The advantage of using the polyphase decomposition of an IIR filter is that it allows for efficient implementation and lower computational complexity. The polyphase decomposition breaks down the original filter into multiple subfilters, each operating on a fraction of the input signal. This reduces the overall number of operations required and allows for parallel processing. Additionally, the polyphase decomposition can be used to optimize the filter's frequency response by applying different scaling factors to each subfilter. This can result in improved passband flatness and stopband attenuation