thanks

good work

There is quantization noise (due to the +1 -1 quantization output) in this simulation. Otherwise would it really be a simulation? This simulation does everything a real SD modulator 1 bit DAC would do except use actual hardware. The LPF gets rid of most of it. The way to minimize quantization noise is by increasing the order of the SDM and/or increasing the over-sampling-rate. If you don’t believe me decimate* the output and try to listen to it.

According to on slide 17:
http://www.digitalsignallabs.com/presentation.pdf

And using OSR, M=10 from above and order, L=1

20log10 ( ((6L+3)/2pi^2L)M^(2L+1) )

The SNR is 53dB this sounds about right, but if someone knows for sure let me know.

* by only throwing away every 10 samples, not using the matlab function “decimate” which throws away samples after runing the data through an FIR LPF. Yes this means the above code is putting the data through an LPF twice. The reason is I did not know the matlab/octave “decimate” procedure also uses an FIR on the data first when I originally coded this.

The noise comes from approximating the signal with a +1 or -1. Any time you throw away information by approximating a signal you introduce noise. The majority of this noise ends up above the frequency range of the original signal. The LPF has a cutoff that eliminates most of thee noise.

What we are simulating here is the output of a Sigma Delta 1-bit DAC. If you were to implement this algorithm here into an FPGA and put a decent RC filter network on the output, you should end up with about the same result as the simulation produces.

The order of the filter is arbitrary, the higher the better in terms of rejecting unwanted high frequency noise. You will also notice that the function “decimate” has an LPF built in so I effectively filter it twice.

oh again once more how do u know that the order of filter is 122?how u decide the order?thx very much.

I use Octave under Ubuntu Linux and it works fine. Both octave and linux are free and GPL. Octave will run under windows(yuck) also. Matlab is $expensive, but more full featured.

You could also just put a sine wave into x by replacing the auload line with:
fs=11000;
x_index=1:.1:1000;
x=sin(x_index);

You may need to tweak fs or x_index length to your needs.

Thanks

The structure for n>=2 keeps the feedback loop on the outside and the quantizer in the same spot. The rest is just a series of the noise shapers.

For SD modulation with orders greater than two, and for some instances of 2nd order modulation, there has to be some weighting of the coefficients. Otherwise you end up with instability. This is where some of that control theory that I never took comes into play. Using heauristical control theory algorithms, one can maximize the coefficients for stability vs. noise in the pass-band.

I have a working SD modulator in C that reads a wav file and puts it out onto the Serial Port using a 4th order SD modulator and the Serial port at 230400 bps. It sounds OK, but when I strip the start/stop bits out with a CPLD FSM it sounds great, like 90-95dB SNR. I have been meaning to post this project. Maybe I will soon. Also, I used a friends matlab controls toolbox for my 4th order coeff’s.