Re: Scaling FIR output


Wal_P wrote:
> We´re working in a Digital Receiver in FPGA.
> It´s a 12 bits ADC (SNR = 70 db) followed by a 12 bits NCO for
> demodulating. And then we have CIC (R= 32, M=1, N= 5), CFIR (Thanks, R.
> Andraka, your M-code worked very well!!) and 2 stages FIR.
>
> We´re scaling FIR output to keep amplitud the same as input.
>
> The questions are:
>
> 1- After multiplication we have 12+12 bits, Is it necesary to keep all of
> them?

The short, naive answer is: No. You only need the 12 most significant
bits
of the product. This introduces some inaccuarcy in the computed
numbers,
as well as problems when multiplying a very large number with a very
small
number.

A more elaborate answer is that this inaccuracy and these problems
is the price you have to pay when dealing with fixed-point fixed-word
length
arithmetic.

> 2- How do we choose the word length for FIR filter whitout affecting the
> SNR of the input signal?

Uhm... what do you mean by *input* signal? Input to the FIR filter? I
can't see
that anything you do with the FIR filter can affect the signal that is
applied to it?

Assuming you actually meant tho say "the SNR of the *output* signal
[from
the FIR filter]", the simple answer is that the more bits/longer
wordlength,
the lower the SNR caused by numerical inaccuracies on the output. Of
course,
longer words means a more expensive DSP processor. So you need to find
out what wordlength is "long enough" for your application, and check if
you
can afford it, either in terms of $$ or in terms of gates in the FPGA.

More practically speaking, I would assume one would try to find out the

typical SNR of the recieved signal, and aim for a wordlength that gives

a "somewhat" lower[*] SNR for the quantization noise.

Rune

[*] The word "somewhat" in hyphens because I suspect this is where one
would be able to separate good engineers from not quite as good
ones.
Choose a word length that gives acceptable performance of the
reciever,
while not using overly expensive parts. Not necessarily an easy task.

.

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