# I have another doubt regarding the same FIR Coefft optimization problem

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#### bmsec

##### Newbie level 6 Plz help, regarding the FIR Coefft optimization problem

The optimum filter coefficients have to be selected iteratively from a coefficient search space.
The maximum allowable deviation of this realized filter from the desired filter is defined as the cost function which is fixed in advance.
The coefficients selectable from the search space will have to lie within a Maximum and a Minimum value, so that above deviation constraint is satisfied.
There is a constraint equation for this purpose.

Summary of the question :
1. The maximum deviation response possible is fixed.(In general notations, this has to be minimized. Here, it is fixed.)
2. The coefficients have to lie in a range of max and min values, to achieve the above constraint.
3. The maximum and minimum allowable values for each coefficient is to be calculated by Mixed Integer Linear Programming.

How to find the coefficient integer value range (Max and Min values) of each coefficient (h1,h2,h3,etc.) ,when the cost function is fixed?

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#### bigdogguru I would be more than happy to do some research for your problem and see if I can come up with any possible solutions.

Give me a day or two to look online and in my library for directions or algorithm to obtain the desired results.

#### bmsec

##### Newbie level 6 Sir,Thank You.
I have a couple of specific questions :

1.
The Constraint equation is

Magnitude[sum{h(m).T(w)} - Hd(w)] must be less than/equal to Delta
where
sum{h(m).T(w)} is the frequency response of the realized filter in current iteration.
Hd(w) is the desired frequency response.

Delta is maximum deviation (Error) allowed.This is fixed in advance for both stop and pass bands.

Now,

sum{h(m).T(w)} : Is it obtained by taking DFT of the coefficients?

2.
Is it possible to rewrite the above equation as

[sum{h(m).T(w)}] less than/equal to [Delta + Hd(w)]

and minimize h(m) for current iteration ?

I would be more than happy to do some research for your problem and see if I can come up with any possible solutions.

Give me a day or two to look online and in my library for directions or algorithm to obtain the desired results.

---------- Post added at 20:13 ---------- Previous post was at 20:09 ----------

Sir, I'm extremely grateful that you agreed to help me. Thank you.

#### bmsec

##### Newbie level 6 Sir, Do I need to clarify my question a little more?
Can you kindly help me in any direction ? Please guide me Sir.
Thanks and Regards.

I would be more than happy to do some research for your problem and see if I can come up with any possible solutions.

Give me a day or two to look online and in my library for directions or algorithm to obtain the desired results.

#### bmsec

##### Newbie level 6 Dear Sir,
Kindly assist me in the implementation. I have certain roadblocks in the MATLAB functions for solving constrained equation as I have mentioned in previous post. Kindly guide me and help me to complete the project. I will be grateful to you.
Thank You
Bharath M S

I would be more than happy to do some research for your problem and see if I can come up with any possible solutions.

Give me a day or two to look online and in my library for directions or algorithm to obtain the desired results.

#### permute The possible issue above is to make sure to include more analysis points than filter coefficients. eg, if you have a 32 tap filter, and use 32 sampling points in the frequency domain, you will get the sinc function as a perfect filter. After all, it is able to exactly match all 32 sampled frequencies. it is not able to match at 33+ sampled frequencies.

• bmsec

### bmsec

Points: 2

#### bmsec

##### Newbie level 6 I'm sorry Sir, I had internet problem in my area, for more than 1 week, so i could not reply. I solved that problem by contacting the author of the paper. Also, I did frequency sampling , at those frequencies, using a simple for loop.

Define step size for the frequencies, Increment the frequency w, from 0 to maximum, in terms of stepsize, and at each
sampled frequency, measure the instantaneous value, by taking DFT at that i and at that w(frequency)
Compare with the desired value at that i and w.
Plot both the curves.

Thanks a lot Sir.
I'll contact you again, if I get any more doubts:grin:
Thank You.
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The possible issue above is to make sure to include more analysis points than filter coefficients. eg, if you have a 32 tap filter, and use 32 sampling points in the frequency domain, you will get the sinc function as a perfect filter. After all, it is able to exactly match all 32 sampled frequencies. it is not able to match at 33+ sampled frequencies.

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