BENG 280A Homework 1
Bhandarkar, Avanti
abhandarkar@ucsd.edu
Rajendran, Kishore
kirajendran@ucsd.edu
Due: October 10, 2025 11:59pm
Homework policy: Late homeworks will be marked down by 20% per day. If you know that you need to
turn in a homework late because of an emergency or academic travel, please let both the TAs know ahead
of time. Collaboration is encouraged on homework assignments, however, the homework that you submit
should reflect your own understanding of the material.
Honor Code: By submitting this assignment, I agree to abide by the UCSD honor code and I declare that
all of this is my own work.
Required Reading
• Prince & Links Ch.2.1-2.3
• Lecture Notes
Supplementary Material
• Supplementary Session 1: Linear Systems [Recording] [Slides]
• For X-Ray Physics Problems, Prince & Links Ch.4, 5.2,& 5.3.2 may be helpful, but not required since
material will also be covered during lecture.
• AAPM/RSNA Physics Tutorial for Residents: X-Ray Production [Link]
• AAPM/RSNA Physics Tutorial for Residents: X-Ray Tubes [Link]
• AAPM/RSNA Physics Tutorial for Residents: X-Ray Interactions [Link]
• AAPM/RSNA Physics Tutorial for Residents: X-Ray Attenuation [Link]
LSI Review:
Problem 1 (10pts)
Prince & Links Problem 2.6: Determine whether the system g(x, y) = f (x, −1) + f (0, y) is
(a) linear
(b) shift-invariant
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Problem 2 (10pts)
Prince & Links Problem 2.7: For each system with the following input-output equation, determine whether
the system is (1) linear and (2) shift invariant.
(a) g(x, y) = f (x, y)f (x − x0 , y)
R∞
(b) g(x, y) = −∞ f (x, η)dη
Convolution Review:
Problem 3 (10pts)
Prince & Links Problem 2.10: Given a continuous signal f (x, y) = x + y 2 evaluate the following:
(a) f (x, y)δ(x − 1, y − 2)
(b) f (x, y) ∗ δ(x − 1, y − 2)
R∞ R∞
(c) −∞ −∞ δ(x − 1, y − 2)f (x, 3)dxdy
(d) δ(x − 1, y − 2) ∗ f (x + 1, y + 2)
Problem 4 (10pts)
Compute and sketch Π(x) ∗ Π( x−1
2 ) using the following rect function definition.
(
1 − 12 ≤ x ≤ 21
Π(x) =
0 otherwise
X-Ray Physics
Problem 5 (5pts)
Explain how and why the photoelectric effect and Compton scattering depend on X-ray energy and atomic
number.
Problem 6 (10pts)
Prince & Links Problem 4.2:
(a) Calculate the mass-equivalent energy of an electron at rest.
(b) Determine the voltage potential difference between a cathode and anode in which electrons accelerated
between the two will obtain speeds equal to 1/10 the speed of light.
(c) Using relativistic equations, determine the speed of an electron that is accelerated across a 120 kV
potential.
Problem 7 (5pts)
Prince & Links Problem 4.10: A bar phantom of thickness 0.4 cm is uniformly irradiated by monoenergetic
x-ray photons, and a screen is placed behind the phantom to detect the x-ray photons. The bars of the
phantom are made from a material that has an HVL of 0.1 cm. In the space between the bars, x-ray photons
pass without attenuation. Assuming the intensity of the image is proportional to the x-ray photons that hit
the screen in a unit area, what is the contrast of the resulting image?
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Problem 8 (10pts)
Prince & Links Problem 5.5(a),5.5(c):
(a) Why is Compton scattering bad for the images produced using projection radiography?
(c) Why do we have to filter x-rays from the x-ray source?
MATLAB Exercise (30pts)
Online Component (20 pts – automatically graded)
Complete the Canvas MATLAB problem on Convolution. The exercise will be assessed online, and you
may submit as many times as you like.
Offline Component (10 pts)
In addition to submitting your code for evaluation by the MATLAB auto-grader, please include your code
and any relevant output images in your Gradescope submission.
Citation & Collaboration
You need to include the following information about both the written problems and the MATLAB problem.
(a) If AI tools (such as ChatGPT or similar) were used to complete any part of this assignment, please
specify which questions and, for each, explain how the AI was used, list the questions you asked, and
describe what you learned from the interaction. If no AI tools were used for the entire assignment,
please clearly state that here.
(b) List any other resource you used to help you on this assignment, including websites, textbooks, videos,
etc.
(c) If you worked with any other student in the course to complete the assignment, please list these
students here. You may also describe the extent of the collaboration (e.g., “discussed approaches but
wrote solutions independently”). If you did not collaborate with anyone, please state that here.
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