Dear users, I want to implement a multirate filter with the ratio 7/8 (Interpolate by 7, decimate by 8). The multirate should have 8 input lines and 8 output lines. At each clock cycle I get 8 parallel samples in space, while they are 8 consecutive samples in time. What is the architecture that I can use, or where can I look to find out some clues how to design it? I found this paper describing the implementation of such filters http://www.rfel.com/Files/Documents/W11013_Resampling_white_paper.pdf but I found out that this method will give me 8 input lines and 7 output lines. Any help would be appreciated! Thanks in advance Hassan

# Parallel implementation of Multirate filter

Started by ●November 26, 2012

Reply by ●November 26, 20122012-11-26

On 11/26/12 11:13 AM, Hassans wrote:> > I want to implement a multirate filter with the ratio 7/8 (Interpolate by > 7, decimate by 8). The multirate should have 8 input lines and 8 output > lines. > At each clock cycle I get 8 parallel samples in space, while they are 8 > consecutive samples in time.i am still trying to decode the meaning of this. is this image processing and you get 8 pixels every clock? or is this a case of what i might call "block processing" where your clock ticks once every 8 samples (in time)? -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."

Reply by ●November 26, 20122012-11-26

On Mon, 26 Nov 2012 10:13:18 -0600, Hassans wrote:> Dear users, > > I want to implement a multirate filter with the ratio 7/8 (Interpolate > by 7, decimate by 8). The multirate should have 8 input lines and 8 > output lines. > At each clock cycle I get 8 parallel samples in space, while they are 8 > consecutive samples in time. > What is the architecture that I can use, or where can I look to find out > some clues how to design it? > > I found this paper describing the implementation of such filters > http://www.rfel.com/Files/Documents/W11013_Resampling_white_paper.pdf > > but I found out that this method will give me 8 input lines and 7 output > lines. > > Any help would be appreciated! > Thanks in advanceThis is worded like homework -- what are you really doing? Why eight lines out when the filter is decimating at a 7:8 ratio? What do you mean by "eight samples in space, eight samples in time"? What's your source data? Are you doing the decimation in both time and space, meaning you're going from 8x8 to 7x7? -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com

Reply by ●November 26, 20122012-11-26

>> I want to implement a multirate filter with the ratio 7/8 (Interpolate >> by 7, decimate by 8).Would using 8 independent filters in parallel solve the "8 input 8 output" part?

Reply by ●November 27, 20122012-11-27

>>> I want to implement a multirate filter with the ratio 7/8 (Interpolate >>> by 7, decimate by 8). > >Would using 8 independent filters in parallel solve the "8 input 8output">part? > >I have an ADC that samples at a frequency (Fs1). This ADC has 8 parallel output lines with a clock (Fs1/8) each. Using an FPGA I read 8 samples at each clock cycle with a rate of (Fs1/8). It is not possible to rearrange the 8 samples in serial and process them with a clock of (Fs1) due to hardware limits. What I want to do is to change the rate of the data to (Fs2) which has a ratio of (Fs2 = 7/8*Fs1). So I am obliged to build a Multirate filter that has 8 parallel inputs. And because the final sampling rate required (Fs2) is still high enough for the FPGA to hold, then I am obliged to have 8 output lines with a rate of (Fs2/8) each. Hopefully this clarifies my problem. Thank you again in advance.

Reply by ●November 27, 20122012-11-27

what I'd do is to start with a conventional polyphase interpolate-by-7 FIR filter: y1 = x1 c1 + x2 c8 + x3 c15 + x4 c22 + x5 c29 + ... y2 = x1 c2 + x2 c9 + x3 c16 + x4 c23 + x5 c30 + ... y3 = x1 c3 + x2 c10 + x3 c17 + x4 c24 + x5 c33 + ... then decimate by 8. That is, calculate only y1, y9, y17, y25 etc, and discard the equations in-between. At this point I've got a single-input single-output 7 up 8 down polyphase resampler. Next, take the remaining equations for eight consecutive (decimated) y samples, and implement them in parallel. What remains is to distribute the parallel inputs, a mere formality. This is just a quick "lunch break study", maybe someone else comes up with a better solution.

Reply by ●November 27, 20122012-11-27

Reply by ●November 27, 20122012-11-27

>what I'd do is to start with a conventional polyphase interpolate-by-7FIR>filter: > >y1 = x1 c1 + x2 c8 + x3 c15 + x4 c22 + x5 c29 + ... >y2 = x1 c2 + x2 c9 + x3 c16 + x4 c23 + x5 c30 + ... >y3 = x1 c3 + x2 c10 + x3 c17 + x4 c24 + x5 c33 + ... > >then decimate by 8. That is, calculate only y1, y9, y17, y25 etc, and >discard the equations in-between. > >At this point I've got a single-input single-output 7 up 8 down polyphase >resampler. >Next, take the remaining equations for eight consecutive (decimated) y >samples, and implement them in parallel. What remains is to distributethe>parallel inputs, a mere formality. > >This is just a quick "lunch break study", maybe someone else comes upwith>a better solution. >Good lunch break study - this is precisely how it should be done. Make sure to design your filter with a convenient number of coefficients. -Doug

Reply by ●November 27, 20122012-11-27

Still, for a structure that generates 7 output samples by consuming 8 input samples, it seems more straightforward to design for 7 parallel outputs. You'd get 7 simple filters with fixed coefficients, and have a common clock rate at input and output. What remains to be done for 8 outputs is to shuffle whole samples from 7 to 8 parallel registers at a slightly lower rate. Both approaches will do the same, but I think I'd prefer the second one for implementation. Apparently, this is the approach taken in the paper (haven't read it yet - has to wait until dinner :-)

Reply by ●November 27, 20122012-11-27

On Tue, 27 Nov 2012 04:37:27 -0600, mnentwig wrote:> what I'd do is to start with a conventional polyphase interpolate-by-7 > FIR filter: > > y1 = x1 c1 + x2 c8 + x3 c15 + x4 c22 + x5 c29 + ... y2 = x1 c2 + x2 c9 > + x3 c16 + x4 c23 + x5 c30 + ... y3 = x1 c3 + x2 c10 + x3 c17 + x4 c24 + > x5 c33 + ... > > then decimate by 8. That is, calculate only y1, y9, y17, y25 etc, and > discard the equations in-between. > > At this point I've got a single-input single-output 7 up 8 down > polyphase resampler. > Next, take the remaining equations for eight consecutive (decimated) y > samples, and implement them in parallel. What remains is to distribute > the parallel inputs, a mere formality. > > This is just a quick "lunch break study", maybe someone else comes up > with a better solution.That looks right to me, once I got my morning-impaired brain wrapped around it. Hassans: Don't be surprised that you'll need to save the previous eight samples or perhaps more: that's kind of a requirement for any filtering. Internally you'll probably want a step in your pipeline that has a vector of the current N * 8 samples all lined up and ready to go into whatever the next step in the pipeline is. If the data is going by too fast to be put into a serial stream then even after you get the algorithm ironed out it's still going to be challenging to get the filter working. I foresee a lot of pipelining, a big FPGA, and a lot of picky book-keeping to get the filter to execute fast enough. I strongly suggest that you make sure that you have a very firm grasp of the algorithm you're trying to implement before you start trying to make it work at speed and with the 7:8 decimation in your output clock. I'd probably want to make sure that I had an accurate behavioral representation simulated in the HDL of my choice that was rock-solid and bone-headed (i.e., optimize the code for transparency and readability, with no attempt to make it synthesizable). Then when I'd made the "real" filter I'd make sure to test against the "bone-head" implementation in simulation. Failing an HDL test article, I'd make sure to simulate the filter action in Matlab or Scilab (or Excell or whatever) and test the input/output behavior of the synthesizable model against that. -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com