ECE 444/644 : HW #3

 ECE 444/644 : HW #3

1. Book problem 2.7-6.
2. Book problem 2.7-14. Use 20 dB of stopband
ripple.
3. Book problems 3.1-2(c,d,e) and 3.1-3(a,c).
4. Book problems 3.1-8 and 3.1-9.
5. Letting A and B designate the first two non-zero
least significant digits of your NDSU student ID,
define a T = 40 periodic signal x(t) as
x(t) =



0 −20 ≤ t < −(B + 10)
−t/(B + 10) −(B + 10) ≤ t < 0
2t/(A + 10) 0 ≤ t < A + 10
0 A + 10 ≤ t < 20
x(t + 40) ∀t
.
In this problem, you will implement a method
to output a periodic signal yK(t), the truncated Fourier series (FS) of the signal y(t) =
c1 + c2x(c3t). That is, output yK(t) as yK(t) =
PK
k=−K Yke
jkω0t
, where Yk are the FS coefficients of the signal y(t).
(a) Plot the signal x(t) over 2 periods.
(b) Determine constants c1 and c2 to maximize
the output amplitude range of yK(t) yet
provide some buffer against saturation and
clipping.
(c) Determine constant c3 so that yK(t) has
highest possible frequency yet maintains
adequate signal quality for 1 ≤ K ≤ 10.
(d) Derive the necessary Fourier series coefficients Yk. Create MATLAB plots of yK(t)
over 2 periods for 1 ≤ K ≤ 10.
(e) Devise an algorithm to output the desired
waveform on the K22F. Validate your algorithm with MATLAB code structured as
close as possible to your final C-code implementation. For example, while MATLAB
seamlessly supports complex numbers and
vector operations, C does not. Thus, represent complex numbers in your MATLAB
code using pairs of reals, and compute vector operations using explicit loops, just as
you would in C. Of course, if you can devise
a way so that you don’t need to use complex
numbers, that may be preferable...
(f) Create a project in Keil to output your designed waveform.
• Output yK(t) on the DAC channel at
a rate of one sample every 0.1 ms (10
kHz sampling rate).
• The number of terms K used in the
approximation yK(t) must be run-time
adjustable between 1 and 10. Adjust
the number of terms through button
presses (preferred method; one button
to increase, the other to decrease) or
watch-window (less preferred method).
• Turn on an LED when you enter the
ISR and turn the LED off when you
exit the ISR.
(g) To test your C program on the DSK, complete the following:
• Verify the output waveform shape for
each case using an oscilloscope. Most
oscilloscope’s in lab will calculate the
period, frequency, amplitude and other
information pertinent to a waveform
automatically. Use these feature to
appropriately measure your waveform.
How close are your waveforms to theoretical?
• Use an oscilloscope to measure the
LED “on-time”. What percentage of
the available processing time is being
used to generate your waveform? Does
the processing time vary with K?
To receive credit for this part of the assignment:
(a) Sign up to demonstrate your working hardware to the course instructor for check-off.
(b) Summarize your approach, findings, and
calculations in a short write-up.
(c) Attach a copy of your properly documented
C-code.