OBSOLETE

AD9853

–20–

REV. C

cos(2

f t)df

..

.

.

BW

0

h1(t) :=

R := 6

f

BW,

.

SRRC (f) if

.

H(0,R)

H

f

FreqScale

,R

,1

MODIFICATION OF SQUARE-ROOT RAISED COSINE (SRRC) FIR FILTER RESPONSE

TO COMPENSATE FOR CASCADED INTEGRATOR-COMB (CIC) FILTER RESPONSE

COMPUTE SRRC FILTER COEFFICIENTS:

...MAP THE FILTER TAP INDEX TO TIME DOMAIN (CENTERED AT t = 0)

...INVERSE FOURIER INTEGRAL COMPUTES SRRC IMPULSE RESPONSE

(TIME DOMAIN) FROM THE SRRC FREQUENCY RESPONSE (FREQUENCY DOMAIN).

THE COS() FUNCTION REPLACES THE NORMAL COMPLEX EXPONENTIAL

BECAUSE WE ARE RESTICTED TO REAL FILTER COEFFICIENTS.

...SRRC FILTER COEFFICIENTS INTEGERIZED AND SCALED

COMPUTE SRRC FILTER COEFFICIENTS MODIFIED

FOR CORRECTION OF CIC RESPONSE:

...CIC INTERPOLATION RATIO (USER PROGRAMMABLE)

...INVERSE FOURIER INTERGRAL MODIFIES THE SRRC RESPONSE

BY THE RECIPROCAL OF THE NORMALIZED CIC FREQUENCY

RESPONSE. THE MODIFICATION IS ONLY PERFORMED OVER THE

FRACTION OF THE SRRC BANDWIDTH AS SPECIFIED BY

.

...MODIFIED SRRC FILTER COEFFICIENTS INTEGERIZED AND SCALED TO 10-BIT RANGE

SRRC AND MODIFIED SRRC IMPULSE RESPONSE

...FIR FILTER COEFFICIENTS

FOR SRRC RESPONSE

...FIR FILTER COEFFICIENTS

FOR SRRC RESPONSE

WITH CIC COMPENSATION

DISPLAY FREQUENCY RESPONSE PLOTS:

f:= 0,0.001.. 0.5

...NORMALIZED FREQUENCY RANGE [A REQUIREMENT OF MATHCAD'S GAIN() FUNCTION]

...SCALE FACTORS TO ADJUST SRRC,

COMPENSATED SRRC, AND CIC

FREQUENCY RESPONSES TO UNITY AT f = 0

...FUNCTION TO COMPUTE NORMALIZED, UNCOMPENSATED FIR RESPONSE (SRRC) IN dB

...FUNCTION TO COMPUTE NORMALIZED CIC RESPONSE IN dB

...FUNCTION TO COMPUTE OVERALL SYSTEM RESPONSE OF SRRC AND CIC TOGETHER IN dB

...FUNCTION TO COMPUTE OVERALL SYSTEM RESPONSE OF COMPENSATED SRRC AND CIC TOGETHER

SRRC, CIC, AND CORRECTED SRRC RESPONSE

10

5

0

15

20

25

30

35

40

TAP

500

0

FREQUENCY SCALE – fn

0

0

–20

–40

–60

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

FIR(f)

CIC(f)

COMP(f)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

0

0

3

2

–2

–5

–2

5

7

1

–7

–7

7

19

7

–34 –71 –48

71

260 438 511

hT =

h1T =

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

0

14

2

–3

–6

–1

7

9

1

–10 –9

8

24

12

–34 –78 –61

56

251 435 511

tap := 0..TAPS – 1

1

FreqScale

tap –

TAPS – 1

2

.

BW

0

h(t) :=

SRRC(f) cos(2

f t)df

..

.

.

htap := h(ttap) h := INT

h PROC_GAINSCALE

max(h)

.

h1tap := h1(ttap)

h1 := INT

h1 PROC_GAINSCALE

max(h1)

.

.

.

.

FIR(f) := dB(SCALEsrrc | gain(h,f) |)

.

CIC(f) := dB(SCALEcic | H(f,R) |)

.

COMP(f) := dB(SCALEcompsrrc | gain(h1,f) |)

.

SYSuncomp(f) := FIR(f) + CIC(f)

SYScomp(f) := COMP(f) + CIC(f)

Figure 34. Mathcad Simulation of 41-Tap SRRC Filter with CIC Compensation