Making a formula based on a blood pressure curve

Can anyone help us out with the following problem: We have measured data from a blood pressure signal. With the fft function, we made a fourieranalysis of this signal. Now we want to derive the first four harmonic components from this signal. How do we do this?

Answer 1

[Image Analyst]

The FFT is a bunch of sine waves at different frequencies. To get the first four, wouldn't you just zero out anything at element 5 and beyond?

[Klaske]

Sounds good. Yet we need to have the sinus-functions of the first four harmonic components and then add these up to have a 'reconstrud' signal.

[Image Analyst]

I don't think you need to explicitly get the first 4 time domain signals and add them, unless that's what an instructor is asking for. But I'm pretty sure that the first 4 elements of the FFT would reconstruct to give a pretty smooth and poor representation of the ecg. I think to get it to be flat inbetween the heartbeats you'd have to include a lot more frequencies. But it's easy enough to play around with zeroing out starting from some element, just do

fftSignal = fft(timeDomainSignal);
filteredSignal = fftSignal; % Initialize.
filteredSignal(4:end) = 0; % Keep only 1-4.
reconstructedSignal = ifft(filteredSignal);
plot(reconstructedSignal);

If you do need the individual signals, just do something like

% Get time domain harmonic #1
filteredSignal = zeros(length(fftSignal)); % Initialize
filteredSignal(1) = fftSignal(1); % Change to 2, 3, 4 for other harmonics.
timeDomainHarmonic1 = ifft(filteredSignal);

Then after you have them all, add them

timeDomainHarmonic = timeDomainHarmonic1 + timeDomainHarmonic2 + ...
                     timeDomainHarmonic3 + timeDomainHarmonic4;

If you're looking for ecg algorithms to remove noise, you can look here: http://iris.usc.edu/Vision-Notes/bibliography/medical888.html#Heart%20Analysis,%20ECG,%20Electrocardiogram,%20Other%20Electrical%20Signals though they are probably more imaging oriented than signal oriented. I'm not really an expert in 1D signals.