Window Definitions

In the following, definitions of some windowing functions are given. All of the windows, except one, the Parzen Window (Section 3.4), can be of arbitrary extend which is specified by a parameter $\tau$. Fig. 2 on the left depicts all windows with width two. Also all frequency responses (Fig. 2 on the right) were generated (using the discrete Fourier transform) with windows of extend two. Consequently, we can directly compare the various windowed cosc filters with cubic spline derivatives which have the same extend (the frequency response of the derivative of the Catmull-Rom spline is depicted in Fig. 1).

• Rectangular Window
• Bartlett Window
• Welch Window
• Parzen Window
• Hann and Hamming Window
• Blackman Window
• Lanczos Window
• Gaussian Window
• Kaiser Window

Figure 2: Frequency responses of windowed cosc functions on the right, the windows themselves on the left.