Changes between Version 53 and Version 54 of Other/Summer/2024/signal
- Timestamp:
- Aug 6, 2024, 7:08:37 PM (4 months ago)
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Other/Summer/2024/signal
v53 v54 55 55 Speaking of complex number properties, signals can also be represented as complex numbers. While we may think of signals as up and down waves, shown left. In reality, signals can be complex 3 dimensional patterns, shown right. 56 56 57 [[Image(Screen Shot 2024-08-06 at 2.31.04 PM.png )]]58 [[Image(Screen Shot 2024-08-06 at 2.31.18 PM.png )]]57 [[Image(Screen Shot 2024-08-06 at 2.31.04 PM.png, 400px)]] 58 [[Image(Screen Shot 2024-08-06 at 2.31.18 PM.png, 400px)]] 59 59 60 60 The 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.
