Changes between Version 78 and Version 79 of Other/Summer/2024/signal

Timestamp:

Aug 6, 2024, 10:08:54 PM (7 weeks ago)

Author:

wesleychen

Comment:

—

Other/Summer/2024/signal

@@ -121 +121 @@
 [[Image(Screen Shot 2024-08-06 at 5.55.59 PM.png, 300px)]]
 
-In reality this is done using a mathematical tool called correlation which compares multiplies the two signals at every time point (you can imagine the shorter barker code scrolling across the longer signal) and takes the integral/area under curve. After correlating with both I and Q, the result of each is squared and added together. The final correlation is shown below
+In reality this is done using a mathematical tool called correlation which compares multiplies the two signals at every time point (you can imagine the shorter barker code scrolling across the longer signal) and takes the integral/area under curve. After correlating with both I and Q, the result of each is squared and added together. The final correlation is shown below left.
 
 [[Image(Screen Shot 2024-08-06 at 6.03.54 PM.png​, 300px)]]
+[[Image(Screen Shot 2024-08-06 at 6.04.02 PM.png, 300px)]]
 
-After finding the frequency offset and phase, we can multiply each IQ sample by some exponential e^(-''i''*<delta>)^ where <delta> stands in for the error / angle offset of that sample. When multiplying numbers in the complex plane, the angle of the two are added allowing us to easily correct every sample. Now we see why complex numbers are useful. The corrected IQ samples are shown below.
-
-[[Image(Screen Shot 2024-08-06 at 6.04.02 PM.png, 300px)]]
+After finding the frequency offset and phase, we can multiply each IQ sample by some exponential e^(-''i''*<delta>)^ where <delta> stands in for the error / angle offset of that sample. When multiplying numbers in the complex plane, the angle of the two are added allowing us to easily correct every sample. Now we see why complex numbers are useful. The corrected IQ samples are shown above right.
 
 == Architecture