Midterm 1

Question 1

Causal Signal

Answer 1

Signal starts on or after time 0

Question 2

Non Causal Signal

Answer 2

Signal starts before time 0

Question 3

Anti Causal Signal

Answer 3

Signal stops before time 0

Question 4

Analog

Answer 4

Continuous range of values for amplitude

Question 5

Digital

Answer 5

Finite number of values for amplitude (ex. 0 or 1)

Question 6

Time shift of signal

Answer 6

Right: T>0
Left: T< 0
x(t-T)

Question 7

Time scale of signal

Answer 7

Compression by a, a>1
Expansion by 1/a, 0<a<1
x(at)

Question 8

Flip signal

Answer 8

signal flips across vertical axis
x(-t)

Question 9

Periodic Signal

Answer 9

Exists repeating for all of t, continuous forever signal, is non causal

Question 10

Additivity

Answer 10

if x1-> y1
x2->y2
then x1+x2 -> y1+y2

Question 11

Homogeneity

Answer 11

if x->y then kx->ky

Question 12

Superposition/Linearity

Answer 12

Order shouldn’t matter so
k1x1 + k2x2 -> k1y1 + k2y2
Additivity and homogeneity both work for system

Question 13

Time-invariant

Answer 13

if x(t) -> y(t)
then x(t-T) should give y(t-T)
doesn’t matter if x is processed by system first or time delay

Question 14

Time-varying

Answer 14

Order of system process or time delay matter, will not yield same answer

Question 15

u(t) plotting

Answer 15

Practice graphing u(t-2), u(3t), sin(t)u(t), etc..

Question 16

Relationship between Step Function (u(t)) & Step Impulse (delta(t))

Answer 16

du(t)/dt = delta(t)

Question 17

Five steps to model Biomedical System

Answer 17

1. Schematic of sys.
2. Identify input & output
3. Establish sys. equations
4. Specify initial conditions
5. Simplify equations to describe input-output relationship

Question 18

Conservation of Electric Charge

Answer 18

Sum current @ node = 0. KCL, resistor, capacitor, inductor

Question 19

Conservation of Electric Energy

Answer 19

Sum voltage in loop = 0. KVL, resistor, capacitor, inductor

Question 20

Conservation of Momentum

Answer 20

Sum of Forces = 0, mechanical sys, springs, dampers, mass, etc.

Question 21

Conservation of Mass

Answer 21

Sum of Q = 0, Fluid mechanical, can convert to electrical ~= sum of current at node = 0. Q –> i, P –> v, R –> R

Question 22

Laplace under Zero State initial conditions

Answer 22

D–>s
ex)(D^2 + 5D + 6)y(t) = (D+1)x(t)
–>
(s^2 + 5s +6)y(s) = (s+1)x(s)

Question 23

Full Laplace question

Answer 23

1. x(t) -> X(S)
2. concert sys. to freq. domain
3. solve sys. in freq. domain for Y(S)
4. Y(S) -> y(t) (could include partial fraction expansion)

Question 24

Transfer function

Answer 24

H(S) = Y(S)/X(S)

Question 25

First Order Reverse Engineering

Answer 25

H(S) = k/(s-p)
Steady state: -k/p
t_1/2 = -ln(2)/p

solve for p, solve for k, get H(S)

Question 26

Second Order

Answer 26

Undamped, Underdamped, Critically Damped, Overdamped
H(S) = k/(s-p1)(s-p2)

Question 27

Undamped

Answer 27

p1 & p2 are imaginary & conjugate roots
p1,2 = +-jw
Oscillation: T = 2pi/w
Decay Constant = 0
Steady state = k/p1p2

Question 28

Underdamped

Answer 28

p1 & p2 are complex & conjugate roots
p1,2 = sigma +- jw
Oscillation T = 2pi/w
Decay = sigma (from e^sigma*t)
Steady state = k/p1p2

Question 29

Critically Damped

Answer 29

p1 & p2 are real & equal roots
steady state: k/p^2

Question 30

Overdamped

Answer 30

p1 & p2 are real & distinct roots
steady state: k/p1p2

Question 31

Positive Feedback System

Answer 31

1. amplification
2. enhanced sensitivity
3. unstable
   Hn(S) = G(S) / (1 - H(S)G(S)

Question 32

Negative Feedback System

Answer 32

1. increased accuracy/reliability
2. reduced sensitivity to disturbances/noise
3. used for automatic control
4. stable
   Hn(S) = G(S) / (1 + H(S)G(S)

Question 33

Stable

Answer 33

Real parts of all poles are smaller than zero Re(p_n) < 0

Question 34

Unstable

Answer 34

Real part of a pol is larger than 0, Re(p_n) > 0
Real part of a repeated pole is 0, Re(p1=p2) = 0

Question 35

Marginally Stable

Answer 35

Real part of non-repeated pole is zero, Re(p_n) =0

Question 36

BIBO stability

Answer 36

Real part for all poles in net transfer function are less than 0
If all subsystems are internally stable –> BIBO stable
but BIBO stable does not mean all subs are internally stable

Question 37

BIBO Steps

Answer 37

1. Derive net transfer function
2. Determine Poles of Net Transfer function
3. Investigate values of k which make system stable

Question 38

Gain

Answer 38

G = lim (s->0) H(s)

Question 39

Single frequency response

Answer 39

1. H(s) -> H(jw), s = jw
2. |H(jw)|
3. <H(jw)

Question 40

Bode Plot Practice

Answer 40

Graph practice