At the right (B) receptor, the intensity is ib(x, t) = Io{1 + sin[k(x - 8 - vt)]}

where Io is the intensity when sin[*] = 0, v is the pattern velocity (v > 0 moving left to right), 8 is the spacing between the two receptors in mm, X is the spatial period of the input sinewave in mm, and k = 2n/X. The output of the left-hand multiplier is the product of the delayed left receptor and the nondelayed right (B) receptor; that is, y(t) = KRl2 {l + sin[k(x - v(t - e))]}{l + sin[k(x - 5 - vt)]}

In Simnon notation, y = ib*DELAY(ia, s), and yprime = ia*DELAY(ib, e). The difference, Ay = y' - y, is low-pass-filtered by the ODE, yo = -a*yo + a*Ay. The DDC output is the analog signal, yo.

Simulate the DDC with Simnon using the following parameters: a = 0.2 r/ms, s = 0.333 ms, 8 = 0.1 mm, x = 0.1 mm, Io = 1, X = 0.5 mm. Use Euler integration with delT = 0.001 ms. t is in ms. [Note that Simnon will not take Greek letters or subscripts, so users will have to use their own notation.]

a. Plot ia, ib, Ay, and yo in the steady state. Let v = 0.5 mm/ms. Vertical scale: 2, 3. Horizontal scale: 15, 20 ms.

b. Now find the DDC static transfer function. Plot the steady-state yo vs. v. Use v values between -1 and +1 mm/ms. Clearly, when v = 0, yo = 0. Note that yo(v) is an odd function so it can sense the direction of object motion.

7.6. Repeat Problem 7.5 using moving black and white stripes (a spatial square-wave pattern). In Simnon notation, ia = io*(i +sQW(k*(x -v*t))) and ib = io*(i + sQw(k*(x - dx - v*t))). dx is 8 used above. Use the constants: a = 0.2 r/ms, X = 1 mm, dx = 0.5 mm, dT = s = 0.333 ms. Let v range from -0.25 to +0.25 mm/ms.

7.7. The input to a one-dimensional is Gaussian white noise with power spectrum, ^(f) = n/2 msu/(cycle/mm) plus a signal s(x) = ^x2 - x2 that is non-negative for |x| 3 xc and zero for |x| S xc (a semicircle centered at the origin). Thus, the input to the SMF is v(x) = s(x) + n(x).

a. Find an expression for hm(x), the SMF weighting function.

b. Give an expression for the maximum output of the SMF due to s(x) at the origin, rs(0).

c. Find an expression for the mean squared noise output from the matched filter, No. (Hint: Use Parseval's theorem.)

d. Give the ms signal-to-noise ratio, p, at x = xo = 0.

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