You are better of sub sampling the Blue signal so that they both have the same sampling frequency.

what is horizontal axis?

I agree with hossain, you should sub sample the blue signale (use the resample function)

Dear Mojtaba, you can use fractional samling and so reach equal sampling for these different signals. And then divide them by using digital filters whith finite impulse response (FIR filter). FIR filyers have linear phase characteristic and not distort the signal in the bandwidth.

Thank you all,

actually those graphs are based on the recording data from two different data recorders for two different things.

first I used the pwelch function ([psd_A, f_A] = pwelch(fluc_A,[],[],[],f_A_sampling); and [psd_B, f_B] = pwelch(fluc_B,[],[],[],f_B_sampling);) and got their psd separately and plot them in loglog scale. the X axis is the frequency and the y axis is the psd. now I want to find their relation to each other so I want to divide them on each other to find kind of lets say transfer function.

since their sampling frequency and subsequently their dimension is not the same, when I simply divide them to each other I get the error which says "Matrix dimensions must agree".

Dear Mojtaba,

If you want to obtain the transfer function from the orange to blue curve, you need to up-sample the signal represented by the orange curve. In getting the transfer function from the blue to orange, you need yo down-sample the blue one. Both upsampling and downsampling can be simply implemented by calling the MATLAB incline function 'resample'; please refer to the following link on the usage of the function. 

https://au.mathworks.com/help/signal/ref/resample.html

I do have one doubt. One of the signal is sampled in 1250Hz, as you described. However, we can see in your attached figure, the maximum frequency is smaller than 1e3. Any explanation?

You have to use upsampling/downsampling.

Hi all,

Thank you, so should I use the re-sampling function on my original data ( in time domain) before taking psd and after that do the psd calculations?? 

Hello, Mojtaba,

Yes, you should use the 'resample' function on your original data before taking the PSD. Probably best to resample to the higher - 1250 Hz - rate i.e., excluding bandpass sampling,  minimum sampling rate is 2*bandwidth of the signal. Thus, the 1250 Hz sampling rate can accurately sample a signal w/ a maximum frequency of 625 Hz. If you know both signals have bandwidths of interest lower than, or equal to 250 Hz, then you could resample to the lower Fs = 500 Hz rate. Then, as you mention, take the PSD.

You actually have to be a bit careful in how you are interpreting the quantities that you have, i.e., in the case where you have a power spectrum of the input, Sxx, and the output, Syy, when you divide these you actually end up with |H(f)|^2. These are all real quantities. If you have Sxy and Sxx, you obtain the cross power spectral density. In this case Sxy (or, Syx) will be complex valued. You can then obtain H(f), but it too will be complex valued. See, i.e., Bendat & Piersol 'Random Data', or Shanmugan & Breipohl, 'Random Signals'.

Any particular reason that you're not working with just the FFT ? If these are both deterministic signals, the FFT may be a more straight-forward approach.

Regards,

Jim

For a very nice explanation on the various quantities, see

https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-011-introduction-to-communication-control-and-signal-processing-spring-2010/readings/MIT6_011S10_chap10.pdf

The entire section is very well explained, some sections more involved than others. As far as I can glean from your question(s), the primary applicable sections are 10.1 and 10.2.1

Regards,

Jim Whitney

Hi Jim,

Thank you. actually my input is the recorded wind data and my output is the reaction and response of the system. the reason why I am using pwelch function instead just FFT is that this is the common approach in wind engineering. I will try the suggestions and also I will look at the document which you have shared with me.

Thanks,

Mojtaba