Sampling and Aliasing.
1) You sample a known signal of equation x(t)=3 cos(2 π 4425 t) with a sampling rate of 3000 Hz. What signal will you get after reconstructing to continuous time (assume perfect interpolation of a discrete time signal).
2) A continuous time signal produces the absolute magnitude Fourier transform as shown below. If this were sampled at 400 Hz and reconstructed to continuous time plot the absolute magnitude Fourier transform of this signal
3) A freshly graduated engineer is working on his first project and remembers to put an analog low pass filter in his circuit before sampling at a rate of 1500 Hz. He decides to use a first order Butterworth filter with corner frequency of 750 Hz to do this. The signal he is sampling is known to have a significant unwanted signal at around 800 Hz. Will his boss be happy or not? Please explain why.
4) Two medical grade signals are being sampled by different machines. One is sampling blood oxygen saturation at a rate of 25 Hz with proper alias filters. The second is sampling the heart rate ECG signal at 100 Hz. The fft of the ECG signal is shown below. The highest frequency in the ECG signal that is important is the 30 Hz spike shown. Your boss asks you to synchronize the data in time so that they are both at the same sample rate. It is up to you whether you interpolate or decimate. Describe a method that will get both signals sampled at the same rate with no issues due to aliasing.
