Data windowing

data windowing

The FFT algorithm considers that the data of the source signal contain an exact number of periods of this signal, so that the data sample has a kind of circular period and can be repeated an infinite number of times. If this rule is not strictly followed, FFT results can be poor, as some leakage appears in frequency results.

The following figure shows data extracted at 10 s. The first signal (red curve) has a frequency of 0.3 Hz meaning that the 10 s sample contains exactly 3 periods. Its extension to 30 s (blue and green curves) shows that both start and end points of data match. This corresponds to the ideal case.

Figure 3: Repetition of a signal with an integer number of points

The second signal has a frequency of 0.35 Hz, so that the 10 s sample does not contain an integer number of periods. The extension to 30 s shows that non-desired oscillations appear in the signal, leading to leakage in the spectral line.

Figure 4: Repetition of a signal with a non-integer number of periods

To overcome this problem, it is necessary to modify the original signal to reduce the influence of the start and end points. This is achieved by applying a window function to the original signal, as shown by the following curves.

Figure 5: Signal before (left) and after (right) application of the Window function

Most window functions take the form of a modulated sine wave. The following window types are accessible within Simcenter Amesim

with N the number of sampled points and j in the range (1, N).

Figure 6: Available window functions

Note

It is important to note that the multiplication of original data by a window has an impact on the amplitude of the signal in the spectral domain. Thus the amplitude of frequency peaks will not correspond to the amplitude of the oscillations of the original data. Simcenter Amesim can apply amplitude correction factors to the FFT.