MODULE 1

Question 1

CONTINUOUS TIME SIGNAL

Answer 1

• This is a signal whose independent variable is time “t”.

Question 2

DISCRETE-TIME SIGNAL

Answer 2

• This is a signal whose independent variable is discrete-time “n”.

Question 3

a. AMPLITUDE SCALING

Answer 3

y(t)=∝x(t)

NOTE: If ∝>1; the signal is amplified
if ∝<1; the signal is attenuated

Question 4

b. AMPLITUDE REVERSAL

Answer 4

y(t)=-x(t)

NOTE: the signal gets flipped with respect to the time axis.

Question 5

c. AMPLITUDE MODULUS

Answer 5

y(t)=|x(t)|

NOTE: The part of the signal below the time axis gets flipped upwards.

Question 6

d. ADDING AND SUBTRACTING CONSTANTS

Answer 6

y(t)=x(t)±k

NOTE: If K is positive, the signal is shifted k units upwards
If K is negative, the signal is shifted k units downward.

Question 7

a. TIME SHIFTING

Answer 7

y(t)=x(t-k):DELAY;RIGHT SHIFT
y(t)=x(t+k):ADVANCE;LEFT SHIFT

Question 8

b. TIME SCALING

Answer 8

y(t)=x(∝t):COMPRESSION
y(t)=x(t/∝):EXPANSION
NOTE: COMPRESSION- divide time by ∝
EXPANSION- multiply time by ∝

Question 9

c. TIME FOLDING

Answer 9

y(t)=x(-t)
NOTE: Flip graph horizontally

Question 10

1. SCALING PROPERTY

Answer 10

δ(-at+b)= 1/|a| δ(t-b/a)

Question 11

2. INTEGRAL

Answer 11

∫_(-∞)^∞▒〖δ(t)dt=1 〗

Question 12

3. SAMPLING PROPERTY

Answer 12

x(t)δ(t-k)=x(k)δ(t-k)

Question 13

4. SIFTING PROPERTY

Answer 13

∫_(-∞)^∞▒〖x(t)δ(t-k)dt=x(k)〗

Question 14

6. Time Scaling PROPERTY

Answer 14

u(∝t)=u(t)

Question 15

ENERGY

Answer 15

∫_(-∞)^∞▒〖|x(t)|^2 dt 〗

Question 16

POWER

Answer 16

1/T ∫_T^∞▒〖|x(t)|^2 dt 〗

Question 17

TRIANGULAR

Answer 17

E=(a^2 b)/3

Question 18

SQUARE

Answer 18

〖E= a〗^2 b

Question 19

CURVE

Answer 19

E=(a^2 b)/2

Question 20

∫_0^∞▒〖〖ae〗^(-bt) 〗

Answer 20

a/b

Question 21

V_RMS

Answer 21

√P

Question 22

(t-k)u(t-k)

Answer 22

r(t-k)

Question 23

f(∝t)

Answer 23

E/∝

Question 24

f(t/∝)

Answer 24

|∝|E

Question 25

f(t±k)

Answer 25

E

Question 26

∝f(t)

Answer 26

∝^2 E

Question 27

g(∝t)

Answer 27

P

Question 28

g(t/∝)

Answer 28

P

Question 29

g(t±k)

Answer 29

P

Question 30

∝g(t)

Answer 30

∝^2 P

Question 31

ENERGY IN DT

Answer 31

∑_(-N)^N▒|x(n)|^2

Question 32

POWER IN DT

Answer 32

1/(2N+1) ∑_(-N)^N▒|x(n)|^2

Question 33

1. SUMMATION

Answer 33

∑_(N=∞)^∞▒〖δ(n)=1〗

Question 34

2. TIME SCALING IN UNIT IMPULSE

Answer 34

δ(∝n)= δ(n)

Question 35

4. MIXED OPERATIONS

Answer 35

δ(an+b)= δ(n+b/a) NOTE: b/a∈Integer

Question 36

5. SUMMATION PROPERTY

Answer 36

∑_(N=n_1)^(n_2)▒〖x(n)δ(n-k)=1〗 NOTE: k ∈ n_1& n_2

Question 37

6. SAMPLING PROPERTY

Answer 37

x(n)δ(n-k)=x(k) or 0

Question 38

EVEN SIGNAL

Answer 38

x_e (t)=(x(t)+x(-t))/2

Question 39

ODD

Answer 39

x_o (t)=(x(t)-x(-t))/2

Question 40

RECTANGULAR SIGNAL

Answer 40

x(t)=ARect(t/T)

Question 41

TRIANGULAR SIGNAL

Answer 41

x(t)=ATri(t/T)

Question 42

SINC SIGNAL

Answer 42

sinc(t)=((sin(πt))/(π(t)))

Question 43

SAMPLING SIGNAL

Answer 43

sa(t)=((sin(t))/t)

Question 44

f_o

Answer 44

1/T_o

Question 45

〖ω〗_o

Answer 45

2π/T_o

Question 46

T_o

Answer 46

2π/ω_o