Frequency Modulation.ppt

Chapter 21
Frequency Modulation
GMSK Modulation
DSP C5000
Copyright © 2003 Texas Instruments. All rights reserved.

ESIEE, Slide 2
Learning Objectives
 Overview of Digital Modulation
 Understanding GMSK Modulation
 Learning how to Implement a GMSK
Modulator on a C54

ESIEE, Slide 3
Digital Modulations
 Baseband and bandpass signalling are used to
transmit data on physical channels such as
telephone cables or radiofrequency channels.
 The source of data (bits or symbol) may be a
computer file or a digitized waveform (speech,
video…)
 The transmitted signal carries information about
the data and its characteristic changes at the same
rate as the data.
 When the signal carrying the data information
 Extends from 0 Hz upwards, the term baseband
signalling is used.
 Has its power centered on a central frequency fc,
the term bandpass signalling or modulation is
used.

ESIEE, Slide 4
Digital Modulation
 Modulation is used because:
 The channel does not include the 0 Hz
frequency and baseband signalling is
impossible
 The bandwidth of the channel is split
between several channels for frequency
multiplexing
 For wireless radio-communications, the
size of the antenna decreases when the
transmitted frequency increases.

ESIEE, Slide 5
Carrier Frequency
 In simple modulation schemes, a single
frequency signal, the carrier, is modified
at the rate of the data.
 The carrier is commonly written as:
 
cos 2 c
A f t
  
fc= Carrier frequency
A = Carrier Amplitude
 = Carrier phase
 The 3 main parameters of the carrier:
amplitude, phase and frequency can be
modified to carry the information
leading to: amplitude, phase and
frequency modulation.

ESIEE, Slide 6
Digital Modulation
 CPM: Continuous Phase Modulation
 Frequency or phase modulation
 Example: MSK, GMSK
 Characteristic: constant envelope modulation
 QAM: Quadrature Amplitude Modulation
 Example: QPSK, OQPSK, 16QAM
 Characteristic: High spectral efficiency
 Multicarrier Modulation
 Example: OFDM, DMT
 Characteristic: Muti-path delay spread tolerance,
effectivness against channel distortion

ESIEE, Slide 7
What is the Complex Envelope z(t) of a
Modulated Signal x(t) ?
     .
2
sin
)
(
2
)cos
(
)
(
)
( 2
t
f
t
z
t
f
t
z
e
t
z
t
x c
Q
c
I
t
f
j c







fc= Carrier frequency
  2 ( )
( ) ( ) ( ) ( ) ( ) ( )
c
j f t j t
H I Q
z t x t jx t e z t jz t A t e

 
    
z(t) = Complex envelope of x(t)
zI(t), zQ(t) are the baseband components
xH(t) = Hilbert transform of x(t) = x(t) with a phase shift of /2
 .
)
(
)
(
2
1
)
( c
z
c
z
x f
f
S
f
f
S
f
S 



Sx(f) = Power spectral density of x(t)

ESIEE, Slide 8
Complex Envelope z of a Modulated Signal x
Frequency Domain
0
1
2
0
1
2
0
1
2
f
f
f
X(f)
Xa(f)
Z(f)
2
1
2

ESIEE, Slide 9
GMSK Modulation
 Gaussian Minimum Shift Keying.
 Used in GSM and DECT standards.
 Relevant to mobile communications
because of constant envelope
modulation:
 Quite insensitive to non-linearities of power
amplifier
 Robust to fading effects
 But moderate spectral efficiency.

ESIEE, Slide 10
What is GMSK Modulation?
 Continuous phase digital frequency
modulation
 Modulation index h=1/2
 Gaussian Frequency Shaping Filter
 GMSK = MSK + Gaussian filter
 Characterized by the value of BT
 T = bit duration
 B = 3dB Bandwidth of the shaping filter
 BT = 0.3 for GSM
 BT = 0.5 for DECT

ESIEE, Slide 11
GMSK Modulation, Expression for the
Modulated Signal x(t)
 
( ) cos 2 ( ) with:
( ) 2 ( )
c
t
k
k
x t f t t
t h a s kT d

  



  
  


2
1
)
( 





 d
s
Normalization
ak = Binary data = +/- 1
h = Modulation index = 0.5
s(t) = Gaussian frequency shaping filter
s(t)= Elementary frequency pulse

ESIEE, Slide 12
GMSK Elementary Phase Pulse
Elementary phase pulse = ( )
( ) 2 ( ) 2 ( ) .
t
t
t hq t h s d

    

  
( ) ( ) .
t
q t s d
 

 
 
 
For ,( 1) ( ) 2 ( ) ( )
( ) cos 2 ( ) cos 2 ( ) .
n n
k k
k k
n
c c k
k
t nT n T t h a q t kT a t kT
x t f t t f t a t kT
 
  
 

      
 
     
 
 
 


ESIEE, Slide 13
Architecture of a GMSK Modulator
Coder
Bits ak
r t
( ) VCO
h
x t
( )
h t
( )
Gaussian filter
GMSK modulator using a VCO
 
k
k
a s t kT


 
k
k
a t kT
 

( ) ( )* ( )
s t r t h t

Rectangular filter
x t
( )
Coder
Bits ak
s t
( )
2h
 

t
 ( )
t
cos()
sin()
+
-
s t r t h t
( ) ( )* ( )

GMSK modulator without VCO
 
k
k
a t kT
 

 
cos 2 c
f t

 
sin 2 c
f t


ESIEE, Slide 14
Equation for the Gaussian Filter h(t)
2 2
2
2
2
2 2
( ) exp
ln(2) ln(2)
ln(2)
( ) exp
2
B
h t B t
H f f
B
 
 
 
 
 
 
 
 
 
The duration MTb of the gaussian pulse
is truncated to a value inversely
proportional to B.
BT = 0.5, MTb = 2Tb
BT = 0.3, MTb = 3 or 4Tb

ESIEE, Slide 15
Frequency and Phase Elementary Pulses
-2 -1 0 1 2
0
0.1
0.2
0.3
0.4
0.5 BT
b

BT
b
05
,
BT
b
03
,
t in number of bit periods Tb
T g t
b ( ) Elementary frequency pulse
-2 -1 0 1 2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
t in number of bit period Tb
BT b
 
BT
b
 0 3
.
BT
b
 0 5
.
Elementary phase pulse
 ( )
t
/2
The elementary frequency pulse is
the convolution of a square pulse
r(t) with a gaussian pulse h(t).
Its duration is (M+1)Tb.

ESIEE, Slide 16
GMSK Signals
Binary sequence
GMSK modulated Signal
 ( )
t
 
z t t
I ( ) cos ( )
 
 
z t t
Q ( ) sin ( )
 
5
1
0 5 10 15 20
-1
0
1
0 5 10 15 20
-1
0
1
t
0 5 10 15 20
1
-1
0 t
0 5 10 15 20
-5
0 t
0 5 10 15 20
-1
0 t
t
in rd

ESIEE, Slide 17
Power Spectral Density of GMSK Signals
0 0.5 1 1.5 2 2.5 3 3.5 4
-140
-120
-100
-80
-60
-40
-20
0
20
Power spectral density of the complex envelope of GMSK, BT=0.3, fe=8, T=1.
Logarithmic scale
Frequency normalized by 1/T

ESIEE, Slide 18
Implementing a GMSK Modulator on a DSP
 Quadrature modulation can be used:
 The DSP calculates the phase  and the 2
baseband components zI and zQ and sends
them to the DAC.
 Or a modulated loop can be used.
 In this case, the DSP generates the
instantaneous frequency finst signal that is
sent to the DAC.
inst ( ).
k
k
f h a s kT



 


ESIEE, Slide 19
Calculation of the Instantaneous Frequency
 finst is obtained by a simple filtering of
the bit sequence ak by a FIR filter of
impulse response s(n).
Open Matlab routine
pul_phas.m to calculate s(n).
Explanation of parameters are
given in following slides.

ESIEE, Slide 20
Expression for the Baseband Components
 The baseband components zI and zQ are
modulated in amplitude by the 2
quadrature carriers.
         
( ) cos 2 ( ) cos ( ) cos 2 sin ( ) sin 2
c c c
x t f t t t f t t f t
  
      
   
( ) ( )cos 2 ( )sin 2
I c Q c
x t z t f t z t f t
 
 

ESIEE, Slide 21
 Baseband components
 The carriers are generally RF analog
signals generated by analog oscillators
 However, we will show how they could
be generated digitally if the value of fc
were not too high.
Baseband Components and Carriers
 
 
( ) cos ( )
( ) sin ( )
I
Q
z t t
z t t
 
 
 
 
I
Q
Carrier cos 2
Carrier sin 2
c
c
f t
f t





ESIEE, Slide 22
Calculation of the Baseband
Components on a DSP
 Calculate the phase  at time mTS
 Ts the sampling frequency.
 Read the value of cos() and sin()
from a table.
 
For ,( 1) ( ) ( ).
( ) ( ).
n
k
k
n
S k S
k
t nT n T t a t kT
mT a mT kT




    
  



ESIEE, Slide 23
Calculation of the Elementary Pulse Phase
with Matlab
 The elementary pulse phase (mTS) is
calculated with Matlab and stored in
memory.
 The duration LT of the evolutive part of
(mTS) depends on the value of BT.
  is called phi in the matlab routine.
( ) 2 ( )
( ) 0 0
( )
t
t h s d
t t
t h t LT
   

 


  
  


ESIEE, Slide 24
with Matlab 1/2
function [phi,s]=pul_phas(T_over_Ts,L,BT,T)
Ts=T/ T_over_Ts ;
% calculates the number of samples in phi in the interval 0 - LT
Nphi=ceil(T_over_Ts*L);
% calculates the number of samples in T
Nts=ceil(T_over_Ts);
phi=zeros(1,Nphi);
s=zeros(1,Nphi);
sigma=sqrt(log(2))/2/pi/(BT/T)
Open Matlab
routine
pul_phas.m
Beginning of the matlab routine

ESIEE, Slide 25
with Matlab 2/2
t=[-L*T/2:Ts:L*T/2];
t=t(1:Nphi);
ta=t+T/2;
tb=t-T/2;
Qta=0.5*(ones(1,Nphi)+erf(ta/sigma/sqrt(2)));
Qtb=0.5*(ones(1,Nphi)+erf(tb/sigma/sqrt(2)));
expta=exp(-0.5*((ta/sigma).^2))/sqrt(2*pi)*sigma;
exptb=exp(-0.5*((tb/sigma).^2))/sqrt(2*pi)*sigma;
phi=pi/T/2*(ta.*Qta+expta-tb.*Qtb-exptb);
s=1/2/T*(Qta-Qtb);
End of the matlab routine

ESIEE, Slide 26
Using the Matlab Routine
 Start Matlab
 Use:
 T_over_Ts=8
 L=4
 T=1
 BT=0.3
 call the routine using to calculate the
phase pulse phi ( ) and the pulse s:
 [phi,s]=pul_phas(T_over_Ts,L,BT,T)
 Plot the phase phi and the shaping pulse s
 plot(phi)
 plot(s)

ESIEE, Slide 27
Results of Matlab Routine

ESIEE, Slide 28
Results for phi
 For L=4 and T_over_Ts=8, we obtain 32
samples for phi. Matlab gives the
following values for phi:
 Phi= [0.0001, 0.0002, 0.0005, 0.0012, 0.0028,
0.0062, 0.0127, 0.0246, 0.0446, 0.0763, 0.1231,
0.1884, 0.2740, 0.3798, 0.5036, 0.6409, 0.7854,
0.9299, 1.0672, 1.1910, 1.2968, 1.3824, 1.4476,
1.4945, 1.5262, 1.5462, 1.5581, 1.5646, 1.5680,
1.5696, 1.5703, 1.5706]
 After this evolutive part of phi, phi stays
equal to /2 (1.57).
 To calculate , the evolutive part and
the constant part of the elementary
phase pulse phi are treated separately.

ESIEE, Slide 29
 
1
1 1
For ,( 1)
( ) ( ) ( ) ( ) with:
( ) 0 0
( )
2
( ) ( ) phimem( ) ( )
2
n n L n
k k k
k k k n L
n L n n
k k k
k k n L k n L
t nT n T
t a t kT a t kT a t kT
t t
h
t h t LT
t a a t kT n a t kT
  

 

 

    

      
 
      
  
   
      
  
  
Calculation of 
 Separation of evolutive and constant
parts of phi.

ESIEE, Slide 30
Memory Part and Evolutive Part of 
 
For ,( 1)
phimem( ) phimem( 1) ( ) .
2
t nT n T
n n a n L

 
   
1
1
( ) phimem( ) ( )
( ) phimem( ) ( )
n
k
k n L
S
n
S k S
k n L
t n a t kT
t mT
mT n a mT kT


  
  
   

   



ESIEE, Slide 31
Recursive Calculation of 
 Names of variables
 Phase = 
 phi = array of evolutive part of ,
 Nphi samples = LT/Ts
 Ns = number of samples per bit = T/Ts
 an = binary sequence (+/- 1)
 2 calculation steps:
 Calculate 
 Calculate zI=cos() and zQ=sin() by table
reading

ESIEE, Slide 32
Calculation of : Initialization
 Initialization step:
 L first bit periods, phimem = 0
 At bit L+1, phimem is set to a1 /2.
 Principle of the initialization processing:
 FOR i=1 to i=L
 for j=(i-1)Ns+1 to j=(i-1)Ns+Nphi
 phase((i-1)Ns+j)= phase((i-1)Ns+j)+phi(j)an(i)
 Endfor
 endFOR
 phimem=an(1) /2

ESIEE, Slide 33
Calculation of : After Initialization
 FOR i=L+1 to last_bit
 For j=(i-1)Ns+1 to j=(i-1)Ns+Nphi
 phase((i-1)Ns+j)= phase((i-1)Ns+j)+phi(j)an(i)
 endFor
 For j=(i-1)Ns+1 to j=i Ns
 phase((i-1)Ns+j)= phase((i-1)Ns+j)+phimem
 xi=cos(phase(i-1)Ns+j)
 xq=sin(phase((i-1)Ns+j)
 endFor
 phimem=phimem+pi/2 an(i+1-L)
 endFOR

ESIEE, Slide 34
Coding and Wrapping the Phase Table
 The phase value in [-,[ is represented
by the 16-bit number Iphase
 Minimum phase = -, Iphase = -215.
 Maximum phase = (1-215), Iphase = 215-1.
15
2 phase
Iphase



ESIEE, Slide 35
Index for the table in Phase Calculation
 Phase increment between 2 table values:
 2 / Ncos and on Iphase 216/Ncos
 For Iphase, the index of the table is:
 i= Ncos Iphase 2-16
 Here Ncos 2-16 = 2-9,
 So the index in the table is given by shifting
Iphase 9 bits to the right.

ESIEE, Slide 36
Coding of phi
 The quantized values of phi can be
obtained with Matlab:
 phi= round(phi*2^15/pi);
 phi is defined and initialized in the file
phi03.asm as:
.ref phi
.sect "phi"
phi .word 1,2,5,13,29,65,133,256
.word 465,795,1284,1965,2858,3961,5252,6685
.word 8192,9699,11132,12423,13526,14419,15100,15589
.word 15919,16128,16251,16319,16355,16371,16379,16382

ESIEE, Slide 37
Calculation of sin() and cos() by
Table Lookup
 We use a table of cosine values
 Length of the table Ncos=128, circular
buffer
 Contents of the table: cosine of angles i
uniformly distributed between - and .










 1
2
,
2
cos
cos N
N
i
N
i
i

 deb_cos = first address of the table
 mid_cos = address of the table middle
 cos(i ) is at address mid_cos + i

ESIEE, Slide 38
Calculation of sin() and cos() by
Table Lookup
 Conversion of the phase modulo 2:
 Wrapping phase in [-,[
 Done by a macro: testa02pi
* Macro to wrap the phase between - et , phase is in ACCU A
testa02pi .macro
SUB #8000h,A,B ; sub -2^(15)
BC suite1?, BGEQ ; test if phase is in [0,2pi[
SUB #8000h,A ; sub -2^(15)
SUB #8000h,A ; SUB -2^(15)
B suite?
suite1? ADD #8000h,A,B ; add -2^(15)
BC suite?,BLT
ADD #8000h,A ; add -2^(15)
ADD #8000h,A ; add -2^(15)
suite? ; end of test
.endm

ESIEE, Slide 39
Generating the Sine Values from a Table of
Cosine Values
 To generate sin() from the table of
cosine values, we use:
 cos(/2 - ) or cos(-/2 + ) or cos(3/2+ )
 If i is the index of the cosine, for the sine we
use:
 i-Ncos/4 if i>= -Ncos/4
 i+3Ncos /4 if i < Ncos/4.

ESIEE, Slide 40
Implementation on a C54x, Test Sequence
 We can test the GMSK modulation on a
given periodical binary sequence an:
 an=[ 0 1 1 0 0 1 0 1 0 0]
 These bits are stored in a circular buffer:
 Size NB = 10
 Declaration of a section bits aligned on an
address which is a multiple of 16 bits.
AR5 deb_bit
NB
an

ESIEE, Slide 41
Testing the Generation of  on the C54x,
Results Buffer
 We calculate  and store it in a buffer
pointed by AR1. The size of the result
buffer is 1000 words.
AR1 resu
1000

Buffer for the last 1000 result values of 

ESIEE, Slide 42
Testing the Generation of  on the C54x
Buffers
AR4 phi
Nphi
phi
Circular Buffer for phi (evolutive part)
Allocated at an address multiple of 64
(Nphi = 32)
AR3 deb_phase
Nphi
phase
Circular Buffer for the variable phase
Allocated at an address multiple of 64
(Nphi = 32)

ESIEE, Slide 43
Listing for the Calculation of 
Definitions
.mmregs
.global debut,boucle
.global deb_cos, phi
.global deb_phase
.global resu
Nphi .set 32
Nphim .set -32
L .set 4
Ncos .set 128
Nsur2 .set 64
Nsur4 .set 32
NB .set 10
NS .set 8
.bss resu,1000

ESIEE, Slide 44
Macro for phase wrapping
* Definition of macro of phase wrapping testa02pi
testa02pi .macro
SUB #8000h,A,B ;sub -2^(15)
BC suite1?, BGEQ ;test if phase in [0,2pi[
SUB #8000h,A ;sub -2^(15)
SUB #8000h,A ;sub -2^(15)
B suite?
suite1? ADD #8000h,A,B ;add -2^(15)
BC suite?,BLT
ADD #8000h,A ;add -2^(15)
ADD #8000h,A ;add -2^(15)
suite? ;end test wrapping [0,2pi[
.endm

ESIEE, Slide 45
Initialization of Registers and Buffers 1/2
.text
* Initialization of BK, DP, ACCUs, and ARi
debut: LD #0, DP
LD #0, A
LD #0, B
STM #deb_bit,AR5
STM #deb_cos,AR2
STM #deb_phase ,AR3
STM #phi,AR4
STM #resu,AR1
STM +1,AR0
STM #Nphi, BK
STM #(NS-1),AR7
RSBX OVM
SSBX SXM

ESIEE, Slide 46
Initialization of Registers and Buffers 2/2
* Initialization of the phase buffer
RPT #(Nphi-1)
STL A,*AR3+%
*initialization of phimem
LD *AR5,T
MPY #04000h,A ; -2^(14) an(1)(pi/2 an(1))
STL A,*(phimem)

ESIEE, Slide 47
Calculation for the first L bits
* processing for the first L bits
STM #(L-1),AR6
Ldeb STM #Nphi-1,BRC
RPTB fin-1 ; from k=0 to k=Nphi
LD *AR3,A ; accu=phase(k)
MAC *AR4+0%,*AR5,A ; A=phase(k)+an(i) phi(k)
testa02pi
STL A,*AR3+% ; A->phase(k)
NOP
fin NOP
STM #(NS-1), AR7
Nsbouc LD *AR3,A ; output of NS values
STL A,*AR1+ ; and reset at 0 of NS words
ST #0,*AR3+%
BANZ nsbouc,*AR7-
STM #NB, BK
MAR *AR5+%
STM #Nphi,BK
BANZ Ldeb, *AR6-

ESIEE, Slide 48
Calculation of the Following Bits 1/2
* begin of the infinite loop
boucle STM #Nphi-1,BRC
RPTB fin2-1 ; for k=0 to Nphi
testa02pi
fin2
* adding phimem to the NS first points of the array
* then taking them out and reset to 0 in phase
STM #NS-1,AR7
nsbouc2 LD *(phimem),B
ADD *AR3,B,A ; B=phimem+phase(k)
testa02pi
STL A,*AR1+
ST #0,*AR3+% ; 0->phase(k)
BANZ nsbouc2,*AR7- ; ....

ESIEE, Slide 49
Calculation of the Following Bits 2/2
fin3
* actualization of phimem
LD *(phimem),A
STM #NB, BK
MAR *+AR5(#unmL)%
LD *AR5,T
MAC #04000h,A ; -2^(14) an(1)(pi/2 an(1))
testa02pi
STL A,*(phimem)
MAR *+AR5(#L)%
STM #Nphi,BK
B boucle
.end

ESIEE, Slide 50
Illustration of the Phase Result Wrapped
Between - and 
 Plot under CCS the buffer of phase results

ESIEE, Slide 51
Generation of the Baseband Components
zI=cos() and zQ=sin()
 We calculate zI and zQ and we do not
need to save the phase any more.
 We output ZI and Zq, in this example
on DXR0 and DXR1.
 We need the table of constants for the
values of cosine.
 This table is defined in the file tabcos.asm
 The cosine values are given in format Q14.

ESIEE, Slide 52
File tabcos.asm
.def deb_cos,mid_cos
.sect "tab_cos"
deb_cos .word -16384,-16364,-16305,-16207,-16069,-15893,-15679,-15426
.word -15137,-14811,-14449,-14053,-13623,-13160,-12665,-12140
.word -11585,-11003,-10394,-9760,-9102,-8423,-7723,-7005
.word -6270,-5520,-4756,-3981,-3196,-2404,-1606,-804
.word 0,804,1606,2404,3196,3981,4756,5520
.word 6270,7005,7723,8423,9102,9760,10394,11003
.word 11585,12140,12665,13160,13623,14053,14449,14811
.word 15137,15426,15679,15893,16069,16207,16305,16364
.word 16384,16364,16305,16207,16069,15893,15679,15426
.word 15137,14811,14449,14053,13623,13160,12665,12140
.word 11585,11003,10394,9760,9102,8423,7723,7005
.word 6270,5520,4756,3981,3196,2404,1606,804
.word 0,-804,-1606,-2404,-3196,-3981,-4756,-5520
.word -6270,-7005,-7723,-8423,-9102,-9760,-10394,-11003
.word -11585,-12140,-12665,-13160,-13623,-14053,-14449,-14811
.word -15137,-15426,-15679,-15893,-16069,-16207,-16305,-16364
mid_cos .set deb_cos+64

ESIEE, Slide 53
Listing for the Calculation of zI and zQ
 The listing for definitions and
initializations is the same as before.
 Processing of the L first bits,
 Processing of the other bits
 (infinite loop)

ESIEE, Slide 54
Processing of the First L Bits 1/2
* Processing of the L first bits
STM #(L-1),AR6
Ldeb STM #Nphi-1,BRC
RPTB fin-1 ; from k=0 to Nphi
testa02pi
fin NOP
STM #(NS-1), AR7
Nsbouc LD *AR3,A ; output of NS values
SFTA A,-9,A
ADD #mid_cos,A,B
STLM B,AR1
NOP
NOP
LD *AR1,B
STL B,DXR0

ESIEE, Slide 55
Processing of the First L Bits 2/2
* Calculation of the sine
ADD #Nsur4,A,B
BC sui,BGT
ADD #(Nsur2),B
B sui1
sui SUB #Nsur2,B
sui1 ADD #mid_cos,B
STLM B,AR1
NOP
NOP
LD *AR1,A
STL A,DXR1
ST #0,*AR3+%
BANZ nsbouc,*AR7-
STM #NB, BK
MAR *AR5+%
STM #Nphi,BK

ESIEE, Slide 56
Processing of the Following bits 1 of 2
* begin the infinite loop
boucle STM #Nphi-1,BRC
RPTB fin2-1 ; for k=0 to Nphi
testa02pi
fin2
*phimem is added to the NS first points of the array
* then they are output and words are reset to 0 in buffer phase
STM #NS-1,AR7
nsbouc2 LD *(phimem),B
ADD *AR3,B,A ; A=phimem+phase(k)
testa02pi
SFTA A,-9,A
ADD #mid_cos,A,B
STLM B,AR1
NOP
NOP
LD *AR1,B
STL B,DXR0

ESIEE, Slide 57
Processing of the Following Bits 2 of 2
* Calculation of the sine
NOP
ADD #Nsur4,A,B
NOP
NOP
BC suii,BGT
ADD #(Nsur2),B
B suii1
suii SUB #(Nsur2) ,B
suii1 ADD #mid_cos,B
STLM B,AR1
NOP
NOP
LD *AR1,A
STL A,DXR1
ST #0,*AR3+% ; 0->phase(k)
BANZ nsbouc2,*AR7-
fin3
* actualization of phimem
LD *(phimem),A
STM #NB, BK
MAR *+AR5(#unmL)%
LD *AR5,T
MAC #04000h,A ; -2^(14) an(1)(pi/2 an(1))
testa02pi
STL A,*(phimem)
MAR *+AR5(#L)%
STM #Nphi,BK
B boucle
.end

ESIEE, Slide 58
Results Observed in CCS

ESIEE, Slide 59
Generation of 2 Quadrature Carriers
 Generation of:
 cos(2fct) and sin (2fct)
 fc is the frequency of the carrier
 In this example we choose fc=1/T
 Sampling frequency = 1/Ts = fS
 In RF applications, the carriers are not
generated by the DSP. It is only possible
to use the DSP for low values of fc.
 The angle (t)= 2fct is calculated then
the value of cos() is read from a table.

ESIEE, Slide 60
Calculation of the Angle of the Carriers
   
( ) 2 ( 1) 2 ( 1)
S c S S c S s
nT f nT n T f T n T
     
       
 Recursive calculation of the angle :
 The precision of the generated
frequency depends on the precision of
.
 The phase increment  corresponds to
an increment I to the integer that
represents .
I=216fcTS rounded to the closest
integer.

ESIEE, Slide 61
Calculation of the Angle of the Carriers
 If the number of samples per period of
the carrier is a power of 2, 2k:
 I=216fcTS=2(16-k) is exact
 Then the precision of the generated
frequency depends only on the
precision of the sampling frequency.
 Otherwise, there is an error dfc in fc:
 |dfc|<2-17fS.
 Error in the amplitudes of the carriers
due to finite precision of the table
reading. (possible interpolation).

ESIEE, Slide 62
Implementation on a C54x
 We use: fs/fc=8=Ns.
 The cosine table has 128 Values in Q14.
AR1 deb_cos
128
Cosine
values
Circular buffer,Table of cosine

ESIEE, Slide 63
Implementation on a C54x
 Here k=3 (8 samples per period) and the
increment
 I=216fcTS=2(16-k) =213
 Simple case of fS/fc as an integer value, the
table is read with an offset from the pointer =
16 = 27/23 to generate a cosine with 8 samples
per period.
 We can work directly on the index i and not
on I.

ESIEE, Slide 64
Generation of the Cosine and Sine Carriers
 For the cosine:
 The circular buffer containing the cosine
values (length N) is accessed with AR1.
 Incremented by the content of AR0=16.
 AR1 initialized with deb_cos.
 For the sine:
 Same circular buffer accessed by AR2.
 AR2 initialized with deb_cos + Ncos/4.
 Decremented by AR0=16.
 Outputs (cos and sin) are sent to DXR0
and DXR1.

ESIEE, Slide 65
Generation of quadrature 2 Carriers
 File porteuse.asm
 A file associated with DXR0 and DXR1
is used to save visual results obtained
with the CCS simulator.
 Here cosine table goes from:
 0 to 2

ESIEE, Slide 66
Listing for the Generation of 2 Carriers 1 of 2
.mmregs
.global debut,boucle
Ncos .set 128
Nsur2 .set 64
Nsur4 .set 32
Inc .set 16
* Definition and initialization of Table of cosine
.sect "tab_cos"
deb_cos .word 16384,16364,16305,16207,16069,15893,15679,15426
.word 15137,14811,14449,14053,13623,13160,12665,12140
.word 11585,11003,10394,9760,9102,8423,7723,7005
.word 6270,5520,4756,3981,3196,2404,1606,804
.word 0,-804,-1606,-2404,-3196,-3981,-4756,-5520
.word -6270,-7005,-7723,-8423,-9102,-9760,-10394,-11003
.word -11585,-12140,-12665,-13160,-13623,-14053,-14449,-14811
.word -15137,-15426,-15679,-15893,-16069,-16207,-16305,-16364
.word -16384,-16364,-16305,-16207,-16069,-15893,-15679,-15426
.word -15137,-14811,-14449,-14053,-13623,-13160,-12665,-12140
.word -11585,-11003,-10394,-9760,-9102,-8423,-7723,-7005
.word -6270,-5520,-4756,-3981,-3196,-2404,-1606,-804
.word 0,804,1606,2404,3196,3981,4756,5520
.word 6270,7005,7723,8423,9102,9760,10394,11003
.word 11585,12140,12665,13160,13623,14053,14449,14811
.word 15137,15426,15679,15893,16069,16207,16305,16364

ESIEE, Slide 67
Listing for the Generation of 2 Carriers 2 of 2
.text
* Initializations of DP, and of the phase Ialpha at 0
* The phase Ialpha is in ACCU A, and the index of table in B
* attention we work in the part of ACCUs
* Initialize AR1 at mid_cos and AR0 at Nsur4
debut:
LD #0, DP
LD #0, A
STM #Ncos,BK
STM #deb_cos,AR1
STM #(deb_cos+Nsur4),AR2
STM #Inc, AR0
* endless loop
boucle:
LD *AR1+0%,A
STL A, DXR0
LD *AR2-0%,B
STL B,DXR0
* Return to the beginning of the endless loop
B boucle

ESIEE, Slide 68
Results Obtained with CCS

ESIEE, Slide 69
Tutorial
 The listing files for the precedent examples
can be found in the directory “tutorial”:
 Tutorial > Dsk5416 > Chapter 21 > Labs_modulation

ESIEE, Slide 70
Further Activities
 Application 5 for the TMS320C5416
DSK and for the TMS320C5510.
 Alien Voices. A very simple application showing the
effect of modulation on audio frequencies. It shows
how the carrier causes sum and difference frequencies
to be generated. Here it is used to generate the
strange voices used for aliens in science fiction films
and television.

Frequency Modulation.ppt

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