Creation and properties of Cosine-sum Window functions
What are window functions?
In signal processing, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval. For instance, a function that is constant inside the interval and zero elsewhere is called a rectangular window, which describes the shape of its graphical representation. When another function or waveform/data-sequence is multiplied by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap, the "view through the window".
Cosine-sum windows are a kind of window functions that have unique advantages:
- Very easy to implement and fast to compute. This can be important for embedded software (like oscilloscope firmware).
- Compact support in the transformed domain where the window has only a few non-zero terms. Because of this the windowing operation can be efficiently performed by convolution in the frequency domain when an unwindowed FFT/DFT is available. This can be important for running FFT/DFT implementations.
- Properly overlapped windows sum to a constant. This can be important for block processing of long waveforms, because it enables perfect reconstruction.