Changes between Version 54 and Version 55 of Other/Summer/2024/signal


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Timestamp:
Aug 6, 2024, 7:12:44 PM (4 months ago)
Author:
wesleychen
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  • Other/Summer/2024/signal

    v54 v55  
    6060The axis going into the page is the time and the vertical / horizontal axis are the phase and amplitude respectively. There are many other ways to think about these axis as well including the coefficients of sine and cosine waves and most notably real and imaginary numbers. This representation gives rise to a new way to represent the signal algebraically as well. S(t) = I(t) + Q(t)i, where S(t) is the signal, I(t) is the real component, Q(t) is the imaginary component and i is the imaginary number sqrt(-1). This imaginary number representation is advantageous in making the math in later stages much simpler.
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    6464The complex signal representation also leads to something known as IQ plots, shown above. This is simply a plot of all points (I(t), Q(t)), placing I(t) on the horizontal/real axis and Q(t) on the vertical/imaginary axis. This graph can also be created by observing the 3 dimensional graph from the front face.