Why my filter output is not accurate?

Question

I am simulating a digital filter, which is 4-stage.

Stages are:

1. CIC
2. half-band
3. OSR
4. 128

Input is 4 bits and output is 24 bits. I am confused about the 24 bits output.

I use MATLAB to generate a 4 bits signed sinosoid input (using SD tool), and simulated with modelsim. So the output should be also a sinosoid. The issue is the output only contains 4 different data.

For 24 bits output, shouldn't we get a 2^24-1 different data? What's the reason for this? Is it due to internal bit width?

Answer 1

Forgive my lack of filter knowledge, but does one of the filter stages interpolate between the input values? If not, then you're only going to get a maximum of 2^4 output values (based on the input resolution), regardless of your output resolution. Just because you output to 24-bit doesn't mean you're going to have 2^24 values... imagine running a digital square wave into a D->A converter. You have all the output resolution in the world, but you still only have 2 values.

Answer 2

I'm not familiar with Modelsim, and I don't understand the filter terminology you used, but...Are your filters linear systems? If so, an input at a given frequency will cause an output at the same frequency, though possibly different amplitude and phase. If your input signal is a single tone, sampled such that there are four values per cycle, the output will still have four values per cycle. Unless one of the stages performs sample rate conversion the system is behaving as expected. As as Donnie DeBoer pointed out, the word width of the calculation doesn't matter as long as it can represent the four values of the input.

Again, I am not familiar with the particulars of your system so if one of the stages does indeed perform sample rate conversion, this doesn't apply.

Answer 3

Its actually pretty simple:

1. Even though you have 4 bits of input, your filter coefficients may be more than 4 bits.
2. Every math stage you do adds bits. If you add two 4-bit values, the answer is a 5 bit number, so that adding 0xf and 0xf doesn't overflow. When you multiply two 4-bit values, you actually need 8 bits of output to hold the answer without the possibility of overflow. By the time all the math is done, your 4-bit input apparently needs 24-bits to hold the maximum possible output.