1. Triangular Wave Function
โข The triangular wave function with period 2a is define by
f(t) = t = 2a-t 0 < t < a
a < t < 2a
F(t)
a0 2a
a
3a 4a
2. โข Express the Fourier Series
for a triangular waveform?
โข Express the Fourier Series
for a triangular waveform
that is amplitude shifted
down by โX0/2 ? Plot the
signal.
To
Xo
To
Xo/2
-Xo/2
3. โข Express the Fourier Series for a
triangular waveform?
โข Express the Fourier Series for a
triangular waveform that is
amplitude shifted down by โX0/2
? Plot the signal.
๏จ ๏ฉ
tkj
oddk
oo o
e
k
XX
tx ๏ท
๏ฐ
๏ฅ
๏ฅ
๏ญ๏ฅ๏ฝ
๏ญ
๏ซ๏ฝ
/
2
2
2
)(
To
Xo
To
Xo/2
-Xo/2
5. What Is โHALF WAVE SINE FUNCTION?โ
๏A Sine wave or Sinusoid is a curve that
describes smooth repetitive oscillation.
๏Half Wave Sine Function is the representation
of positive part of the sine function.
6. HALF WAVE RECTIFIED SINUSOIDAL
FUNCTION...
๏It has a period of 2โ(Pi).
๏It is defined as a function of f(x) with period
2๐,
โขF(x) = { sinx 0<x<๐
=0 ๐ <x<2 ๐ }
โขF(x+2๐) =f(x)
7. The triangular wave rectified sinusoidal function with period ๐
is define by
f(t) = a sin t 0 < t < ๐
F(t)
a
0 ๐ 2๐
Full Wave Rectified Sinusoidal Function
9. is not an orthogonality interval for both sines and cosines
.0
,
1
22
)(cossin
2
2
0
oddn
evenn
n
ttdntan
๏ฝ๏ฝ
๏ฝ
๏ญ
๏ญ๏ฝ
๏ฝ ๏ฒ
๏ฐ
๏ท๏ท๏ท
๏ฐ
๏ฐ
Note carefully that ๏ ๏๏ฐ,0
together and we do not get zero for even n. The resulting series is
.
1
cos42
)(
,6,4,2
2๏ฅ
๏ฅ
๏ฝ ๏ญ
๏ญ๏ฝ
๏n n
tn
tf
๏ท
๏ฐ๏ฐ