MODULE 1 Flashcards
CONTINUOUS TIME SIGNAL
- This is a signal whose independent variable is time “t”.
DISCRETE-TIME SIGNAL
- This is a signal whose independent variable is discrete-time “n”.
a. AMPLITUDE SCALING
y(t)=∝x(t)
NOTE: If ∝>1; the signal is amplified
if ∝<1; the signal is attenuated
b. AMPLITUDE REVERSAL
y(t)=-x(t)
NOTE: the signal gets flipped with respect to the time axis.
c. AMPLITUDE MODULUS
y(t)=|x(t)|
NOTE: The part of the signal below the time axis gets flipped upwards.
d. ADDING AND SUBTRACTING CONSTANTS
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.
a. TIME SHIFTING
y(t)=x(t-k):DELAY;RIGHT SHIFT
y(t)=x(t+k):ADVANCE;LEFT SHIFT
b. TIME SCALING
y(t)=x(∝t):COMPRESSION
y(t)=x(t/∝):EXPANSION
NOTE: COMPRESSION- divide time by ∝
EXPANSION- multiply time by ∝
c. TIME FOLDING
y(t)=x(-t)
NOTE: Flip graph horizontally
- SCALING PROPERTY
δ(-at+b)= 1/|a| δ(t-b/a)
- INTEGRAL
∫_(-∞)^∞▒〖δ(t)dt=1 〗
- SAMPLING PROPERTY
x(t)δ(t-k)=x(k)δ(t-k)
- SIFTING PROPERTY
∫_(-∞)^∞▒〖x(t)δ(t-k)dt=x(k)〗
- Time Scaling PROPERTY
u(∝t)=u(t)
ENERGY
∫_(-∞)^∞▒〖|x(t)|^2 dt 〗
POWER
1/T ∫_T^∞▒〖|x(t)|^2 dt 〗
TRIANGULAR
E=(a^2 b)/3
SQUARE
〖E= a〗^2 b
CURVE
E=(a^2 b)/2
∫_0^∞▒〖〖ae〗^(-bt) 〗
a/b
V_RMS
√P
(t-k)u(t-k)
r(t-k)
f(∝t)
E/∝
f(t/∝)
|∝|E
f(t±k)
E
∝f(t)
∝^2 E
g(∝t)
P
g(t/∝)
P
g(t±k)
P
∝g(t)
∝^2 P
ENERGY IN DT
∑_(-N)^N▒|x(n)|^2
POWER IN DT
1/(2N+1) ∑_(-N)^N▒|x(n)|^2
- SUMMATION
∑_(N=∞)^∞▒〖δ(n)=1〗
- TIME SCALING IN UNIT IMPULSE
δ(∝n)= δ(n)
- MIXED OPERATIONS
δ(an+b)= δ(n+b/a)
NOTE: b/a∈Integer
- SUMMATION PROPERTY
∑_(N=n_1)^(n_2)▒〖x(n)δ(n-k)=1〗
NOTE: k ∈ n_1& n_2
- SAMPLING PROPERTY
x(n)δ(n-k)=x(k) or 0
EVEN SIGNAL
x_e (t)=(x(t)+x(-t))/2
ODD
x_o (t)=(x(t)-x(-t))/2
RECTANGULAR SIGNAL
x(t)=ARect(t/T)
TRIANGULAR SIGNAL
x(t)=ATri(t/T)
SINC SIGNAL
sinc(t)=((sin(πt))/(π(t)))
SAMPLING SIGNAL
sa(t)=((sin(t))/t)
f_o
1/T_o
〖ω〗_o
2π/T_o
T_o
2π/ω_o
