EE473 Homework #3



Reading : Chapter 4

  1. (3pts) Problem 4.26 from Textbook

  2. (3pts) Problem 4.34 from Textbook

  3. (3pts) Motion pictures are produced by displaying a sequence of still pictures or frames at a frequency, or frame rate, of fs (in hertz). Consequently, since this corresponds to a form of image sampling, aliasing is sometimes observed. For instance in old western movies the wagon wheels often appear to rotate slowly forward or backward or even to stand still.

        1. If the rotation rate of the wheels is f0 (in hertz) and there are K spokes on each wheel, state the condition for the wheels to appear to stand still.

        2. Assume that the frame rate is 15 Hz and that a wagon wheel has a diameter of 1.5 m with 40 spokes per wheel and that the wagon is travelling at a constant speed of 25 km/hour. Do the wheels appear to move backward, forward, or stand still?

  4. (5pts) It is discovered that a foreign power intends to kidnap one of our top level scientists. An encoded image of the target scientist was intercepted and must be decoded quickly so that the scientist can be identified and protected. You, as a well-respected EE473 student and signal processing expert, have been selected for the task. The encoded image is stored as a MATLAB matrix in file image.mat . Download this file to your MATLAB working directory. The matrix can be read into MATLAB with load image command (type help load for further information). The matrix will be named "img" after it is loaded into MATLAB. You can view the encoded image with the colormap(map); image(img) command.

    Further work by encryptologists uncovered the fact that each scan line of the original image (row of the matrix) was encoded separately. The encoder has the following input/output relationship:

> y[n] = x[n]+x[n-1]+x[n-2]+ .... + x[-infinity]

In addition to providing a hard-copy of the encoded and decoded images

identify the scientist, and respond to the following:

          1. Find the impulse response of the encoder.

          2. Determine the encoder's frequency response function

          3. Find a linear constant coefficient difference equation that describes the encoder.

          4. What is the frequency response of your image decoder?

          5. Write the input/output relationship of your decoder in the form of a LCCDE.

          6. What is the impulse response of your decoder?

The kidnappers have implemented the decoder in two lines of MATLAB code. Please try to do as well. (Hint: See "help :" for information on selecting submatrices from a given matrix)

Ref: Tony Richardson lecture notes.