Window functions have numerous application in digital signal processing. They are used to truncate signals in the time-domain or spectra in the frequency-domain. This process is referred to as windowing.
No matter if windows are applied in the time- or frequency domain, the properties of their Fourier- or inverse Fourier transform is usually important. A window might have favorable properties in the time-domain but show undesired features in its transform. This section lists a couple of common windows with their Fourier transform and discusses their central features.
The Fourier transforms of common window functions usually show a main lobe, with several side lobes. A desirable window will have a narrow main lobe, allowing for good peak detection and low side-lobe level. There is a trade-off between these properties.
Boxcar Window¶
The boxcar window is the default and therefor most common window function. It is involuntarily applied when a signal is simply truncated without using a specific window. As a result of its sharp edges, the Fourier transform has prominent side lobes:
Hann Window¶
Blackman Window¶
Hamming Window¶
Blackman-Harris Window¶
