How to Compare Two Groups of Signals?

Imagine I have two groups of signals A and B having four and three samples, respectively.

A1 = [1 3 -1 2];
A2 = [1 3 -2 3];
A3 = [1 4 -3 4];
A4 = [2 4 -2 3];

B1 = [2 3 -1 5];
B2 = [2 4 -2 6];
B3 = [2 4 -4 5];

How can I find out whether there is a statistically significant difference between groups A and B?

Answer 1

[the cyclist]

To determine whether these signals are significantly different, you first need to define a null hypothesis that will define the range of typical differences. This generally involves an underlying theoretical model, such as "these samples are all drawn from the a normal distribution with the same parameters".

What is your null hypothesis? If your answer is, "I don't have one", then you cannot do hypothesis testing, or determine statistically significant differences.

[Rightia Rollmann]

My null hypothesis is "these samples are all drawn from the a normal distribution with the same parameters"

and

there is no difference between these two groups of signals.

[the cyclist]

I'm sorry, but that simply cannot be your null hypothesis. You would not get exact integers if you were drawing from a normal. I'm not sure why you would just reflect my words back to me.

Maybe you need to give a more detailed explanation of exactly how you get your A1-A4 and B1-B4 samples, and what you are looking for. With that context, maybe we can help you.

[Rightia Rollmann]

Okay, here’s the more detailed description of my example. Imagine there are speakers A and B and I want to see whether they produce the same output audio or not. In other words, I want to test whether these two speakers are identical or not. I play a certain sound with speaker A for 4 times and record it and therefore I create samples A1, A2, A3, and A4. I also play that certain sound with speaker B for 3 times and create samples B1, B2, and B3. Each sample consists of 4 samples.

A1 = [1 3 -1 2];
A2 = [1 3 -2 3];
A3 = [1 4 -3 4];
A4 = [2 4 -2 3];
B1 = [2 3 -1 5];
B2 = [2 4 -2 6];
B3 = [2 4 -4 5];

[the cyclist]

And what do the four numbers in A1 represent? Four different amplitudes, at four different time points? Why are they always integers, rather than values like 1.63?

Answer 2

[John BG]

When comparing signals this way you could start averaging both signals amplitude this way:

A=[A1;A2;A3;A4];B=[B1;B2;B3];

   mean(A)
   =
            1.25          3.50         -2.00          3.00
   mean(B)
   =
            2.00          3.67         -2.33          5.33

then could check time average

mean(mean(A))
 =
          1.44
 mean(mean(B))
 =
          2.17

that was 1st order statistical all-weather very useful mean, now 2nd order, variance:

var(mean(A))
ans =
          6.18
 var(mean(B))
ans =
         10.85

the more samples the better, the longer the signals the more accurate the measurements

You may also want to see if the signals match a known statistical probability distributions that you may think would fit, for instance normal

fitdist(A,'Normal')

this in turn will give the probability distrition, then you can generate the pdf curve and measure how far the points of the signals are from the probability. The distance of the samples to an expected curve is an error measurement you may find useful

Error Vector Measurements are common in for instance DVB-T or for the case, any IQ signals.

if you find these lines useful would you please mark my answer as Accepted Answer?

To any other reader, if you find this answer of any help, would you please click on the thumbs-up vote link,

thanks in advance for time and attention

John BG

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