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how to decide the percision of the fixed point ?

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boeysue

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When we use filter in fixed point,how to decide the multiplicand and adder and output format in matlab to reach our performance?Thanks for help?
 

Hi boeysue,


Supose you have to implement a digital filter with coefficents:

5 2.5 0.625

Since you have a fixed point processor you must use only integer numbers.

First step is to divide coeficients by the biggest number (step called normalization of the coeficients)

Normalized coeficients are (dividing each coeficiient by 5):

1 0.5 0.125

for an 8 bit procesor you can represent those numbers in binary like:

1=1111 1111 b

0.5=1000 0000 b

0.125=0010 000 b

Now you can put an imaginary decimal point everywhere you like, for instance:

1=1111 . 0000 b

0.5=1000 . 0000 b

0.125=0010 . 0000 b


Observe that precision of 1 coeficient had reduced, but you gained 4 decimal places to represent fractional numbers in the result.
 

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    boeysue

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>>Now you can put an imaginary decimal point everywhere you like, for instance:
>>1=1111 . 0000 b
>>0.5=1000 . 0000 b
>>0.125=0010 . 0000 b
>>Observe that precision of 1 coeficient had reduced, but you gained 4 decimal >>places to represent fractional numbers in the result.
Do you mean that the lost 4 bit can use the multiplicant and adder to compresent it?

Added after 21 seconds:

>>Now you can put an imaginary decimal point everywhere you like, for instance:
>>1=1111 . 0000 b
>>0.5=1000 . 0000 b
>>0.125=0010 . 0000 b
>>Observe that precision of 1 coeficient had reduced, but you gained 4 decimal >>places to represent fractional numbers in the result.
Do you mean that the lost 4 bit can use the multiplicant and adder to compresent it?
 

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