How to compute the mean amplitude of each frequency across trials?

This is probably so easy but I can't get it. After doing a fourier transform (the data matrix is trials x time so I think I do a fft in the column dimension), I first compute (for each trial) the amplitude of each frequency based on the Fourier transformed data, what I've done so far is below. It gives me a 1x450 vector.

Data=fft(data,[],2);
Dataamp = abs(Data)/n;
Dataamp = 2*Dataamp(1:n_cutoff); % scales the amps and cuts off at Nyquist
Dataamp(1) = Dataamp(1)/2; % not to scale the first term

But I now need to calculate (and later plot) the mean amplitude of each frequency across trials and would have thought I need to get the mean across each row, as in a column vector, but besides using the mean function (which only gives a single value as Dataamp is now a vector and I need multiple values) I don't know how else to think about it / go about it? i.e. what am I doing wrong?

Answer 1

[David Goodmanson]

Hi Becky,

I assume you have trials changing down, time changing across (each row is a trial as a function of time). The first two lines are good, but on then since you want to still preserve the rows, take a look at

Dataamp = 2*Dataamp(:,1:n_cutoff) % scales the amps and cuts off at Nyquist
Dataamp(:,1) = Dataamp(:,1)/2; % not to scale the first term
Meanamp = mean(Dataamp);

which produces a row vector of mean(abs(amplitude)).

If n is odd this is all right but if n is even I don't believe you want to double the nyquist term, so you should test for n even and if so then do

Dataamp(:,n_cutoff) = Dataamp(:,n_cutoff)/2; % not nyquist either

[Becky CNS]

Hi David,

Thanks for this! The (:,1) did the job perfectly.

I have one issue though:

meanAmp=mean(Dataamp);

gives a row vector of mean of each column, is that what I want when I need mean frequency amplitudes across trials? I would have thought I need instead a 450x1 column vector containing averages of the amplitudes across trials?

I think my confusion is in what this gives

Dataamp = abs(Data)/n;

Is it trials x amplitude or trials x frequencies or frequencies x amplitude values?

[David Goodmanson]

Hi Becky,

I'm assuming as before that you have trials changing down, time changing across. So a matrix that is, say, 100 x 400 has 100 trials, each trial being a row vector with 400 samples in time,is that correct? If so, a picture being worth 2^10 words:

       time --->

tri-   d d d d d d d d
als    d d d d d d d d
 |     d d d d d d d d
 |     d d d d d d d d
\/     d d d d d d d d

When you take the fft along the rows as you did, you get

       frequency --->

tri-   d d d d d d d d
als    d d d d d d d d
|      d d d d d d d d
|      d d d d d d d d
\/     d d d d d d d d

Then to get the mean at each frequency you take the mean down the columns to get

                   frequency --->

mean over trials   d d d d d d d d

[Becky CNS]

Ahhh yes, thank you!