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HW #6 : ECE 444/644 

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HW #6 : ECE 444/644

1. Write your own MATLAB program/function that designs a digital IIR BPF that meets the following
specifications:
• Sampling frequency of Fs = 10 kHz.
• INPUT: Selectable factor-of-2 filter order K.
• INPUT: Selectable 2 dB lower passband frequency = 250 ≤ fp1 ≤ 2000 [in Hz]. The upper 2 dB
passband frequency is determined as fp2 =
Fs
2 − fp1
.
• Family is inverse Chebyshev BPF with maximum stopband gain of 1
10 .
• Design method is bilinear transform with prewarping that preserves the 2 dB passband frequencies.
• OUTPUT: Filter coefficients (32- or 64- bit floats) for realization as cascade of second-order DFII
filter stages. It is recommended that your MATLAB code automatically generate a header file that
contains the filter coefficients for your project. For example:
fid = fopen(’coef.h’,’w’);
fprintf(fid,’#define NS %d \n’,NS);
fprintf(fid,’float A[NS][3] = { \n’);
for ns = 1:NS-1,
% fprintf statement here
end
% fprintf for last row of A matrix
% Repeat technique for B matrix
fclose(fid);
• OUTPUT: Digital filter pole/zero plot that clearly indicates pole-zero groupings for each secondorder section as well as section ordering.
• OUTPUT: Frequency response plot over −
Fs
2 ≤ f =
ΩFs
2π ≤
Fs
2
.
Verify code operation by designing a 20th-order filter with lower passband frequency of fp1 = 1 kHz.
2. Create a KEIL project to implement an IIR filter on our K22F hardware. Design requirements include:
• Sampling rate of 10 kHz.
• Filter realized as a cascade of second-order DFII IIR filter sections. Your structure should accommodate a range of filter orders (determined by a program parameter K).
• Highest order possible while meeting timing requirements.
• Use efficient programming techniques and compiler optimizations. You must write your own filter
code – it is not acceptable to use predesigned filter code or functions. Any code optimizations should
not alter the generality of the implemented filter – that is, by simply changing a coefficient header
file, you should be able to change the implemented filter.
• Run-time filter selection (none plus four different filters) by single-button presses.
• Since we will be implementing a BPF with a unipolar DAC, add an appropriate dc offset to keep
your final output in range (0 to 4095).
Test your filter code for correct operation using some simple filter (like an all-pass filter). Determine (or
make an educated estimate) of the highest order that will still correctly operate.
3. Once you determine the highest filter order K that your K22F program can achieve, use your MATLAB
code from problem 1 to design four Kth-order filters with lower passband frequencies of 250 Hz, 500
Hz, 1000 Hz, and 2000 Hz, respectively. Integrate these filter designs with your K22F program. When
dowloaded, the K22 should operate as a digital wire. When the button is pressed, the system should
cyclically switch between filters as:
none → fp1 = 250 Hz → fp1 = 500 Hz → fp1 = 1000 Hz → fp1 = 2000 Hz → repeat
Test your system for proper operation. Use the K22F LEDs to demonstrate timing is being met. What
is the maximum order K you can successfully achieve?
Deliverables:
1. Demonstrate correct operation to the course instructor. You will need to demonstrate the frequency responses of your filters, including passband/stopband characteristics, cutoff frequencies, transition bands,
and so forth.
2. E-mail ([email protected]) a zipped MATLAB mat-file that contains your final design coefficients.
Name your file using your initials (e.g., rag.mat). Assume each section is represented by a difference
equation y[n] + a1y[n − 1] + a2y[n − 2] = b0x[n] + b1x[n − 1] + b2x[n − 2]. Your file should include:
• A 4-by-NS-by-3 matrix A where the first dimension indicates filter number (4 filters, one for each
of the 4 lower passband frequencies), the second dimension indicates section number, and the third
dimension indicates the feedback coefficients [1, a1, a2] for that particular section and filter. Notice,
the number of sections NS should be K/2.
• A 4-by-NS-by-3 matrix B where the first dimension indicates filter number (4 filters, one for each
of the 4 lower passband frequencies), the second dimension indicates section number, and the third
dimension indicates the feed-forward coefficients [b0, b1, b2] for that particular section and filter.
For both matrices, sections should be ordered according the how you ordered the sections of your filter (first section first), and filters should be ordered with the smallest lower passband frequency filter
occurring first.
3. You should prepare a report summarizing your design and implementation. This is a complex design,
so it is incumbent upon you, the designer, to provide results in a clear and readable format. I will not
waste time trying to make sense of a poor report, even if the underlying design is the best. Attach code
and other bulky supporting material as appendices.

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