Signals and Systems (Time Domain)

Question 1

Compare and contrast continuous and discrete signals

Answer 1

Continuous:
- measures all possible values
- often records signals as they are being recorded

Discrete:
- measures only specific values
- often takes samples of a continuous physiological signal

Example:
Body temp measured every 2 hours:
- in time: discrete (only measures every 2 hours)
- in amplitude: continuous (does not have fixed values to measure)

Question 2

Compare and contrast analog / digital signals

Answer 2

Analog: continuous both in time and amplitude
- good for getting data instantaneously

Digital: discretized in time and quantized in amplitude
- good for processing signals after

Question 3

Compare and contrast non/periodic signals

Answer 3

period: repeats

! no bio physiological signal is perfectly periodic

Question 4

BIBO stability

Answer 4

system is bounded-input/ bounded-output (BIBO) stable if:

bounded input –> bounded output
(small change in input does not lead to large changes in output)

Question 5

compare and contrast causal and memoryless systems

Answer 5

Memorlyless:
- output only depends on current input
y(t) at time T0 = x(t) for t = T0

Causal:
- output ONLY dpends on current / past inputs
y(t) at time T0 = x(t) for t < T0

• causal –> used for pre-processing / real time signals
• non-causal –> good for post-processing

Question 6

A 7-day rlling average is used for reporting new cases of COVID-19. This avering system is… (3)

Answer 6

1. Stable
   averages are BIBO stable (smaller than biggest number in data set)
2. Causal
3. can be non-causal
   (if used for post-processing / retrospective studies)

Question 7

Compare and contrast non/linear and time -(in)variant

Answer 7

Linear: (convenient to have)
- system satisfies:
1. additivity
- sum of inputs = sum of outputs

2. homogeneity
   - scaled input = scaled output

Time-invariant: (required to have)
- time-shifted input = time-shifted output
(equipment that have the same function throughout a procedure or throughout different types of the day)

Question 8

Why do we want an LTI system response?

Answer 8

• LTI system can be fully characterized by its impulse response
• “predict output based on input” –> allows system to be described by math

Question 9

What are some compensation techniques (2)

Answer 9

1. Altering design
   - address inherent insensitivity
2. Adding new components
   - negative feedback
   - signal filtering
   - opposing inputs