about vhdl code for cic interpolation filter

according to given equation :for decimator, last comb output bits = 9 * log2(8*1) + 23 = 50 bits

and it says, the same should be used at each comb or integrator stage. Leave truncation to final output.

for interpolator:

last stage = 23 + 9 -1 = 31 bits

and stage before last requires 23+8-1 = 30 bits and so on

--- Quote Start ---

according to given equation :for decimator, last comb output bits = 9 * log2(8*1) + 23 = 50 bits

and it says, the same should be used at each comb or integrator stage. Leave truncation to final output.

for interpolator:

last stage = 23 + 9 -1 = 31 bits

and stage before last requires 23+8-1 = 30 bits and so on

--- Quote End ---

whether this increase in bits should be applied at each stage of comb and integrator section or only at end of each stage of comb section or only at end of each stage of integrator section

--- Quote Start ---

For interpolating CIC I assume (from the wording of the document) that it applies to each stage(be it comb or integrator). You try it and tell us.

--- Quote End ---

After further work it turned out that my last statement needs correction.

The best thing is run this matlab program and read (d):

Bin = 23; %input width

N = 9; %stages of comb or integrator

M = 1; %differential delay

R = 8; %interpolation rate

%cic decimator at any stage

Bout = N * log2(R*M) + Bin;

%cic interpolator per ith stage

%stages 1~N

for i = 1:N

G = 2^i;

Bout = Bin + log2(G);

d(i) = Bout;

end

%N+1 ~ 2N stages

for i = N+1:N*2

G = (2^(2*N-1)*(R*M)^(i-N))/R;

Bout = Bin + log2(G);

d(i) = Bout;

end

for i = 1:N*2

fprintf('%i %i\r',i,d(i));

end

--- Quote Start ---

After further work it turned out that my last statement needs correction.

The best thing is run this matlab program and read (d):

Bin = 23; %input width

N = 9; %stages of comb or integrator

M = 1; %differential delay

R = 8; %interpolation rate

%cic decimator at any stage

Bout = N * log2(R*M) + Bin;

%cic interpolator per ith stage

%stages 1~N

for i = 1:N

G = 2^i;

Bout = Bin + log2(G);

d(i) = Bout;

end

%N+1 ~ 2N stages

for i = N+1:N*2

G = (2^(2*N-1)*(R*M)^(i-N))/R;

Bout = Bin + log2(G);

d(i) = Bout;

end

for i = 1:N*2

fprintf('%i %i\r',i,d(i));

end

--- Quote End ---

after checking the matlab code above the value of d is as below

1 24

2 25

3 26

4 27

5 28

6 29

7 30

8 31

9 32

10 40

11 43

12 46

13 49

14 52

15 55

16 58

17 61

18 64

Now my question is with 23 bit input data how to write vhdl code so that the ouput data width is 24 and follows.Since addition of 2 23 bit input data as shown in the comb section of the cic interpolation is 23 bit data and if i specify output data widthto be 24 there will be syntax error while synthesizing the vhdl code that datatypes are not matching.Can you give solution for this problem?

you need sign extend:

data_24 <= std_logic_vector(resize(signed(data_23)),24) + resize(signed(data_23b)),24);

--- Quote Start ---

After further work it turned out that my last statement needs correction.

The best thing is run this matlab program and read (d):

--- Quote End ---

The quoted paper doesn't explain the bit growth exactly, neither for decimation nor interpolation filters. Besides the Matlab tool, I would always refer to the original Hogenauer paper introducing CIC filters. Bit growth in the comb section of interploation filters is in fact simple, one bit per stage.

--- Quote Start ---

The quoted paper doesn't explain the bit growth exactly, neither for decimation nor interpolation filters. Besides the Matlab tool, I would always refer to the original Hogenauer paper introducing CIC filters. Bit growth in the comb section of interploation filters is in fact simple, one bit per stage.

--- Quote End ---

Thanks FvM.

I assume the equations for bit growth given in attached doc look too involved to be wrongly typed from original source(Hogenauer's).

But I did notice discrepancy of last equation when applied to i = N as Bout = Bin + N -1

Anyway do you have access to Hogenauer's doc? or do you know where those given equations go wrong.

I know Hogenauer also included method for register pruning to reduce bit growth by distributing quantisation noise across stages. Naturally too involved and too specialised corner and may be unwarranted with FPGAs applications.

--- Quote Start ---

Thanks FvM.

I assume the equations for bit growth given in attached doc look too involved to be wrongly typed from original source(Hogenauer's).

But I did notice discrepancy of last equation when applied to i = N as Bout = Bin + N -1

Anyway do you have access to Hogenauer's doc? or do you know where those given equations go wrong.

I know Hogenauer also included method for register pruning to reduce bit growth by distributing quantisation noise across stages. Naturally too involved and too specialised corner and may be unwarranted with FPGAs applications.

--- Quote End ---

I have got the Hogenauer's doc.i am attaching that document .In that observe cic interpolation filter design.In that observe register growth equation and design example.with the matlab code as below

Bin = 8;

%input width

N = 4;

%stages of comb or integrator

M = 2;

%differential delay

R = 512;

%interpolation rate

%cic decimator at any stage

Bout = N * log2(R*M) + Bin;

%cic interpolator per ith stage

%stages 1~N

for i = 1:N

G = 2^i;

Bout =( Bin + log2(G));

d(i) = Bout;

end

%N+1 ~ 2N stages

for i = N+1:N*2

G = (2^(2*N-1)*(R*M)^(i-N))/R;

Bout =( Bin + log2(G));

d(i) = Bout;

end

for

i = 1:N*2

fprintf(

'%i %i\r',i,d(i));

end

I got the bout values

1 9

2 10

3 11

4 12

5 16

6 26

7 36

8 46

which is not matching the values

9,10, 11,12, 12,21,30, and 39, respectively,which is not equal to the got values.is there any mistake in the matlab code?

and where did you attach the doc to?

I tried my luck numbers and here I managed to get expected values:

Bin = 8; %input width

N = 4; %stages of comb or integrator

M = 2; %differential delay

R = 512; %interpolation rate

%cic decimator at any stage

Bout = N * log2(R*M) + Bin;

%cic interpolator per ith stage

%stages 1~N

for i = 1:N

G = 2^i;

Bout = Bin + log2(G);

d(i) = Bout;

end

%N+1 ~ 2N stages

for i = N+1:N*2

G = 2^(2*N-1)*(R*M)^(i-N)/R;

Bout = Bin + log2(G) - i + 1;

d(i) = Bout;

end

for i = 1:N*2

fprintf('%i %i\r',i,d(i));

end