Part1:

For both
parts of this part, modify and run the FFT test program ffttest_rev.m.

(a) Periodic triangular waveform

4 t / T (t < T/4)

x(t) =

(4/3) (1 – t /
T) (t >= T/4)

Run the
program for 16, 32 and 64 samples and record the relative magnitudes of the FFT
coefficients X(2) to X(10), which correspond to the fundamental frequency along
with 2nd to the 9th
harmonics. Show the percent errors for the three runs. Explain the result you
get for the 9th harmonic when N=16.

Derive the
Fourier series coefficients for the triangular waveform and compare to the
MATLAB results.

Hint: Use
the exponential form of the Fourier series and integrate by parts.

(b)
Periodic pulse used

1 (0 < t < T/4)

x(t) = 0
(T/4 < t < T)

Run the
program for 64 samples

Note:
For each run in (a), submit print-out only for the relative magnitudes of
FFT coefficients X(1) to X(10)

For (b), submit print-out only for
the relative magnitudes of FFT coefficients

X(1) to X(5)

Submit the time plots for the
reconstructed signals, but not the frequency bar graphs.

Part2:

The bridge
circuit shown below is balanced when R2 / R4
= R3 / R5 , resulting in zero
current through R6. A “small“ unknown resistor can be measured accurately by
placing it in series with R5 for example. The current and voltage to R6 are
then proportional to the unknown resistance.

The
balance of the bridge obviously depends greatly on the accuracy of the
resistors used. Test the imbalance caused by resistor tolerance by programming
a Monte Carlo analysis with MATLAB. This can be done by randomizing R2, R3, R4
and R5 and solving the mesh equations in a loop (similar to the approach
recommended for the analysis of this circuit in MATLAB Assignment 2). Use a
tolerance of 9.4 % and a uniform distribution.

Insert rng(1946091) at the start of the program

Display
the minimum and maximum voltages across R6, along with the mean and standard
deviation. Show a histogram of the voltages for 1000 runs.

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