38.6.9.1 Video Scaler Description

The scaling operation is based on a vertical and horizontal resampling algorithm. The sampling rate of the original image is increased when the video is upscaled, and decreased when the video is downscaled. A Vertical resampler is used to perform a vertical interpolation by a factor of vI, and a decimation by a factor of vD. A Horizontal resampler is used to perform a vertical interpolation by a factor of hI, and a decimation by a factor of hD. The horizontal and vertical low pass filters are both designed to minimize the aliasing effect. The frequency response of the low pass filter has the following characteristics:

H ω = I      when    0   ≤ ω ≤ min ( π I , π D ) 0     otherwise

Taking into account the linear phase condition and anticipating the filter length M, the desired frequency response is modified.

H ω = I e − jω M 2      when    0   ≤ ω ≤ min ( π I , π D ) 0     otherwise
Figure 38-7. Video Resampler Architecture

The impulse response of the defined low pass filter is:

h n = I × ω c π  when  n = 0 I × ω c π × sinωcn ω c n otherwise

Or, for the filter of length M:

h n = I × ω c π  when  n = M 2 I × ω c π × sinωcn−M2 ω c n − M 2 otherwise

This ideal filter is non-causal and cannot be realized. The unit sample response h(n) is infinite in duration and must be truncated depending on the expected length M of the filter. This truncation is equivalent to the multiplication of the impulse response by a window function w(n).

Table 38-46. Window Function for a Filter Length M
Name of Window Function Time Domain Sequence w(n)
Barlett
1 − 2 × n − M − 1 2 M − 1
Blackman
0.42 − 0.5 × cos 2πn M − 1 + 0.08 × cos 4πn M−1
Hamming
0.54 − 0.46 × cos 2πn M−1
Hanning
0.5 − 0.5 × cos 2πn M−1

The horizontal resampler includes an 8-phase 5-tap filter equivalent to a 40-tap FIR described in the figure below.

Figure 38-8. Horizontal Resampler Filter Architecture

The vertical resampler includes an 8-phase 3-tap filter equivalent to a 24-tap FIR described in the figure below.

Figure 38-9. Vertical Resampler Filter Architecture