EE 311
Assignment 01
January 15, 2016
Due: January 20, 2016
Instructions: Download this file as a Word document and type your answers directly
under each question. Turn in a hard copy of your results.
1. Use the technique outlined in class and Example 1.9 to find the frequency response of
the system given by: yn  0.5xn  0.75 xn 1  2 yn 1
Take the sample frequency to be 1000 Hz and use MATLAB to plot the magnitude and
phase of the frequency response. Turn in your MATLAB code and your response graphs.
2. A system has an impulse response given by hn  {1, 2, 0.5, 0.2, 0, 0, 0, } . Construct a
convolution table to find the response of the system to an input given by
xn  {1, 2, 0.5, 0, 0, 0, }
3. Suppose I have an FIR filter with an impulse response given by:
h(nT )  {b0 , b1,bN 1, bN )
the implementation difference equation is given by
y(n)  b0 x(n)  b1x(n  1)    bN x(n  N )
Suppose the impulse response function for an FIR difference equation is symmetric. For
example the response might be given by
h(nT )  {b0 , b1 , b2 , b3 , b4 , b5 , b4 , b3 , b2 , b1 , b0 } .
The difference equation be written as
y(n)  b0 x(n)  b1 x(n  1)  ...  b4 x(n  4)  b5 x(n  5)  b4 x(n  6)  ...  b0 x(n  10)
Because of the symmetry we can factor out some of the coefficients to write:
y(n)  b0 [ x(n)  x(n  10)]  b1[ x(1)  x(n  9)]  ...  b4 [ x(n  4)  x(n  6)]  b5 x(n  5)
What is the advantage of using this symmetric implementation equation instead of an
equation that is not symmetric?