Side-channel attacks are an effective method for obtaining keys by utilizing signals such as power consumption and electromagnetic radiation generated by cryptographic devices. Intuitively, multiple channels provide richer information than a single channel, suggesting that multi-channel fusion attacks (MCFAs) should outperform single-channel attacks. However, existing MCFAs show only limited improvement and sometimes even perform worse than single-channel attacks. Moreover, current research does not clarify when MCFAs are a better choice. To alleviate this, we use the Hadamard Product Fusion Algorithm (HPFA) proposed in this paper as an example to conduct a thorough analysis and derive the Signal-to-Noise Ratio (SNR) equation for the fused data obtained by HPFA. We find that whether HPFA is superior depends on the correlation coefficient of the noise between channels and the ratio of SNRs of the individual channels. When the noise correlation coefficient is high, HPFA only shows advantages if the SNRs of the single channels are very close to each other. Conversely, when the noise correlation coefficient is low, HPFA can outperform single-channel attacks even if there are significant differences in SNRs. Based on this, we optimize HPFA by incorporating time-frequency decomposition, further enhancing its performance. Experiments validate the theoretical analysis and demonstrate that our methods significantly outperforms existing work when the conditions mentioned earlier are met.