Polyphase Analysis Filter Bank I have a question regarding the polyphase DFT filter bank implementation in this page. (https://cnx.org/contents/Peqc-TK2@16/Uniformally-Modulated-DFT-Filterbank) 

In figure 2, to analyze the kth filter bank branch, the signal $x(n)$ was multiplied with $e^\dfrac{j2\pi kn}{M}$. But to downconvert a signal to baseband and low pass filter it, the signal should be multiplied with $e^ -\dfrac{j2\pi kn}{M}$. I made this change and continued derivation, I ended with getting IDFT block instead of getting DFT block as shown in Figure 7. 

I referred multiple books and papers for this. Everywhere I found a DFT block in the block diagram. But, I couldn't find where I am doing wrong. Please help me in knowing the correct block diagram.
With every polyphase filter bank I have worked with, the first block in the analysis phase is an IFFT, and the block in the synthesis phase is a DFT. These operations essentially cancel one other, so it should be fairly intuitive. Think of the DFTs acting as sinusoids modulators in this case rather than an operation to convert to the frequency domain. By having complementary DFTs, the modulation is essentially performed in analysis and then removed in synthesis. From looking at the figure in the text you linked, it appears that they’re may be a misprint, at least in comparison to my industry experience implementing this types of filter banks.

The following is a great, compact and concise resource on polyphase filter banks, multi-rate identities, and DFT based filter banks:
https://apps.dtic.mil/dtic/tr/fulltext/u2/a457390.pdf