We propose CSIApx, a very fast and lightweight method to compress the channel state information (CSI) of Wi-Fi networks. CSIApx approximates the CSI vector as the linear combination of a small number of base sinusoids on constant frequencies and uses the complex coefficients of the base sinusoids as the compressed CSI. While it is well-known that the CSI vector can be represented as the linear combination of sinusoids, fixing the frequencies of the sinusoids is the key novelty of CSIApx, which is guided by our mathematical finding that almost any sinusoid can be approximated by a set of base sinusoids on constant frequencies. CSIApx enjoys very low computation complexity, because key steps in the compression can be pre-computed due to the constant frequencies of the base sinusoids. We extensively test CSIApx with both experimental and synthesized Wi-Fi channel data, and the results confirm that CSIApx can achieve very good compression ratio with little loss of accuracy.