This is the sum of a rectangle and a Hanning window. An amplitude weighting of the time signal used with gated continuous signals to give them a slow onset and cut-off in order to reduce the generation of side lobes in their frequency spectrum. This window has similar properties to the Hanning window with the added feature that it suppresses the first sidelobe. However, the fall-off rate of the sidelobes is only 20dB per decade compared to 60dB per decade for the Hanning window.
The magnitude graph of sin(x) exhibits the embarrassment of DFT leakage. Instead of having a signal magnitude 1.0 value at an x-axis location this case corresponds to the number of sin(x) periods, there is a magnitude that is slightly less than 1.0 and several sub-magnitudes. For sin(x) this is not a big problem, since it is easy to distinguish the major component of the signal. However, if it is a complex signal, which smaller components, the smaller components may be obscured by the DFT leakage.
One solution to the humiliating problem of DFT leakage is windowing. Lyons discusses three windowing functions:
- Triangular window
- Hanning window
- Hamming window
These functions smoothly "tail off" the signal at both ends, reducing DFT leakage. Each point, si in the signal is multiplied by a window scaling factor wi before the DFT is calculated.
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