Such intense calculation takes a higher time. Here a signal is tested with 5 frequencies, so signal needs to be multiplied by five frequencies. However for the value, f2 and f5 output won't be zero, but significantly higher than the rest of the values. So if our signal is multiplied by f1 summation of multiplication will be zero (near to zero for real application). In our case, If these two multiplication frequency has the same (or very close) frequency that sum of multiplication is the nonzero number. It can be shown mathematically that -summation of multiplication of two harmonic data-set having different frequency tends to zero(higher number of data can lead to batter result). This signal is multiplied by test sine waves of values f1 to f5. In the image, a signal is shown which is a combination of two frequencies f2 and f5. These methods are extremely slow for any real-time application. I tried to explain the working of DFT(discrete Fourier transform)in one of the previous instructable (. So any time-based signal can be also shown as a combination of the various sine of different amplitudes. Any signal can be composed of a combination of various sinusoidal waves.
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