Lecture 23
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Assignment 4 (review) COMMUNICATION SYSTEMS
Transmitter π (i − 1) ⎤ ⎡ , s i (t ) = cos ⎢ 2π f c t + 2 ⎥⎦ ⎣
Lecture # 23 2nd
May 2007
i = 1, 2 ,3, 4 0 ≤ t ≤ Ts
The four symbols are s1,3 (t ) = ± cosωct , φ − shift o f 00 and 1800
Instructor
WASEEM KHAN
s2, 4 (t ) = ± sin ω c t , φ − shift o f 900 and 2700
Centre for Advanced Studies in Engineering
Transmitter (another possible symbol set) π (i − 1) π ⎤ ⎡ + ⎥, s i (t ) = cos ⎢ω c t + 2 4⎦ ⎣
i = 1, 2 ,3, 4 0 ≤ t ≤ Ts
This expression can be expanded as ⎡ π (i − 1) π ⎤ ⎡ π (i − 1) π ⎤ si (t ) = A cos ⎢ + ⎥ cos(ω c t ) − A sin ⎢ + ⎥ sin(ω c t ) 4⎦ 4⎦ ⎣ 2 ⎣ 2
In-phase part
i 1 2 3 4
⎡ π (i − 1) π ⎤ cos ⎢ + ⎥ 4⎦ ⎣ 2
0.707 -0.707 -0.707 0.707
Quadrature part ⎡ π (i − 1) π ⎤ sin ⎢ + ⎥ 4⎦ ⎣ 2
0.707 0.707 -0.707 -0.707
Quadrature Modulator
Example Run of QPSK Modulator I baseband 1 0.5 0
Baseband I and Q parts
Input bitstream
-0.5 -1
0
0.01
0.02
0.03
0.04 0.05 0.06 time(seconds) Q baseband
0.07
0.08
0.09
0.1
0
0.01
0.02
0.03
0.04 0.05 0.06 time(seconds)
0.07
0.08
0.09
0.1
1
1
0
1 0.5 0 -0.5 -1
bits =
I bandpass 1 0.5 0
Bandpass I and Q parts
-0.5 -1
0
0.01
0.02
0.03
0.04 0.05 0.06 time(seconds) Q bandpass
0.07
0.08
0.09
0.1
0
0.01
0.02
0.03
0.04 0.05 0.06 time(seconds)
0.07
0.08
0.09
0.1
1 0.5 0 -0.5 -1
1 0.5 0 -0.5 -1
0
0.05 time(seconds)
0.1
0
0
1
1
1
1
0
Transmitter π (i − 1) ⎤ ⎡ , s i (t ) = cos ⎢ 2π f c t + 2 ⎥⎦ ⎣
Lecture # 23 2nd
May 2007
i = 1, 2 ,3, 4 0 ≤ t ≤ Ts
The four symbols are s1,3 (t ) = ± cosωct , φ − shift o f 00 and 1800
Instructor
WASEEM KHAN
s2, 4 (t ) = ± sin ω c t , φ − shift o f 900 and 2700
Centre for Advanced Studies in Engineering
Transmitter (another possible symbol set) π (i − 1) π ⎤ ⎡ + ⎥, s i (t ) = cos ⎢ω c t + 2 4⎦ ⎣
i = 1, 2 ,3, 4 0 ≤ t ≤ Ts
This expression can be expanded as ⎡ π (i − 1) π ⎤ ⎡ π (i − 1) π ⎤ si (t ) = A cos ⎢ + ⎥ cos(ω c t ) − A sin ⎢ + ⎥ sin(ω c t ) 4⎦ 4⎦ ⎣ 2 ⎣ 2
In-phase part
i 1 2 3 4
⎡ π (i − 1) π ⎤ cos ⎢ + ⎥ 4⎦ ⎣ 2
0.707 -0.707 -0.707 0.707
Quadrature part ⎡ π (i − 1) π ⎤ sin ⎢ + ⎥ 4⎦ ⎣ 2
0.707 0.707 -0.707 -0.707
Quadrature Modulator
Example Run of QPSK Modulator I baseband 1 0.5 0
Baseband I and Q parts
Input bitstream
-0.5 -1
0
0.01
0.02
0.03
0.04 0.05 0.06 time(seconds) Q baseband
0.07
0.08
0.09
0.1
0
0.01
0.02
0.03
0.04 0.05 0.06 time(seconds)
0.07
0.08
0.09
0.1
1
1
0
1 0.5 0 -0.5 -1
bits =
I bandpass 1 0.5 0
Bandpass I and Q parts
-0.5 -1
0
0.01
0.02
0.03
0.04 0.05 0.06 time(seconds) Q bandpass
0.07
0.08
0.09
0.1
0
0.01
0.02
0.03
0.04 0.05 0.06 time(seconds)
0.07
0.08
0.09
0.1
1 0.5 0 -0.5 -1
1 0.5 0 -0.5 -1
0
0.05 time(seconds)
0.1
0
0
1
1
1
1
0
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