*Cross correlation and Fourier transform. of signal
*Curve fitting
The original signals show below (as attached in email) shows surface waves propagating in material A. The signals are 1 mm, 2 mm, 3 mm, 4 mm, 5 mm and 6mm from the wave resource. The sample frequency is 100 MHz and 1000 points are collected for each signal.
Please try the following:
1) FFT power spectrum for each of the signal. What is the frequency resolution?
2) Tell what is the frequency bandwidth for each signal if the stop band is -20 dB?
3) What is the time gap between each surface wave signal (use cross correlation to find it out)?
4) What is the average velocity of surface wave?
5) Based on the Equation if we assume density is 1100 kg/m3 and Poisson’s ratio is 0.45, what is the Young’s modulus of this material?
6) Use the similar method to calculate the SAW velocity of Material B (data 2). The signals are 4 mm, 6 mm, 8 mm, 10 mm, 12 mm and 14 mm away from the wave resource. The sample frequency is 91.2 kHz and 256 points are collected for each signal.
7) One of the materials is agar and one is Aluminium. From the analysis you did before, identify the correct material to Material A (data 1) and material B (data 2) and explain.
8) Each signal has some longitudinal components (see figure below the blue arrows), how this longitudinal wave component attenuated with the distance it travelled? Find the attenuation curve and using fitting technique to find out the physics it follows?
