If you have a 1D uniform $M$-channel multirate filter bank (FB), and $N$ is the decimation ($M \ge N$), rational oversampling ratios ($M/N$) are indeed possible (see Fig. 2), or from Figure 1 in Optimization of Synthesis Oversampled Complex Filter Banks, J. Gautier et al., IEEE Trans. Signal Processing, 2009 (doi), which provides optimized synthesis FB with any ratio (like $7/4$).

More precisely: for an analysis filter bank, you can choose any decimation you want. But you may loose information, and the invertibility of the analysis/synthesis system. In a lot of practical applications (for instance in speech processing), integer oversampling ratios are quite common, by choosing $N = M/k$, for instance $k=M/2$ or $k=M/4$. Such choices make the computations and some calculations much simpler: for instance, an inverse synthesis filter bank may take a closed form, related to the analysis window for DFT FBs.

However with redundancy, there are an infinity of inverses, and polyphase formulations help finding synthesis FBs.

If you have a 1D uniform $M$-channel multirate filter bank (FB), and $N$ is the decimation ($M \ge N$), rational oversampling ratios ($M/N$) are indeed possible (see Fig. 2), or from Figure 1 in Optimization of Synthesis Oversampled Complex Filter Banks, J. Gautier et al., IEEE Trans. Signal Processing, 2009 (doi), which provides optimized synthesis FB with any ratio (like $7/4$).

More precisely: for an analysis filter bank, you can choose any decimation you want. But you may loose information, and the invertibility of the analysis/synthesis system. In a lot of practical applications (for instance in speech processing), integer oversampling ratios are quite common, by choosing $N = M/k$, for instance $k=M/2$ or $k=M/4$. Such choices make the computations and some calculations much simpler: for instance, an inverse synthesis filter bank may take a closed form, related to the analysis window for DFT FBs.

However with redundancy, there are an infinity of inverses, and polyphase formulations help finding synthesis FBs.

A set of useful books (to me):

• Subband compression of images: principles and examples, T. Ramstad et al., 1995
• Wavelets and Subband Coding, M. Vetterli et al., 1995
• Wavelets and filte banks, G. Strang et al., 1996

If you have a $M$-channel multirate filterbank, and $N$ is the decimation, rational oversampling ratios ($M/N$) are possible, see Fig. 2, or Figure 1 in Optimization of Synthesis Oversampled Complex Filter Banks, J. Gautier, IEEE Trans. Signal Processing, 2009.

If you have a 1D uniform $M$-channel multirate filter bank (FB), and $N$ is the decimation ($M \ge N$), rational oversampling ratios ($M/N$) are indeed possible (see Fig. 2), or from Figure 1 in Optimization of Synthesis Oversampled Complex Filter Banks, J. Gautier et al., IEEE Trans. Signal Processing, 2009 (doi), which provides optimized synthesis FB with any ratio (like $7/4$).

More precisely: for an analysis filter bank, you can choose any decimation you want. But you may loose information, and the invertibility of the analysis/synthesis system. In a lot of practical applications (for instance in speech processing), integer oversampling ratios are quite common, by choosing $N = M/k$, for instance $k=M/2$ or $k=M/4$. Such choices make the computations and some calculations much simpler: for instance, an inverse synthesis filter bank may take a closed form, related to the analysis window for DFT FBs.

However with redundancy, there are an infinity of inverses, and polyphase formulations help finding synthesis FBs.