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How does the Windows operating system convert DFT or FFT?
Mathematical model Fourier Transform shows that the calculation is carried out over an infinite period, that is, with an infinite integral,
Where in reality using DFT or FFT it is impossible to sample a signal continuously continuously to infinity. Contact signals or generally called analog signals are shown in Figure 1.
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| Figure 1. 200Hz continuous signal |
When collecting sample data, it is necessary to limit the number of samples N A particular (sample data block) then samples again with the number of samples N However, it is not necessary to use DFT/FFT data to set similar data blocks. Ideal sampling of continuous signals is shown in Figure 2 where the sampler is taken N First delivered in black, then sampling N Here's what people are saying about the world and the same country N all three presentations are purple. Ideal sampling can be illustrated by simply taking one block or several blocks of samples marked with the start and end of the sample in the position big 0.
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| Figure 2. Ideal sampling of signal content. |
This means that DFT/FFT has a similar pendant that matches Figure 2 and the other side of the screen is the same as the other 3 parts of the world. big The signal frequency is 200Hz.
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| Figure 3. Frequency spectrum of a continuous signal Figure 2. |
If this happens, the same data will be blocked over time and will not be able to display the information created by DFT and FFT. This is because the signal continues over time but sampling will always stop after a certain number of samples N which indicates a period of sampling data to be able to carry out DFT and FFT calculations. By stopping the same data collection, the final point of data collection occurs discontinuity signals where the start and end of sampling are most likely not in position big 0 which is considered by DFT/FFT as another frequency that gives rise to the value or big Other frequencies in the calculation results are considered interference. Illustration discontinuity signal due to data sampling is shown in Figure 4.
In DFT/FFT it is required Window which aims to reduce frequency interference that appears outside the information frequency to a minimum in the calculation results caused by sampling (discontinuity) on a continuous signal or analog signal.
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