Walsh transform

For a function $f:\\{−1,1\\}^n\\to \\{−1,1\\}$ the relationship between the sum of its linear Fourier coefficients $\\hat{f}(i)$ (defined by $\\hat{f}(i)≔\\frac{1}{2^n}\\sum_{x\in \\{−1,1\\}^n} f(x)x_i$ for $i=1,2,\\ldots,n$ and …