5 Why We Window

When computing an FFT, you need to assume that an integer number of cycles of the signal need to fit in the number of samples analyzed in the FFT. Also, if you were to take the sampled waveform and put the sampled waveform end to end, you create a continuous sampled signal. Figure 5-1 shows a coherent signal example that completes five cycles in a 1,024 sample data set. Notice how the sine wave’s start and end points blend into each other seamlessly, creating a continuous signal without any interruptions, jumps or discontinuities.

Figure 5-2 shows a noncoherent sine-wave signal. You can see that the start and end points of the sine wave do not coincide with each other, and if placed end to end can cause huge discontinuity. The resulting signal can end up being noncoherent, and you can see the signal power smeared across bins in the FFT measurement.

This is where applying a window function can make the difference between a coherent and noncoherent sampling. Window functions, Blackman-Harris, Hamming, etc., have specific shapes associated with them; however, there are several different functions from which to choose. By default, TI’s high-speed data converter pro software uses the Blackman-Harris window function. Multiplying the window function with the noncoherent signal and zeros at both ends, removing any discontinuity and creating a more accurate FFT plot. Figure 5-3 shows an outline of the Blackman-Harris window function.

When multiplying a noncoherent signal like that shown in Figure 5-2 with the window function shown in Figure 5-3, the output signal can be the windowed version of the noncoherent signal, as shown in Figure 5-4. You can see that both ends are zeroed out and that there is no discontinuity between end points.