AD9853 Analog Devices, AD9853 Datasheet - Page 18

• Manufacturer Part Number: AD9853
• Description: Programmable Digital OPSK/16-QAM Modulator
• Manufacturer: Analog Devices

AD9853
COMPUTE AND PLOT SRRC FILTER COEFFICIENTS:
tap := 0..TAPS – 1
h(t) :=
h tap := h(t tap )
COMPUTE AND PLOT SRRC FREQUENCY RESPONSE:
freq_pts := 250
n := 0..freq_pts – 1
K := (| gain(h,0) |)
GLOBAL DECLARATIONS
CONSTANTS:
FUNCTIONS:
dB(x)
SRRC(f)
0
BW
PROC_GAIN
SCALE
TAPS
FreqScale
InRange (x,a,b)
INT(x)
BW
0.5
500
–20
–40
–60
0.5 (1 + )
0
0
SRRC(f) cos(2
41
if (| x | = 0, 200, 20 log (| x |))
h := INT
0
0
floor (x + 0.5)
.
511
t
passband
stopband
0 otherwise
if InRange (f, 0, stopband)
tap
–1
4
f :=
h T =
1 if InRange (f, 0, passband)
cos
:=
1
H n := K | gain (h,f n ) |
.
f n := f n
(x
FreqScale
h SCALEPROC GAIN
freq_pts – 1
.
4 .
0
1
a) . (x
0.5
0.2
.
.
.
0.5 (1 + )
0.5 (1 – )
0
0
max(h)
.
. .
.
5
f t)df
(2 f +
.
.
3
b)
.
1
tap –
SQUARE-ROOT RAISED COSINE (SRRC) FIR FILTER
2
2
– 1) if InRange (f, passband, stopband)
Figure 33. Mathcad Simulation of a 41-Tap SRRC Filter
0.4
TAPS – 1
–2
...DEFINE NUMBER OF FREQUENCY POINTS AND FREQUENCY STEP SIZE (FOR PLOTTING PURPOSES)
...CREATE VECTOR OF UNIFORMLY SPACED FREQUENCY POINTS {f max = 0.5; A REQUIREMENT OF THE GAIN() FUNCTION},
...NORMALIZED FREQUENCY RESPONSE
3
2
...RETURNS 1 IF a <= x <= b, 0 OTHERWISE
...RETURNS NEAREST INTEGER TO x
...RATIO TO DECIBEL CONVERSION FUNCTION
10
...EXCESS BANDWIDTH FACTOR FOR SRRC FREQUENCY RESPONSE
...BANDWIDTH OF SRRC FILTER (RELATIVE TO SYMBOL RATE)
...PROCESSING GAIN OF CIC FILTERS (USED TO CORRELATE RESULTS WITH AD9853 EVAL. BD.)
...SETS MAX VALUE OF SRRC FILTER BASED ON FINITE WORD SIZE
...NUMBER OF FIR PULSE SHAPING FILTER TAPS
...UPSAMPLING RATIO OF FIR PULSE SHAPING FILTER (RELATIVE TO THE SYMBOL RATE)
...SRRC FREQUENCY RESPONSE FUNCTION
–5
(f IS RELATIVE TO THE SYMBOL RATE)
4
...MAP THE FILTER TAP INDEX TO TIME DOMAIN (CENTERED AT T=0)
...INVERSE FOURIER INTEGRAL COMPUTE SRRC IMPULSE RESPONSE (TIME DOMAIN) FROM
...SRRC FILTER COEFFICIENTS INTEGERIZED AND SCALED
–2
SRRC NORMALIZED FREQUENCY RESPONSE
0.6
THE SRRC FREQUENCY RESPONSE (FREQUENCY DOMAIN). THE COS() FUNCTION REPLACES
THE NORMAL COMPLEX EXPONENTIAL BECAUSE WE ARE RESTRICTED TO REAL
5
FILTER COEFFICIENTS.
5
6
15
7
7
SRRC IMPULSE RESPONSE
0.8
8
1
FREQUENCY SCALE – f n
–7
FREQUENCY SCALED TO SYMBOL RATE
9
–18–
–7
10
TAP
20
1.0
11
7
12
19
13
7
1.2
25
–34 –71 –48
14
15
1.4
16
17
71 260 438 511
30
18
1.6
19
20
35
...FIR FILTER
COEFFICIENTS
1.8
40
2.0
REV. C