## Problems

7.1. A Fukushima-type, one-dimensional, linear, spatial filter has the spatial impulse response:

c (x)_ A sin(xn/^) _ A sin(xn/A2) BP A1 (x k/A1 ) A 2 (x n/A 2)

a. Plot and dimension CBP(x).

b. Plot and dimension the spatial frequency response, CBP(u). u is the spatial frequency in rad/mm.

c. Calculate the Q of CBP(u). (Q = center frequency/bandwidth.)

7.2. A Fukushima-type, one-dimensional linear spatial filter has the spatial impulse response:

a. Plot and dimension cF(x).

c. Can this filter pass dc (constant, overall illumination)?

7.3. A one-dimensional Zorkoczy system is shown in Figure P7.3. The receptors emit pulses at a constant rate when illuminated. All receptors are separated by mm. The unit delay, *, is equal to the receptor clock period, T, and T = 8/u. u is the "unit object speed." The one-dimensional, black and white object can be stationary, or have a unit velocity of ±u (in the ±x direction). T2(ak) is the unit OFF operator.

a. Write the Boolean expression for the system output. Give the system output for:

b. ON of general illumination.

c. OFF of general illumination.

d. A light edge moving to the right at +u.

e. A light edge moving to the left with -u.

f. A dark edge moving to the right with +u.

g. A dark edge moving to the left with -u.

h. A light unit spot (width = 8) moving to the right with +u.

i. A light unit spot (width = 8) moving to the left with -u. j. A dark unit spot moving to the right with velocity +u. k. A dark unit spot moving to the left with velocity -u.

7.4. a. Design a one-dimensional Boolean Zorkoczy system that will respond selectively only to a unit white spot moving with -u (to the left at unit speed). Receptors produce a clocked output when illuminated. The objects are black and white. The unit spots can cover only one receptor at a time. Use T1, T2, AND, OR, and unit delay operators. Find the Boolean expression for the output, Qo.

b. Verify the design by finding the responses to tests b through k in the preceding problem.

c. Sketch a one-dimensional retinal neuron equivalent that will respond selectively to a white spot moving to the left. That is, replace the AND, OR, and delay elements of the Zorkoczy system with neuronal elements that will approximate the same behavior.

7.5. This problem will simulate the dynamics of Reichardt's DDC described in Section 7.1.2. The organization of the DDC is shown in Figure 7.1-8 in the text. The input signal is to be an intensity sinewave pattern moving in the x direction with velocity v mm/ms. At the left (A) receptor, it is ia(x, t) = I0{1 + sin[k(x - vt)]}

(Light edge)

(Light edge)