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Resources for Farrow/Transpose farrow filter design.

Started by umeshdeshmukh 11 months ago4 replieslatest reply 11 months ago244 views

Hi, I want to design transpose farrow filter for sample rate conversion. There are some blogs explaining how it works on internet and on dsprelated.com as well, but I found only one with detailed design process and matlab code (link). I don't have matlab optimization toolbox, therefore I implemented matlab code from the document in python, scipy.optimize.linprog is used to solve linear program problem. To check my implementation I used example 1 from Matlab code section of the document but the outputs are not matching. I debugged my python implementation and made sure that the input matrix, vectors to a linprog

matches to the matlab version. can you please point me to any more resources/examples/tutorial/code for

farrow/transpose farrow filter design, filter design using linear programming etc.

Thanks,

Umesh. 

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Reply by neiroberAugust 10, 2023

Umesh,

A good reference on piecewise polynomial interpolators, including Farrow, is Digitial Communications, a Discrete-Time Approach, by Michael Rice, section 8.4.2.

regards,

Neil



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Reply by umeshdeshmukhAugust 10, 2023

Thank you, I will take a look at this.

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Reply by kazAugust 10, 2023

If you mean fractional delay rather than sample rate change. This matlab model may be easier to understand as it applies each polyphase separately then adds up as per second order transpose structure. The function "filter" is based on convolution:

h = [1/2,-1/2,0; -1,0,1; 1/2,1/2,0]; %coefficients, 2nd order Farrow

d = 0.7; %delay

x = randn(1,1000); %random input

y = (filter(h(:,1),1,x) * d + filter(h(:,2),1,x)) * d + filter(h(:,3),1,x);

plot(x,'.-'); hold;

plot(y,'r.-');


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Reply by umeshdeshmukhAugust 10, 2023

Not a fractional delay, Input sampling frequency is changing and output sampling frequency remains constant. Output sample rate always less than input sample rate, net down-sampling.