Smoothing a Signal which contain White Noise
A boxcar filter is a FIR filter, suppose your frame has length N and your boxcar has a length of M, you will have M+N-1 filtered values.There are 2 properties, time invariance and superposition that you can use.

Assume your boxcar has length 5, and examine 2 sequential frames,data is $x$

$$ 
\begin{align}xxxxxxxxxxxxxxxxxxxx&amp;0000  \quad \text{Frame 1 with 4 zeros post appended} \\
                0000&amp;xxxxxxxxxxxxxxxxxxxxxxx \quad \text{Frame 2, 4 zeros pre appended} 
\end{align}
$$

If we could time align the 2 frames, and added them together, we would have continuity across the frames.  This is a consequence of superposition.

If we run the boxcar over each frame,including the zeros
$$ 
\begin{align}yyyyyyyyyyyyyyyyyyyyy&amp;yyyy \quad \text{Filtered Frame 1 } \\
                yyyy&amp;yyyyyyyyyyyyyyyyyyyyy \quad \text{Filtered Frame 2 } 
\end{align}
$$

Adding the 2 time aligned filtered frames, is the same as filtering a gapless buffer.  This is superposion, and time invariance of the filter.