CE 108/263 PROJECT ASSIGNMENT 2 (For grads only)
Now that you have selected your data set and started playing with it, it's time to design a
serious compressor! You can mix and match compression techniques from our bag of
tricks, including:
Lossy:
Non-un

CE 108 HOMEWORK 4
EXERCISE 1.
Suppose you are sampling the output of a sensor at 10 KHz and quantize it with a
uniform quantizer at 10 bits per sample. Assume that the marginal pdf of the signal is
Gaussian with mean of 0 Volts and variance of 4 Volts2.

CE 108 HOMEWORK 2 (DUE TUESDAY, Jan 27 IN CLASS)
EXERCISE 1.
Prove that, for a given source, the Huffman code achieves 100% efficiency when the
symbol probabilities are inverse powers of 2.
EXERCISE 2.
Prove that, by grouping n symbols of a non-memoryless

CE 108 HOMEWORK 4
EXERCISE 1.
Suppose you are sampling the output of a sensor at 10 KHz and quantize it with a
uniform quantizer at 10 bits per sample. Assume that the marginal pdf of the signal is
Gaussian with mean of 0 Volts and variance of 4 Volts2.

CE 108/263 HOMEWORK 2
EXERCISE 1.
Prove that, for a given source, the Huffman code achieves 100% efficiency when the
symbol probabilities are inverse powers of 2.
N
The efficiency of a code is the ratio between the entropy H = pi log pi of the source
i=1

CE 108/263 HOMEWORK 3
EXERCISE 1.
Suppose a memoryless source has (marginal) entropy H equal to 4. What are the
minimum and the maximum coding efficiency achievable by an arithmetic encoder that
encodes groups of 5 symbols at a time?
EXERCISE 2.
Consider

CE 108/263 PROJECT ASSIGNMENT 1
PART 1
Write a piece of code (in whichever computer language you prefer) that implements
midtread or midrise uniform quantization. Assume the input data has zero mean and
symmetric pdf. The function should accept as input:

CE 108 HOMEWORK 1
EXERCISE 1. (ALL)
Consider the sequence x(n) of values in
http:/www.soe.ucsc.edu/classes/cmpe108/Fall07/ce108HW1.txt
http:/www.soe.ucsc.edu/classes/cmpe108/Fall07/ce108HW1.xls.
1. If possible, plot the sequence (using any available softw

Transform Coding CMPE 108/263
1. Introduction
Consider a data stream, and subdivide the data into non-overlapping segments of length M: [ x ( kM + 1), x ( kM + 2),., x ( kM + M )] .
!
x(kM+1)
x(kM+2)
x(kM+M)
x(k+1)M+2) x(k+2)M+1)
x(k+2)M+2)
x(k+1)M+1)
Now

CE 108 HOMEWORK 5
EXERCISE 1. (GRADS)
Consider a stationary, zero-mean process, and assume that E[x(n)2]=4 and
E[x(n-1)x(n)]=3. Suppose you want to quantize this signal with 6 bits.
1. What is the theoretical SNR using PCM and using DPCM?
SNRPCM = 10 log1

CE 108 HOMEWORK 5
EXERCISE 1. (GRADS)
Consider a stationary, zero-mean process, and assume that E[x(n)2]=4 and
E[x(n-1)x(n)]=3. Suppose you want to quantize this signal with 6 bits.
1. What is the theoretical SNR using PCM and using DPCM?
2. Repeat the ex

CE 108 HOMEWORK 1
EXERCISE 1. (ALL)
Consider the sequence x(n) of values in
http:/www.soe.ucsc.edu/classes/cmpe108/Spring06/ce108HW1.txt
http:/www.soe.ucsc.edu/classes/cmpe108/Spring06/ce108HW1.xls.
1. If possible, plot the sequence (using any available s

CE 108/263 HOMEWORK 3
EXERCISE 1.
Suppose a memoryless source has (marginal) entropy H equal to 4. What are the
minimum and the maximum coding efficiency achievable by an arithmetic encoder that
encodes groups of 5 symbols at a time?
The maximum efficienc