Quality Engineering Associate – Pre interview questions

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EE417506 2022 HW 2, please see course web-page for due dates

You can read in the Anderson textbook, Digital Transmission Engineering, in Chapter 2. For

this assignment, either MATLAB or python can be used, since no special toolboxes are employed.

I strongly encourage two person teams on this assignment.

Formulas

Use my de�nition of the sinc and rect functions:

1. rect(x/X) = 1, only when |x| < X/2,(two-sided width is X and zero else. 2. sinc(x) = sin(πx)/πx., with zero-crossings ZC at the integers, ±1,±2, . . .

Remember that

rect

(
t−a
B

)

has width B, and is centered at a. Both rect and sinc are used in both the time (t) and frequency
(f) domain. Bandwidth is always de�ned over positive frequencies. The cross-correlation integral is
(`cross’ implies two di�erent signals, `auto’ implies the same signal)

Rxc(τ) =

∫
x(t + τ)c∗(t)dt

and the output of a matched �lter to pulse s(t) at time o�set τ is

Rss(τ) =

∫
s(τ − t)s∗(−t)dt =

∫
s(τ + t)s∗(t)dt

and can be computed for sampled signals (vectors x and c ) using MATLAB’s xcorr.m, using Rss
= xcorr(s,s) = xcorr(s). Note that we use xcorr to produce the auto-correlation xcorr(s,s).

These can be computed in the frequency domain as

Rss(τ) =

∫
|S(f)|2 exp(−2πfτ)df

Mnemonic: The CD-Rule. For complex valued signals (think phasors) , placement of the complex

conjugate is a matter of de�nition. The CD rule states that the Conjugate goes with the Delay.

Problem 1

We often need to put AWGN (additive white Gaussian Noise) through �lters. The general result

is that if w(t) is AWGN with spectral level No/2 (Watts per Hz), then the output of the �lter h,
given by the convolution y(t) = h(t) ∗ w(t). The output is a random process, which we take to
be wide sense stationary after all transients have decayed. The process y(t) is spectrally-shaped
Gaussian noise (zero-mean), with spectrum

Sy(f) =
No

2

|H(f)|2, and average power Py =

No
2
Eh

where Eh < ∞ is the energy in the �lter h(t). This can be calculated in the time or frequency domain, since by Parseval

Eh =

∫
|h(t)|2dt =

∫
|H(f)|2df

Although AWGN has in�nite power, the output process y(t) has �nite power Py. Since noise is
zero-mean and Gaussian (normally) distributed, this means the RMS value is σy =

√
Py, and one

2

can compute the probability that the noise exceeds a given level. With MATLAB, for a random

variable RV x with a zero mean Gaussian distribution with variance σ2, we can compute, using
erfc.m.

P{x > a} = Q(
a

σ
) =

1

2
erfc(

a/σ
√
2
)

So, most of these computations, reduce to calculating the power out of the process, since σ2y = Py.
Compute the output power for an No/2 input AWGN, when (only the magnitude response is

given)

1. A rectangular �lter with bandwidth B, |H(f)| = Horect(f/2B)
2. A sinc �lter with �rst null at f = B, |H(f)| = Hosinc(f/B)
3. A Manchester pulse matched-�lter, where h(t) = rect((t−T/4)/(T/2))−rect((t−3T/4)/(T/2))
4. An exponential �lter with h(t) = Aexp(−t/τ), t > 0.
5. The n-th order Butterworth Filter with frequency response

|H(f)|2 =
1

1 + (2πf)2n

These are all calculations you can do with basic calculus, or by Fourier transform. The Butter-

worth �lter response must be plotted and you can compute the noise gain.

Problem 2

A pulse matched �lter is often used in signal processing. To examine the output of the MF, to

input pulse s(t), we can either (1) compute the �lter response or (2) compute the auto-correlation
function. For example, for discrete time pulse s, the MATLAB command would be

b = conj(s([end:-1:1])); y = filter( b, 1, s); plot(y); grid

y = xcorr( s, s); plot(y);grid

Compute and display plot these for signals. Comment on the di�erences between the input

signal and the output of xcorr.

1. A rectangular �lter with bandwidth B, |H(f)| = Horect(f/2B)
2. A sinc �lter with null-to-null bandwidth B, |H(f)| = Hosinc(f/B)
3. A Manchester pulse matched-�lter, where h(t) = rect((t−T/4)/(T/2))−rect((t−3T/4)/(T/2))
4. A rect pulse coded Barker-13 pulse,

s(t) =
N=13∑
k=1

bkp(t−kT), p(t) = rect(t−T/2)/T

The bk is the Barker-13 code, see Wikipedia:

https://en.wikipedia.org/wiki/Barker_code

Note this is di�erent from the plots shown in class, because we have added the rect signal. This is

the analog baseband signal that would be transmitted. Other pulse shapes can be used – the root

raised cosine.

Problem 3 Matched Filtering and Timing

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Use Matlab (or other ) to generate the following signals at sampling rate Fs = 1/Ts, Ts = T/50.
(1MHz). This is called oversampling relative to the baud rate. Using the p(t) = sinc(t/T) pulse,
write a program to implement the matched �lter.Be sure to use both sides of the sinc. Plot the

resulting matched �lter output and show that the MF works as expected. To show that be sure you

can predict where the MF peak will occur.

You can implement a matched �lter in several ways, for example, using filter.m or conv.m.

The di�erence is in the length of the output signal. Convolution always gives the full length, but

the �lter output is limited to the length of the input. See MATLAB help as needed. Sometimes

zero-padding is needed to see the full response.

You can use the T = 1e− 06 with the above. Vary the time o�sets to see the e�ect on moving
the MF peak. Pick a plot and submit it. Label all axes. Explain any scaling you use. The scaling

depends on the oversampling rate, here 50x

Problem 4. Matched Filtering to a known pulse

Matched Filter theory tells us that the best (maximum SNR) linear receiver to the observation

y(t) = As(t) + w(t)

is the �lter

hMF (t) = s(T − t)

Here we are taking the pulse s(t) to be non-zero only on [0,T]. Sketch the MF response to the pules
1.

s(t) = rect(
t−T/2
T

)

2.

s(t) = rect(
t−T/4
T/2

)− rect(
t−3T/4
T/2

)

Recall the exact de�nition of rect(x) = 1, only when |x| < 1/2; otherwise 0. I strongly advising sketching these analog pulse shapes. The convolutions can be done graphically and it is known that

the convolution of 2 rectangles is a triangle. The issue is (1) where are the triangles located, and
(2) what are their horizontal widths and vertical heights.

Determine SNR at the optimal sampling time for each of these signal. Assume the noise is

WGN of spectral level No/2.

Quality Engineering Associate – Pre interview questions

Waste Conversion LTD is a company that treats organic waste using worms to form organic
fertilizer and an insect based animal feed. In this simplified process, different types of organic
waste (cabbages, bananas, tomatoes, manure…etc) are delivered to the factory using trucks.
As a pre-processing step, an industrial waste mixer is used to mix the waste at different
predetermined compositions to form several recipe batches. These waste recipe batches are A,
B, C and E.

Depending on the production plan, a predetermined number of beds (with unique identifiers) are
loaded with the batches of waste at different recipes. Typically, one bed is loaded with one
mixed waste batch that weighs 1500 kilograms. Thereafter, young/small worms at either of two
loading densities (17.8 kg or 32 kg) are added to the beds and left to feed on the waste for a
specified amount of days. After the days have passed, the grown/adult worms are harvested
from the beds and weighed – from which growth factors are calculated. The remaining
waste/compost is routed to the next processing step.

Please use the data sheet provided (excel workbook) labeled “Quality Engineering Team
Interview Questions – Excel” to answer the questions below.

1. Please review the database (excel workbook) provided and do the following:
a. Using measures of central tendencies, develop a dashboard on MS Excel or

Google Sheets showing both weekly and monthly production performance at
loading densities of 17.8 kgs and 32 kgs with regard to: (1) Growth factors and
(2) Feed yields. In this analysis, clearly distinguish between production beds with
a cycle time below 17 days and those with cycle times above 18 days.

b. Improve on the above by developing a control chart displaying daily production
performance with regard to growth factors for beds with cycle times below 11
days at loading densities of 17.8 kgs. Include upper and lower control limits to the
plots.

2. Typically, waste mixed with the recipe A composition is used owing to higher historical
yields. However, during the production period (Jan to October 2018), it was noted that
the worm growth factor varied significantly when recipes B, C and E were used at
different loading densities (17.8 kg and 32 kg). As the quality engineering associate,
please use analysis of variance or other known statistical methods to answer the
following pending questions (using the data in the spreadsheet):

a. Is it best to use recipe A for all beds at any loading density?
b. In the event that recipe A is not available, what recipes (between B, C and E) do

you recommend using and at what loading density? Please give these in
descending order based on growth factors.

Please note that the data is not clean i.e. there are outliers as well as missing data points. All
definitions have been provided in the data sheet (excel workbook)

https://docs.google.com/spreadsheets/d/1kaez8imm6hxZKUUjbVTnQihVg2VZAT-DdNEmjxuLco4/edit#gid=1172231761

Please provide your answers/responses in the MS Excel with referenced calculations/analyses
where necessary. If successful, note that you will be required to interpret your responses in
detail.

3. A supervisor was walking into a processing area, he noticed a small pool of water on the
floor. He called the crew lead and instructed him to have the floor mopped/dried. After 5
minutes the crew lead noticed that the pool of water was building up again.With the help
of other operators they noticed that there was a steam pipe that was leaking. Using one
of the root cause analysis tools, briefly illustrate on an excel sheet/google sheet how you
would conduct the root cause analysis.

4. From question 2 above, identify the corrective and preventive actions that the supervisor
should have taken.

5. Biomass briquettes is one of the products produced at Sanergy used as a source of
fuel/energy. The briquette manufacturing process uses different recipes that involve
mixing two or more waste substances (Feedstocks). During the manufacturing process,
we have 2 feedstocks,A and B that have to be mixed at a ratio of 60:40. The mixed
feedstocks need to be dried to achieve a moisture content of between 5% to 10%.
Additionally, the mixed feedstock should be free of physical contaminants like plastic
papers, metallic and glass pieces e.t.c. With this in mind, develop a monitoring record
sheet to be used to ensure we produce quality briquettes (use random values)

6. A Quality Associate is tasked with the responsibility of coming up with and implementing
a new sampling procedure for the GIGO checks. Before implementation of the sampling
procedure, the Quality Associate will need to have a discussion with all stakeholders
about his/her plans and incorporate their recommendations and suggestions into those
plans.

The Quality Associate will also need to test out the new sampling method and make any
changes/improvements from insights gathered from the test. The next step will be to
create a draft standard operating procedure for the method and have it approved by all
the relevant stakeholders.

Upon approval he/she will need to put in place work instructions for the procedures and
train the team on the new method.Afterwards, he/she will need to track the process for a
period of time before full handover of the new method to the team.

i. Prepare a project plan outlining the steps to take th.is idea from the ideation stage to

implementation of updated specifications in the factory. Build a schedule for this project
with a Gantt view, and list out your assumptions where you have made them.

ii. How can you accelerate your project timeline?

iii. What risks or costs does that introduce?

iv. How could you manage those risks?