A stationary random displacement signal was digitised at 64 samples a second and analysed to obtain an auto-spectral density. The signal was calibrated in mm units. The frame size for the Fast Fourier Transform (FFT) was 2048 data values. Fifty frames were averaged to obtain the final result but over-lap averaging of 25% was used. Due to a malfunction the displacement transducer output included a very large 50 Hz electrical noise component. This was not completely removed by the anti-aliasing filters prior to the analog-to-digital conversion process.
(a) What are the units of the y-axis of the auto-spectral density if the x-axis is in Hz?
(b) What approximately would be the cut-off frequency of the anti-aliasing filters?
(c) What is the bandwidth of the analysis?
(d) What is the total length of signal analysed to obtain the auto-spectral density?
(e) At what frequency would the 50 Hz noise signal appear on the auto-spectral density?
(f) How would you obtain the auto-spectral density for the velocity from the auto-spectral density of the displacement?