39.6.9.1 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) = \{\begin{matrix} I when 0 \leq |ω| \leq \min (\frac{π}{I}, \frac{π}{D}) \\ 0 otherwise \end{matrix}

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

H (ω) = \{\begin{matrix} I e^{- jω \frac{M}{2}} when 0 \leq |ω| \leq \min (\frac{π}{I}, \frac{π}{D}) \\ 0 otherwise \end{matrix}

Figure 39-7. Video Resampler Architecture

The impulse response of the defined low pass filter is:

h (n) = \{\begin{matrix} I \times \frac{ω_{c}}{π} when n = 0 \\ I \times \frac{ω_{c}}{π} \times \frac{sinωcn}{ω_{c} n} otherwise \end{matrix}

Or, for the filter of length M:

h (n) = \{\begin{matrix} I \times \frac{ω_{c}}{π} when n = \frac{M}{2} \\ I \times \frac{ω_{c}}{π} \times \frac{sinωcn−M2}{ω_{c} (n - \frac{M}{2})} otherwise \end{matrix}

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 39-46. Window Function for a Filter Length M
Name of Window Function	Time Domain Sequence w(n)
Barlett	$1 - \frac{2 \times \|n - \frac{M - 1}{2}\|}{M - 1}$
Blackman	$0.42 - 0.5 \times \cos \frac{2πn}{M - 1} + 0.08 \times \cos \frac{4πn}{M−1}$
Hamming	$0.54 - 0.46 \times \cos \frac{2πn}{M−1}$
Hanning	$0.5 - 0.5 \times \cos \frac{2πn}{M−1}$

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

Figure 39-8. 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 39-9. Vertical Resampler Filter Architecture