Deriving PDF from a given signal without using the hist() function?

Hello,

       I'm newbie at this and am enjoyably although a bit painfully trying to work my way around Matlab. As my question implies I have a signal and I would like to derive it's PDF function numerically without using the hist () function ? I looked in the documentation that it would be:

    p1=pdf('name',X,A)  or extra B,C depending if we have 1 or three parameters. Although I read the documentation I don't understand what X stands for (what I should replace it with?). From what I understand if it's for example normal pdf it would be:

    p1=(pdf('name', X, A, B), being A the mean and B the standart derivation and X I don't know.  I really don't understand how do I relate the pdf function with the signal I generated on matlab???

   Hope I'm making sense and someone is able to help.

   Thank you very much

   Catarina

Answer 1

[bym]

I am not sure I understand, but take a look at:

doc ksdensity

[David Young]

catarina: I'm very puzzled. If you can't use hist(), how is that ksdensity() is a good solution?

[King Fisher]

Thanks proecsm ! you helped in solving my issue as well !

Answer 2

[David Young]

The pdf function is not useful for this. It generates the theoretical PDF for a named distribution, but does not estimate an empirical PDF from data.

You are probably being asked to write code that does what hist does. This involves taking each element of the signal vector, working out the index of the bin it falls into, and incrementing an element of a histogram vector. To get an estimated PDF, you'd finally normalise the counts in the histogram vector.

You can do this with loops, or using MATLAB's vectorised style of programming. The essential ideas are the same in both cases, but vectorised code is more compact and often somewhat more efficient.

[catarina]

Hi David,

Thank you for your help. I don't think i explained myself very well. All I'm given is the signal function e.g : x(t)=4-cos(2*pi*f*t) where f=2500hz, I'm told to generate the signal and numerically find the PDF, CDF and mean without using the hist() function. Don't think I can do what you were telling me with the information I have, although I'm not sure???? Any more suggestion??

Thank you

Catarina

[David Young]

Yes, my answer still applies. You are being asked to generate some synthetic data, and then estimate some results from it. So the first part is to generate the signal numerically, which in MATLAB can be done like this:

f = 2500;

deltaT = 0.0001;

Tmax = 0.01;

t = 0:deltaT:Tmax;

x = 4-cos(2*pi*f*t);

Here, I've just made up values for deltaT (the time increment between samples) and Tmax (the duration of the signal). As you can see, it's a matter of getting a vector of time values, and then applying the formula you were given to it.

Now you have x, your "data", from which you can estimate parameters numerically. For example, you can get the signal mean with

mean(x)

The fact that you are asked not to use the hist function for the PDF confirms, I think, that you are expected to write code that does roughly the same as hist. This involves counting how many values of x occur in a set of ranges. One approach: see what happens when you call hist(x), understand how that relates to the PDF, and then write code to produce the same results.

[catarina]

Hi David,

Thank you so much for your help. Will try what you told me. Will let you know how it goes. Happy New Year....

Catarina

[catarina]

Hi David (and other people that might be able to help),

I'm still having problems in deriving the PDF without the hist() function but I think is because I'm stuck in how to code certain stuff. Would you able to look at my script and if possible give me some tips? I explained my doubts in the script.

Here is my script:

%Estimating PDF numerically without using hist() function

%Dividing amplitude range into M=60 segments

delta=20 %Amplitude range

n=0:1:M-1;

An=-10+n*(delta/M);

%sampling the signal

%Time points

N=1024; %(number of samples)

j=0:1:N-1;

T=1; %(number of cycles for tis problem T=1)

tj=j*(T/N)

%function points

yj=10*sin(2*pi*tj);

%counting number of samples falling in each segment:

%by constructing a 2D array with elements defined as:

%fnj={1, if An<=yj<=An+1,0 otherwise - I'm not being able to represent

%this statement in matlab, I tried using if statements

%but keeps giving me an error

%Counting the number of samples Fn in amplitude segment number n as:

% N-1

% Fn=sigma(fnj) -not able to represent this in matlab code

% j=0

%Now plot Fn agains An - can't do this because of my previous the doubts

Cheers,

Catarina

[Walter Roberson]

No point debugging this in two Questions. See the answer in your newer Question on this point, http://www.mathworks.com/matlabcentral/answers/27188-estimating-pdf-numerically-without-using-hist-function

Answer 3

[Peter Perkins]

Catarina, the pdf function (I assume this is the one in the Statistics Toolbox) evaluates a known PDF at a set of points. That isn't what you want, at least initially.

If you have a set of data, then I think what you're asking for is a way to estimate their PDF. For a normal distribution, that's the normfit function, for other distributions there are other corresponding functions. Once, you have estimated the parameters of the distribution you want to use, then you can use the pdf function to plot the PDF over some range. There is also the ksdensity function, which creates a non-parametric estimate.

You might find it easier to use the fitdist function, and even easier still to use dfittool, which lets you do all this using a GUI.

Hope this helps.

[catarina]

Hello Peter,

Thank you for your help. I understood you explanations but I don't have data, at least the data I think you referring to. All I have is the signal function e.g : x(t)=4-cos(2*pi*f*t) where f=2500hz, I'm told to generate the signal and numerically find the PDF, CDF and mean without using the hist() function. I'm so confused, I really don't understand how to do this with the signal I'm given. Any more ideas?

Thanks again.

Catarina

[David Young]

Peter: I suspect the fact that hist() is mentioned is an indication that the empirical PDF based on the histogram is required, not a fit to a specific model. Since hist() is forbidden, and the object is to become familiar with MATLAB rather than analyse some real data, I doubt that ksdensity() will be the right kind of answer.

[King Fisher]

u r right ! david !