Haar scaling function
= Haar scaling function
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{title2=$\phi_{J,k}=2^{J/2}\mathbf1_{I_{J,k}}$}
= Haar father wavelet
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{synonym}
At level $J$, a <Haar scaling function> is the normalized <indicator function> $2^{J/2}\mathbf1_{I_{J,k}}$ of a <dyadic interval>. The <functions> at that level form an <orthonormal basis> of the cellwise-constant subspace. Their normalization is what turns white-noise coefficient variances into $1/n$ and cellwise variances into $2^J/n$.