Window Functions

The Window function choices appear when the filter design methods is eithe the Windows design method or the Frequency-sampling design method.

For the Windows design method, a window function is applied to truncate an infinite impulse response in the time domain by having a number of non-zero values equal to the filter length and zero values both before and after that.

For the Frequency-sampling design method, the window is applied in the frequency domain before values are converted to the time domain using a discret cosine transform.

The windows function makes a tradeoff between attenuation outside the passband and the width of the transition region between bands.

The Hamming, Blackman Harris 92 dB, Chebyshev, or the Kaiser window function are commonly used for simple filters.

Window Function Choices

• Rectangular - The rectangular window is all values equal to 1.0. This results in peaks and troughs at the band edges. This is rarely used.
• Bartlett (Length + 2) - The Bartlett window is a triangular window. It is a low value at the edges, and linearly increases to one or two peaks at the center. The first and last value are 0.0, so a Bartlett window that is two larger than the filter length is used to prevent shortening the filter length.
• Hanning (Length + 2) - The Hanning window is a cosine-shaped window that is a special case of the Hamming window.

  w(n) = 0.5 - 0.5 * cos(2 * Pi * n) where 0 <= n < N - 1

  The first and last value are 0.0, so a Bartlett window that is two larger than the filter length is used to prevent shortening the filter length.

• Hanning (Length + 2) - The Hanning window is a cosine-shaped window that is a special case of the Hamming window.

  w(n) = p - ((1- p) * cos(2 * Pi * n)) where 0 <= n < N - 1

  p is a constant where 0 <= p <= 1.0

  Typically p = 0.54

  The user can set the value of 'p' for this window in an edit control in the filter design dialog.

• Blackman Harris 67 dB - This window has a fairly narrow transition region and 67 dB attenuation away from the passband.

  The attenuation falls off continuously.

• Blackman Harris 92 dB - This window has a wider transition region than the windows above, and 92 dB attenuation away from the passband.

  The attenuation falls off continuously.

• Chebyshev - This window gives the narrowest transition region for any given attenuation outside of the passband.

  However, the peak attenuation remains constants, i.e. does not decrease as frequencies go further from the passband. This can make this window function less desirable for filters that are used for decimation.

  The user can set a value that trades off the transition width and the attenuation. This defaults to the value 90, which is the approximate attenuation value the window provides.

• Kaiser - This is a complicated window that gives many tradeoffs between transition width and attenuation.

  The user can set a value that trades off the transition width and the attenuation. This defaults to the value 9. The user might want to set it to 11, or higher, if they want more attenuation at the expense of a larger transition width.