You are using a single transducer to examine a heart valve. Assume that in a given heart cycle the range of the valve is given by z(t) = 16 + 0.5e−t/τ u(t) cm where τ = 10 ms, u(t) is the unit step function, and the speed of sound is 1,540 m/s.
(a) Sketch z(t) over a couple of heart cycles (assume the heart rate is 1 Hz).
(b) Assume your transducer generates a pulse at t = 0 using a typical transmit waveform. Carefully sketch the A-mode signal (as a function of time) that you would observe on an oscilloscope.
(c) Now assume that you repeatedly fire your transducer every 1 ms. Sketch the M-mode image that would be generated, being careful to label the axes.
(d) Suppose you wanted to image the motion of this valve by making a Bmode image of it. Suppose it could be covered by 10 scan lines (given the beam size at a 16 cm range). Describe what steps you would take to make this image in real-time. Do you think it is possible?
