Chapter 15, Problem 15.39P

Matched filter in the frequency domain (1.5) (a) Consider the signal s(t) in 3(c). Assuming that the unit of time is a millisecond and the desired frequency resolution is 1 Hz, use the function contFT to compute and plot |S(f). (b) Use the function contFT to compute and plot the magnitude of the Fourier trans- form of the convolution s * SMF numerically computed in 3(d). Also plot for comparison |S(f)12, using the output of 5(a). The two plots should match. (c) Plot the phase of the Fourier transform of s✶ SMF obtained in 5(b). Comment on whether the plot matches your expectations.

Find Eigenvalues and Eigenvectors for the following matrices: [10 4 A=0 2 0 3 1 1 -3

1. (20 pts) Plot the pulse and the FFT for a pulse with the following properties at x=0 and x=10 cm. f=2 MHz m=3 Ncyc=2, 6, 20 po 1 MPa (source pressure) x=10 cm (propagates in a Newtonian fluid for 10 cm as a plane wave-not a sound beam) a=0.5 dB/(MHz cm) Consider 3 types of waves: sine, square, and sawtooth. (square and sawtooth only for grad students) Observe your plots and draw some conclusions. Discuss any possible issues you encounter. 2. (20 pts) We have the following 3 ultrasonic transducers: a. Focused 1 MHz, 2.54 cm diameter, 5.08 cm focus b. Focused 3 MHz, 2.54 cm diameter, 5.08 cm focus c. Unfocused 0.1 MHz, 2.54 cm diameter The transducers are operating in water (c=1486 m/s). I. Plot the axial field for all transducers II. Plot the focal transverse field for the focused transducers and the transverse field at the Rayleigh distance (R_0) and at 2R_0 for the unfocused. III. Assume source pressure of 0.1 MPa, and find the acoustic pressure in MPa at the location (r=0, z=4.5…