# DFT Polyphase Filter bank

What is the purpose of DFT & IDFT blocks which are placed after the Analysis filter bank & before the Synthesis filter bank. The reason i am asking this question is because I tried to design Polyphase DFT filter bank & got the same output with & without DFT-IDFT block.

• what is the major difference between th dft and polyphase dft with contrast of improving resolution and what is the size of dft for n point polyphase 2,4 and 8. – kranthi kumar Jul 9 '15 at 13:32
• This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post - you can always comment on your own posts, and once you have sufficient reputation you will be able to comment on any post. – MBaz Jul 9 '15 at 14:02

## 1 Answer

I guess you are referring to an implementation like the one shown here. If you leave out the DFT/IDFT blocks, then you don't have the modulation step which is necessary for actually implementing a filter bank, and you will not be able to do appropriate sub-band processing between the analysis and synthesis stages.

When you test your analysis and synthesis stages without sub-band processing in between you will obviously get the same result if you leave out the DFT/IDFT blocks. Analysis and synthesis together are then a pure delay and you might as well replace everything by a pure delay, but this defeats the purpose of the filter bank which is to split the input signal into sub-bands for further processing, and then to reconstruct the original signal from these separate sub-bands.

• Thanks for this answer. Cleared some of my concepts. Also, when u say sub-band processing(separating i/p into different freq. bands) does the DFT block does sub-band processing or does it just facilitates it. I mean to say, does the output of DFT block give me M sub-band signals in frequency OR do i have to add some more blocks after DFT to break the signal into M freq sub bands? – KharoBangdo Jun 24 '13 at 9:01
• Each DFT bin corresponds to 1 sub-band, so with an $M$-point DFT you have $M$ sub-bands. – Matt L. Jun 24 '13 at 9:14
• I have 4 signals in the freq band from -35MHz to 35Mhz. Using direct form I am able to split the signals into 4 sub-bands at 4 outputs of analysis filter. But when i try to implement this in Polyphase form, i am not able to split them. I am using 4 pt DFT matrix as given in the Wikipedia article. Is there a mistake i am making? – KharoBangdo Jun 24 '13 at 9:33
• ykt is a 4x65567 matrix is the output of Analysis bank. W is a 4x4 DFT matrix. My output yktDFT=W X ykt . Is this the correct way to generate output? – KharoBangdo Jun 24 '13 at 9:42
• You should add some more information to your original question, and formulate any other more detailed questions there. Try to be as clear as possible as to what you've done and how you've implemented everything. This will make it easier to help you. – Matt L. Jun 24 '13 at 12:53