How do I write MATLAB code for a 1 bit DAC?

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Sharada Reddy 2017-1-20

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编辑： MathWorks Support Team 2021-6-17

I am doing my final year project where I am struck with the 1 bit Digital to Analog Converter block. I want to convert my Digital 1 bit pulse signal into an analog sinusoidal signal. Can anybody tell me how to write1 the MATLAB code to do it? Even the basic command syntax is enough. Thank you.

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Walter Roberson 2017-1-25

在 MATLAB Online 中打开

It appears to me that it cannot be converted using a 1-bit DAC.

If it could be converted with a 1 bit DAC, then whether the analog signal is above 0 or not should depend exactly to whether the digital is above 0 or not, or else should depend upon it in a simple repeating pattern. For example one could imagine that the analog signal being above 0 should be in agreement with the digital for the first half of a cycle of period 2, and should be exactly opposite it for the second half of the cycle of period 2. So if you use

ydigital = digital signal
yanalog = analog signal
ydr = (yanalog > 0) * 2 - 1;   %y reconstructed
seq = ydigital == ydr;
ff_seq = fft(seq);
ff_seq(1) = 0;
plot(abs(ff_seq))

then you would expect to see a simple plot with a single frequency peak corresponding to the analog-to-digital concurrence period. But you do not: you see lots of peaks, none of which is clearly dominant, and it is not a "signal and overtones" matter either.

We have to conclude from this that the analog signal is not generated by the principle of being the same polarity as the digital signal, and not generated by the principle of being same or opposite polarity in short pattern. This leads us to the conclusion that the analog signal must have more than 1 bit of state and so cannot be generated by a 1 bit DAC.

Walter Roberson 2017-2-7

Your signal generator outputs signals only, except for the command inputs that tell it what signal to output. Sending the commands to it over optical channel would not appear to be useful ? It would seem more likely to me that you want to connect to your signal generator as usual but have it somehow output an optical signal ?

You need a digital or electrical signal to control voltages to one or more LED in order to have them transmit information as light. You also need one or more optical receivers to receive the light and turn it into an analog signal, and you need some kind of high speed analog to digital device to be able to convert the electrical signal (from optical) to digital form that can be read in by MATLAB. (You might be able to find direct optical to digital devices without having to go through a specific analog to digital step.) Getting digital input device that works fast enough might not be easy.

Your MGX can handle up to 6 output channels. If you do not have more than 6 LED then you could potentially take the outputs of the MGX channels and connect them to LEDs fairly directly, perhaps with some resistors; possibly with an induction coil as well.

It is not clear to me, though, that the MGX is doing anything useful for you, compared to just using a standard digital to analog device. The MGX might perhaps be much faster than most digital to analog devices, but really to take advantage of faster you need to keep the data channel filled, which is going to be difficult. The MGX would be most useful in creating a repeated signal for debugging your receiver portion. Debug your receiver first and then use the receiver to debug the transition.

Walter Roberson 2017-2-7

You wrote "The signal generator has will process electrical signal.. but i want to use optical channel using LED"

The signal generator "process electrical signal" only as command input, telling it what to generate. Are you asking that an optical connection be used between MATLAB and the signal generator to tell the signal generator what to output?

If what you want is a normal connection between MATLAB and the signal generator, and you want to convert the electrical output of the signal generator into optical signals, then you have choices. If you do not need to drive more than 6 LED, then one choice is to simply wire the output signals of the signal generator to the LEDs, just with enough resistors to prevent the voltage of the signal generator output from exploding the LEDs. Just attach a wire to the signal generator output, and attach the wire to a breadboard, add some resistors, and connect the LEDs.

But then you start talking about "without physical LED and MGX". For that you need simulated optical, which is what I was talking about in http://www.mathworks.com/matlabcentral/answers/321197-how-do-i-write-matlab-code-for-a-1-bit-dac#comment_426548. You need a program that models the characteristics of light in some medium, including diffraction and reflection and the way that different frequencies of light travel at different speeds in ways related to the index of refraction. If you are simulating over any significant distance in air, you also need to model in temperature differences (light refracts near temperature boundaries) and you might also need to model dust (which is going to scatter the light, but the way it scatters the light is going to depend upon the size of the dust and possibly even the composition of the dust.)

You might also need to model the activation of LEDs, whether they turn on strictly according to a threshold voltage, whether they turn off at the same voltage or a lower one, whether brightness varies with current, whether shape of the pulse matters to how the LED produces light.

Sharada Reddy 2017-2-21

编辑：Sharada Reddy 2017-2-21

My digital data is for instance 101011101. How should I convert it into analog signal? Do you have any MATLAB code (not Simulink) that can convert digital data into analog? I have searched a lot and all gave ADC code only and none DAC. Hope u can give a sample code or logic that will convert digital into analog. The above code uses ,fig i dont have GUI output. I have a normal digital output in terms of 0 and 1. In accordance to your previous comment :"The power of a signal is the sum of the absolute squares of its time-domain samples divided by the signal length, or, equivalently, the square of its RMS level" the power digital signal will be 1 as it contains only 0 and 1. which is of no use to my project. could you please give a valid dac code?

Walter Roberson 2017-2-21

You cannot convert your digital data into analog signal without using hardware to do so. You can at most create simulated analog signals. Which is what we have been discussing.

The digital data you have is nice and clean. There is no point post filtering it and so on. Your simulation of the transport layer would be useless without some distortion of the signal.

But how should be simulate distortion of the signal reasonably accurately? Well, I posted links to File Exchange contributions that allow detailed simulation of optical signal distortion. You said that was too complicated.

So I went back to the GUI output you posted. You posted it in https://www.mathworks.com/matlabcentral/answers/321197-how-do-i-write-matlab-code-for-a-1-bit-dac#comment_423138 . And I used that as a template for how your distortion should look.

This is not a matter of you going through a graphical output and reading off the graph and so on: you already posted representative readings, and I showed you how to use those representative readings to calculate parameters that you can use from now on as your simulated distortion function. Provided, that is, that you transmit in batches of 272 samples.

"the power digital signal will be 1 as it contains only 0 and 1"

First of all, that will not be true for the (simulated) distorted signal: it will have a range of values.

Secondly: your digital signals (1 and 0) are being ideally mapped into +1 to -1. The squares of +1 and -1 are both +1, so Yes, the ideal is constant power. However, you asked for half sine waves, not for square waves, and sine waves take time to transition between +1 and -1.

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MathWorks Support Team 2021-6-17

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编辑：MathWorks Support Team 2021-6-17

在 MATLAB Online 中打开

When you go to convert your 1-bit digital signal to an analog signal using an ideal DAC on [-1, 1], you will get the same square wave signal out of the DAC that you put in. This is because the analog signal only changes when the digital one does, and their amplitudes and biases are the same. Any samples not corresponding to a digital value change would inherit their value from the most recent sample that did.

How Do We Make an Ideal DAC in MATLAB?

Since we can’t work with truly continuous signals, the simplest method to approximate them is to use a time step size that is small relative to your digital time step size. You can use

xq = interp1(t, x, tq, ‘previous’)

as an ideal DAC, given digital sampling points t and “analog” sampling points tq. Once in the new higher sample rate you can low-pass filter, add noise, etc. until the response sufficiently represents your device. This is, however, inefficient, due to the sample points spread all over a square wave instead of being concentrated at the transitions.

How Do We Do This More Efficiently, Sample Timing-Wise?

To get efficiently placed sample points, use Simulink®. The solver will take care of placing sample points for you; an ideal DAC therefore would be the gain and bias required to change from the digital scale to the analog scale. A ZOH (Zero-Order Hold) block will keep the sample rate on the digital side constant if placed between it and the analog side, and Gain and/or Bias blocks can handle the amplitude conversion between the digital and analog realms.

Non-ideal DAC Models with Impairments

Everything I said above assumes you, like the original asker, want an ideal DAC as fast as possible. If you want to model the effects a practical DAC would have on your system a ZOH and/or Gain block will not suffice. The Mixed-Signal Blockset™ contains a Binary Weighted DAC block, which models offset error, gain error and settling time. If you want to model stochastic noise impairments (thermal, environmental, etc.), Simulink offers a selection of configurable random sources in the standard library.