FFT in matlab. and Use Matlab to obtain a clean ECG

1.For x(t)=cos(6t)*sin(4t), inMatlab (a) Apply Euler’s formla to determine the frequencies of x(t).

(b) Plot the magnitude and phase of its Fourier transform. Think about what time interval and duration that you should use. In doing the plots, use frequency for your x-axis instead of index.

(c) Reconstruct x(t) from Euler’s formula in Matlab and also by using ifft.

(d) Compare the original x(t), the reconstructed x(t) ‘s in (b) by plotting the three curves in one plot (use different symbols/colors to distinguish the three). The three should be the same!

2.The file pecg01_noise.mat contains periodic ECG data with noise. Use Matlab to obtain a clean ECG. What are the PR (distance between peaks of P and R waves) and RT intervals? What are the R/P and R/T ratios (magnitude of R wave over P and T waves, respectively)?