Window Function (Part One)
The topic here is window functions. The window function, which is often mentioned in articles relating to digital signal processing, is a function which extracts a part to be analyzed or monitored from a signal.
At first, consider that the extraction brings what? Since signals in the natural world have an infinite length in general. Of course, you can analyze individual syllables such as "sa" and it could be a good way in some situation. However, it is frequently required to extract a part from signals to analyze it such as for analyzing a stable part of the vowel.
The red bar on the signal (is not a voice) in the above applet is an example of the window. Click the "Expand" button after moving the window to somewhere, and click the "Spectrum" button to display the spectrum corresponding to the part selected by the window. How do you think the spectrum? Do you think the spectrum reflects the wave shape? Try various cases by moving the window.
Next, we are using a simpler wave to consider the window function. The following applet shows executing FFT on a part of a sine wave. Which part of the sine wave is extracted is simulated by varying the frequency and phase of the sine wave on the left part of the applet. Modifying the frequency and phase by respective ">" and "<", make observation of the spectrum shown in the right part of the applet. In the spectrum, the red line shows amplitudes for each frequency component and the green line shows the phase characteristics.
If you change the phase, you will notice that the amplitudes do not change significantly but the phase significantly changes. What happens if we vary the frequency? The amplitude of spectrum changes dramatically! This is because the energy of the sine wave is dispersed to the other components and it makes impossible to determine the amplitude. This is a big issue.
I told you the window that simply extracts a part (multiplying one for the part extracted and zero for the other parts) or "rectangular window" so far. However, there are other methods or shape to extract. Since a function is used to define the shape, they are called "window function." I will explain typical window functions in next time.
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