Random square wave of varying individual pulse width but fixed total duration

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Deepayan Bhadra 2022-5-30

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https://ww2.mathworks.cn/matlabcentral/answers/1729985-random-square-wave-of-varying-individual-pulse-width-but-fixed-total-duration

评论： Ishaan Mehta 2022-6-25

The problem I have at hand is as follows:

A square wave (total duration: a sec) which can be (randomly) 1 for either 33 ms or 66 ms but the sum of the 1-duration is fixed (a x b x 33ms). It's 0 elsewhere. b is a fixed parameter.

I'm referring to this existing solution but the sum part in my problem is throwing me off:

https://nl.mathworks.com/matlabcentral/answers/80755-how-to-generate-a-square-wave-with-random-normal-distributed-period-and-pulse-width

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Deepayan Bhadra 2022-5-30

@Sam Chak: Thanks for the clarification. I framed the title incorrectly. Corrected. Hopefully, it's clear now.

Ishaan Mehta 2022-6-25

在 MATLAB Online 中打开

Hey Deepyan

I understand that you are trying to generate square waves with following characteristics:

total time duration: a seconds
for each second, the duration of 1's can be b*0.033 seconds only
the duration of each pulse must be either 0.033s of 0.066s only

I assume there is no restriction that a given pulse must start and end in the same second.

If my understanding and assumptions are valid, here is a code to generate such random waves:

a = 4;
b = 30;
t = 0:0.001:a;
y = zeros(1, a*1000 +1);
for i = 1:a
    pulsesLeftForCurrentSecond = b;
    j = (i-1)*1000 +1;
    while j <= i*1000
        if pulsesLeftForCurrentSecond <= 0
            break;
        end
        
        % pulseSpacing should decrease with an increase in value of b
        pulseSpacing = min([0.99 (0.92 + (16 - b) * 0.01)]);
        if(rand(1) > pulseSpacing) 
            random1or2 = randi([1 2]);
            if pulsesLeftForCurrentSecond <= 1
                random1or2 = 1;
            end
          
            pulseWidth = random1or2 * 33;
            y(j:j+pulseWidth-1) = 1;
            j = j + pulseWidth -1;
            pulsesLeftForCurrentSecond = pulsesLeftForCurrentSecond - random1or2;
        end
        j = j+1;
    end
    pulsesLeftForCurrentSecond
end
y(a * 1000+2: end) = [];
plot(t,y);
ylim([-1 2]);

Please note that due to the random nature of the waves, sometimes the last pulse might end up exceeding the 'a' second duration, in such cases rest of the portion is truncated and the sum of 1-duration would be less than a*b*0.033s. But such cases are extremely rare and occur only if b > 27.

(I understand that the maximum value of b can be 31 to satisfy a*b*33ms < a*1000ms)

I hope this helps while we wait for a more reliable solution.

Ishaan

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Random square wave of varying individual pulse width but fixed total duration

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Random square wave of varying individual pulse width but fixed total duration

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