wm*t - 2*w0) + cos(wm*t + 2*wo*t)] Q(t) = sout(t) * -sin(wo*t) = 1/2 * [ cos(wm*t-wo*t) + cos(wm*t+wo*t) ] * -sin(wo*t) = 1/4 * [ -sin(wm*t) + sin(wm*t - 2*wo*t) - sin(wm*t + 2*wo*t) + sin(wm*t) ] = 1/4 * [ sin(wm*t - 2*wo*t) - sin(wm*t + 2*wo*y) ] After the low pass filter, which removes 2*wo+wm and 2*w0-wm components, we end up with: I(t) = 1/2 * cos(wm*t) Q(t) = 0 But in the USRP I don’t get Q(t)=0… Thanks, Roee On 16 Nov 2015, at 18:06, James Humphries <address@hidden> wrote: I'm referring to the receiver. It's essentially two receivers in parallel, one mixing down with the local oscillator (cosine) and the other mixing down with the same local oscillator, but phase shifted -90 degrees (sine). This is how it generates two components for the input signal. Of course, you can only input a real signal, but the receiver can generate both the I and Q components in the 'dual' receiver mode. This is similar to how a vector network analyzer (VNA) operates. Did the images I sent on the first e-mail come through ok? They were pretty basic, but show the layout of the transmitter and receiver. -Trip On Mon, Nov 16, 2015 at 5:47 PM, Roee Bar <address@hidden> wrote:
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