Changes between Version 51 and Version 52 of Other/Summer/2024/signal
- Timestamp:
- Aug 6, 2024, 7:06:53 PM (7 weeks ago)
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Other/Summer/2024/signal
v51 v52 45 45 Because every signal is composed of sine waves of varying frequency and phase, we can actually represent the signals in terms of the frequencies and phases of those sine waves. This is called the Frequency Domain and is an equivalent representation for any signal. Below and left is a square wave in the time domain and to the right is the same signal in the frequency domain. 46 46 47 [[Image( )]]47 [[Image(Screen Shot 2024-08-06 at 3.01.41 PM.png, 300px)]] 48 48 49 49 The conversion from time domain to the frequency domain occurs by multiplying each possible frequency sine wave with the signal and integrating over 1 period. This gives the magnitude of that frequency in the signal. In reality, an algorithm call Fast Fourier Transform (FFT) is used to do this multiplication and integration much quicker. FFT is a divide and conquer algorithm that makes use of complex number properties. 50 50 51 [[Image( )]]51 [[Image(Screen Shot 2024-08-06 at 3.01.51 PM.png, 300px)]] 52 52 53 53 **Complex Signals**
