Programming Problems 4

1. Wavelets. Applications to computer vision, human vision, speech processing, compressing the FBI fingerprint database, filtering noisy data, detecting self-similarity in time series, sound synthesis, computer graphics, medical imaging, analyzing the clumping of galaxies, and analyzing turbulence. The Haar function is definite by Φ(x) = 1 if 0 ≤ x < 1/2, Φ(x) = -1 if 1/2 ≤ x < 1, and Φ(x) = 0 otherwise. For integer m and n, the Haar basis function Φ_m,n(x) = 2^-m/2 Φ(2^-mx - n). Write a program Haar.java that takes two integer input M and N, and one real input x and prints Φ_m,n(x). Or maybe plot it?

2. US postal barcodes. The POSTNET barcode is used by the US Postal System to route mail to the individual delivery carrier. Each decimal digit in the zip code is encoded using a sequence of 3 half-height and 2 full-height bars for use by scanners as follows: Value 0 1 2 3 4 5 6 7 8 9 Encoding ||╷╷╷ ╷╷╷|| ╷╷|╷| ╷╷||╷ ╷|╷╷| ╷|╷|╷ ╷||╷╷ |╷╷╷| |╷╷|╷ |╷|╷╷

The barcode starts and ends with a full-height bar (the guard rail). A checksum digit is appended (after the 5 digit zip code or ZIP+4): it is computed by summing up the original digits mod 10. Write a program that reads in a five (or nine) digit zip code as the command line parameter and prints out the corresponding postal bar code.

• Function to plot a half-height and full-height bar.
• Function to plot the sequence of bars for a given digit.
• Function to compute the check digit.
• Function to pad a number with leadings zeros (if necessary).
• Function to parse the input string "08544-1234" into digits (or command line should be ZIP then +4 or just ZIP).
• Function to check whether a given zip code + check digit is valid.