1. INTRODUCTION TO DSP PROCESSORS
A signal can be defined as a function that conveys information, generally about the
state or behavior of a physical system. There are two basic types of signals viz Analog
(continuous time signals which are defined along a continuum of times) and Digital
(discrete-time).
Remarkably, under reasonable constraints, a continuous time signal can be adequately
represented by samples, obtaining discrete time signals. Thus digital signal processing
is an ideal choice for anyone who needs the performance advantage of digital
manipulation along with today’s analog reality.
Hence a processor which is designed to perform the special operations (digital
manipulations) on the digital signal within very less time can be called as a Digital
signal processor. The difference between a DSP processor, conventional
microprocessor and a
Microcontroller is listed below.
Microprocessor or General Purpose Processor such as Intel xx86 or Motorola
680xx
family
Contains - only CPU
-No RAM
-No ROM
-No I/O ports
-No Timer
Microcontroller such as 8051 family
Contains - CPU
- RAM
- ROM
-I/O ports
- Timer &
- Interrupt circuitry
Some Micro Controllers also contain A/D, D/A and Flash Memory
DSP Processors such as Texas instruments and Analog Devices
Contains - CPU
- RAM
-ROM
- I/O ports
- Timer
Optimized for – fast arithmetic
- Extended precision
- Dual operand fetch
- Zero overhead loop
- Circular buffering
1
The basic features of a DSP Processor are
Feature
Use
Fast-Multiply accumulate
Most DSP algorithms, including
filtering, transforms, etc. are
multiplication- intensive
Multiple – access memory
architecture
Many data-intensive DSP operations
require reading a program instruction
and multiple data items during each
instruction cycle for best performance
Specialized addressing modes
Efficient handling of data arrays and
first-in, first-out buffers in memory
Specialized program control
Efficient control of loops for many
iterative DSP algorithms. Fast interrupt
handling for frequent I/O operations.
On-chip peripherals and I/O
interfaces
On-chip peripherals like A/D converters
allow for small low cost system designs.
Similarly I/O interfaces tailored for
common peripherals allow clean
interfaces to off-chip I/O devices.
2
2. ARCHITECTURE OF 6713 DSP PROCESSOR
This chapter provides an overview of the architectural structure of the TMS320C67xx
DSP, which comprises the central processing unit (CPU), memory, and on-chip
peripherals. The C67xE DSPs use an advanced modified Harvard architecture that
maximizes processing power with eight buses. Separate program and data spaces
allow simultaneous access to program instructions and data, providing a high degree
of parallelism. For example, three reads and one write can be performed in a single
cycle.
Instructions with parallel store and application-specific instructions fully utilize this
architecture. In addition, data can be transferred between data and program spaces.
Such
Parallelism supports a powerful set of arithmetic, logic, and bit-manipulation
operations that can all be performed in a single machine cycle. Also, the C67xx DSP
includes the control mechanisms to manage interrupts, repeated operations, and
function calling.
Fig 2 – 1 BLOCK DIAGRAM OF TMS 320VC 6713
3
Bus Structure
The C67xx
-bit buses (four
program/data buses and four address buses):
 The program bus (PB) carries the instruction code and immediate operands
from program memory.
 Three data buses (CB, DB, and EB) interconnect to various elements, such as
the CPU,data address generation logic, program address generation logic, onchip peripherals, and data memory.
 The CB and DB carry the operands that are read from data memory.The EB
carries the data to be written to memory.
 Four address buses (PAB, CAB, DAB, and EAB) carry the addresses needed
for
instruction execution.
The C67xx DSP can generate up to two data-memory addresses per cycle using the
two auxiliary register arithmetic units (ARAU0 and ARAU1). The PB can carry data
operands stored in program space (for instance, a coefficient table) to the multiplier
and adder for multiply/accumulate operations or to a destination in data space for data
move instructions (MVPD and READA). This capability, in conjunction with the
feature of dual-operand read, supports the execution of single-cycle, 3-operand
instructions such as the FIRS instruction. The C67xx DSP also has an on-chip
bidirectional bus for accessing on-chip peripherals. This bus is connected to DB and
EB through the bus exchanger in the CPU interface. Accesses that use this bus can
require two or more cycles for reads and writes, depending on the peripheral’s
structure.
Central Processing Unit (CPU)
The CPU is common to all C67xE devices. The C67x CPU contains:
 40-bit arithmetic logic unit (ALU)
 Two 40-bit accumulators
 Barrel shifter
 17 X 17-bit multiplier
 40-bit adder
 Compare, select, and store unit (CSSU)
 Data address generation unit
 Program address generation unit
Arithmetic Logic Unit (ALU)
The C67x DSP performs 2s-complement arithmetic with a 40-bit arithmetic logic unit
(ALU) and two 40-bit accumulators (accumulators A and B). The ALU can also
perform Boolean operations. The ALU uses these inputs:
 16-bit immediate value
 16-bit word from data memory
 16-bit value in the temporary register, T
 Two 16-bit words from data memory
4


32-bit word from data memory
40-bit word from either accumulator
The ALU can also function as two 16-bit ALUs and perform two 16-bit operations
simultaneously.
Fig 2 – 2 ALU UNIT
5
Accumulators
Accumulators A and B store the output from the ALU or the multiplier/adder block.
They
can also provide a second input to the ALU; accumulator A can be an input to the
multiplier/adder. Each accumulator is divided into three parts:



Guard bits (bits 39–32)
High-order word (bits 31–16)
Low-order word (bits 15–0)
Instructions are provided for storing the guard bits, for storing the high- and the low
order accumulator words in data memory, and for transferring 32-bit accumulator
words in or out of data memory. Also, either of the accumulators can be used as
temporary storage for the other.
Barrel Shifter
The C67x DSP barrel shifter has a 40-bit input connected to the accumulators or to
data memory (using CB or DB), and a 40-bit output connected to the ALU or to data
memory (using EB). The barrel shifter can produce a left shift of 0 to 31 bits and a
right shift of 0 to 16 bits on the input data. The shift requirements are defined in the
shift count field of the instruction, the shift count field (ASM) of status register ST1,
or in temporary register
T (when it is designated as a shift count register).The barrel shifter and the exponent
encoder normalize the values in an accumulator in a single cycle. The LSBs of the
output are filled with 0s, and the MSBs can be either zero filled or sign extended,
depending on the state of the sign-extension mode bit (SXM) in ST1. Additional shift
capabilities enable the processor to perform numerical scaling, bit extraction,
extended arithmetic, and overflow prevention operations.
Multiplier/Adder Unit
The multiplier/adder unit performs 17 X 17-bit 2s-complement multiplications with a
40- bit addition in a single instruction cycle. The multiplier/adder block consists of
several elements: a multiplier, an adder, signed/unsigned input control logic,
fractional control logic, a zero detector, a rounder (2s complement),
overflow/saturation logic, and a 16-bit temporary storage register (T). The multiplier
has two inputs: one input is selected from T, a data-memory operand, or accumulator
A; the other is selected from program memory, data memory, accumulator A, or an
immediate value. The fast, on-chip multiplier allows the C54x DSP to perform
operations efficiently such as convolution, correlation, and filtering. In addition, the
multiplier and ALU together execute multiply/accumulate (MAC) computations and
ALU operations in parallel in a single instruction cycle. This function is used in
determining the Euclidian distance and in implementing symmetrical and LMS filters,
which are required for complex DSP algorithms. See section 4.5, Multiplier/Adder
Unit, on page 4-19, for more details about the multiplier/adder unit.
6
Fig 2 – 3 MULTIPLIER/ADDER UNIT
These are the some of the important parts of the processor and you are instructed to go
through the detailed architecture once which helps you in developing the optimized
code
for the required application.
7
3. FREQUENCY RESPONSE OF A GIVEN SYSTEM GIVEN IN (TRANSF ER
FUNCTION/ DIFFERENCE EQUATION FORM)
AIM: To find the frequency response of the given LTI system given in difference
equation form or Transfer function form and plot the same.
SOFTWARE REQUIRED: MATLAB 7.0 or Above.
MATLAB CODE:
clc;
clear all;
close all;
num=input('type the numerator vector: ');
den=input('type the denominator vector: ');
N= input(' enter the number of frequency points: ');
w=0:pi/N:pi;
H=freqz(num,den,w);
figure;
subplot(2,1,1);
plot(w/pi,real(H));
xlabel('\omega/\pi');
ylabel('Amplitude');
title('real part');
subplot(2,1,2);
plot(w/pi,imag(H));
xlabel('\omega/\pi');
ylabel('Amplitude');
title('imag part');
figure;
subplot(2,1,1);
plot(w/pi,abs(H));
xlabel('\omega/\pi');
ylabel('Magnitude');
title('Magnitude spectrum');
subplot(2,1,2);
plot(w/pi,angle(H));
xlabel('\omega/\pi');
ylabel('phase(radians)');
title('Phase spectrum');
OUTPUT:
type the numerator vector: [0.5 0 0.5]
type the denominator vector: 1
enter the number of frequency points: 512
8
GRAPHS:
real part
Amplitude
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6
0.7
0.8
0.9
1
0.7
0.8
0.9
1
0.7
0.8
0.9
1
/ 
imag part
Amplitude
0.5
0
-0.5
0
0.1
0.2
0.3
0.4
0.5
/ 
Magnitude spectrum
Magnitude
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
/ 
Phase spectrum
phase(radians)
2
1
0
-1
-2
0
0.1
0.2
0.3
0.4
0.5
0.6
/ 
INFERENCE : The frequency response of the given system is generated using the
‘freqz’ command. The real part is the real part of the complex number representing
the transfer function of the given system and the imaginary part is the imaginary part
of the transfer function. The magnitude plot is the absolute value of magnitude versus
the frequency and the phase plot is the phase angle versus the frequency is plotted for
different systems. This program is very simple and requires defining the system and
finding Frequency response and plotting.
RESULT: The frequency response of the given system is found and the real and
imaginary parts along with the magnitude and phase plots of the same are plotted.
9
10
11
4. IMPULSE RESPONSE OF A GIVEN SYSTEM (OF ANY ORDER)
AIM: To find the impulse response of the given LTI system given in difference
equation form or Transfer function form of any order and plot the same.
SOFTWARE REQUIRED: MATLAB 7.0 or Above.
MATLAB CODE:
clc;
clear all;
close all;
num=input('type the numerator vector');
den=input('type the denominator vector');
N= input(' enter the desired length of the output sequence');
n=0:N-1;
imp=[1 zeros(1,N-1)];
H=filter(num,den,imp);
disp(' the impulse response of the system is ');
disp(H);
stem(n,H);
xlabel('time index');
ylabel('h(n)');
title(' Impulse response of the given system');
OUTPUT:
type the numerator vector[ 1 2 -2 -1 2]
type the denominator vector1
enter the desired length of the output sequence6
the impulse response of the system is
1 2 -2 -1 2 0
GRAPHS:
Impulse response of the given system
2
1.5
1
h(n)
0.5
0
-0.5
-1
-1.5
-2
0
0.5
1
1.5
2
2.5
time index
3
3.5
4
4.5
5
12
INFERENCE: The impulse response of the given system is generated using the
‘filter’ command. This program is very simple and requires defining the system and
finding impulse response and plotting.
RESULT: The impulse response of the given system is found and is plotted.
13
14
15
5. GENERATION OF DISCRETE FOURIER TRANSFORM (DFT) OF A
SEQUENCE
AIM : To find the Discrete Fourier Transform of a sequence.
SOFTWARE REQUIRED : MAT LAB 7.0
PROGRAM DESCRIPTION : In this program the Discrete Fourier Transform
(DFT) of a sequence x[n] is generated by using the formula,
N-1
X(k) = Σ x(n) e-2πjk / N
n=0
Where, X(k)  DFT of sequence x[n]
N represents the sequence length and it is calculated by using the command ‘length’.
The DFT of any sequence is the powerful computational tool for performing
frequency analysis of discrete-time signals.
MATLAB CODE :
clc;
clear all;
close all;
a=input('Enter the sequence :');
N=length(a);
disp('The length of the sequence is:');N
for k=1:N
y(k)=0;
for i=1:N
y(k)=y(k)+a(i)*exp((-2*pi*j/N)*((i-1)*(k-1)));
end;
end;
k=1:N
disp('The result is:');y
figure(1);
subplot(211);
stem(k,abs(y(k)));
grid;
xlabel('sample values n-->');
ylabel('Amplitudes-->');
title('Mangnitude response of the DFT of given sequence');
subplot(212);
stem(angle(y(k))*180/pi);
grid;
xlabel('sample values n-->');
ylabel('phase-->');
title('Phase response of the DFT of given sequence');
16
OUTPUTS:
Enter the sequence : [1 2 3 4]
The length of the sequence is: N = 4
k= 1 2 3 4
The result is: y = 10.0000
-2.0000 + 2.0000i
2.0000i
-2.0000 - 0.0000i
-2.0000 -
GRAPHS :
Mangnitude response of the DFT of given sequence
Amplitudes-->
10
5
0
1
1.5
1
1.5
2
2.5
3
3.5
sample values n-->
Phase response of the DFT of given sequence
4
200
phase-->
100
0
-100
-200
2
2.5
sample values n-->
3
3.5
4
INFERENCE : To perform the frequency analysis on a discrete-time signal x[n] can
be generated from a continuous signal x(t). Here in the program y(k) refers to the DFT
of the sequence a. The DFT consists of two parts. The magnitude and phase angle of
x(k) are calculated by using abs and angle commands and plotted using stem
command.
RESULT : The Discrete Fourier Transform ( DFT ) of a sequence is obtained and
response is plotted.
17
18
19
6. GENERATION OF INVERSE DISCRETE FOURIER TRANSFORM (IDFT)
OF A SEQUENCE
AIM: To find the Inverse Discrete Fourier Transform of a sequence.
SOFTWARE REQUIRED : MAT LAB 7.0
PROGRAM DESCRIPTION :
In this program the Inverse Discrete Fourier Transform ( IDFT ) of a sequence X(k)
is generated by using the formula,
N-1
x [n] =Σ X(k) e2πjk/N
n=0
Where, x[n]  IDFT of sequence X (k)
N represents the sequence length and it is calculated by using the command ‘length’.
The IDFT results in the sequence from its DFT.
MATLAB CODE :
clc;
clear all;
close all;
a=input('Enter the sequence :');
N=length(a);
disp('The length of the sequence is:');N
for n=1:N
y(n)=0;
for k=1:N
y(n)=y(n)+a(k)*exp((2*pi*j*(k-1)*(n-1))/N);
end;
end;
n=1:N
y1=1/N*y(n);
disp('The result is:');y1
figure(1);
stem(n,y1);
grid;
xlabel('sample values n-->');
ylabel('Amplitudes-->');
title('Mangnitude response of the IDFT of given DFT');
OUTPUTS:
Enter the sequence : [1 0 1 0]
The length of the sequence is: N = 4
n= 1 2 3 4
The result is: y1 = 0.5000
0 + 0.0000i
0.5000 - 0.0000i
0 + 0.0000i
20
GRAPHS :
Mangnitude response of the IDFT of given DFT
0.5
0.45
0.4
Amplitudes-->
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1
1.5
2
2.5
sample values n-->
3
3.5
4
INFERENCE: To perform the frequency analysis on a discrete-time signal x[n] can
be generated from a continuous signal x(t). Here in the program IDFT of y(k) results
in the sequence a. The IDFT consists of only magnitude response. The magnitude is
calculated using abs command and plotted using stem command.
RESULT: The Inverse Discrete Fourier Transform ( IDFT ) of a sequence is obtained
and response is plotted.
21
22
23
7. FINDING THE FFT OF DIFFERENT SIGNALS
AIM : To find the FFT of different signals like impulse, step, ramp and exponential.
SOFTWARE REQUIRED: MAT LAB 7.0
PROGRAM DESCRIPTION: In this program using the command FFT for impulse,
step, ramp and exponential sequences the FFT is generated. In the process of finding
the FFT the length of the FFT is taken as N. The FFT consists of two parts:
MAGNITUDE PLOT and PHASE PLOT. The magnitude plot is the absolute value of
magnitude versus the samples and the phase plot is the phase angle versus the
samples.
MATLAB CODE:
% FFT of the impulse sequence : magnitude and phase response
clc;
clear all;
close all;
%impulse sequence
t=-2:1:2;
y=[zeros(1,2) 1 zeros(1,2)];
subplot (3,1,1);
stem(t,y);
grid;
input('y=');
disp(y);
title ('Impulse Response');
xlabel ('time -->');
ylabel ('--> Amplitude');
xn=y;
N=input('enter the length of the FFT sequence: ');
xk=fft(xn,N);
magxk=abs(xk);
angxk=angle(xk);
k=0:N-1;
subplot(3,1,2);
stem(k,magxk);
grid;
xlabel('k');
ylabel('|x(k)|');
subplot(3,1,3);
stem(k,angxk);
disp(xk);
grid;
xlabel('k');
ylabel('arg(x(k))');
24
OUTPUTS:
y=
0
0
1
0
0
enter the length of the FFT sequence: 10
1.0000
0.9511i
1.0000
0.9511i
0.3090 - 0.9511i
-0.8090 - 0.5878i
-0.8090 + 0.5878i 0.3090 +
0.3090 - 0.9511i
-0.8090 - 0.5878i
-0.8090 + 0.5878i 0.3090 +
GRAPHS:
--> Amplitude
Impulse Response
1
0.5
0
-2
-1.5
-1
-0.5
0
time -->
0.5
1
1.5
2
|x(k)|
1
0.5
0
0
1
2
3
4
5
6
7
8
9
5
6
7
8
9
k
arg(x(k))
5
0
-5
0
1
2
3
4
k
25
% FFT of the step sequence : magnitude and phase response
clc;
clear all;
close all;
%Step Sequence
s=input ('enter the length of step sequence');
t=-s:1:s;
y=[zeros(1,s) ones(1,1) ones(1,s)];
subplot(3,1,1);
stem(t,y);
grid
input('y=');
disp(y);
title ('Step Sequence');
xlabel ('time -->');
ylabel ('--> Amplitude');
xn=y;
N=input('enter the length of the FFT sequence: ');
xk=fft(xn,N);
magxk=abs(xk);
angxk=angle(xk);
k=0:N-1;
subplot(3,1,2);
stem(k,magxk);
grid
xlabel('k');
ylabel('|x(k)|');
subplot(3,1,3);
stem(k,angxk);
disp(xk);
grid
xlabel('k');
ylabel('arg(x(k))');
OUTPUTS:
enter the length of step sequence: 5
y= 0 0 0 0 0 1 1 1
1
1
1
enter the length of the FFT sequence: 10
5.0000
-1.0000 + 3.0777i
0
-1.0000 + 0.7265i
0
-1.0000 - 0.7265i
0
-1.0000 - 3.0777i
0
-1.0000
26
GRAPHS:
--> Amplitude
Step Sequence
1
0.5
0
-5
-4
-1
-2
-3
3
2
1
0
time -->
4
5
|x(k)|
5
0
0
1
2
3
4
5
6
7
8
9
5
6
7
8
9
k
arg(x(k))
5
0
-5
0
1
2
3
4
k
27
% FFT of the Ramp sequence: magnitude and phase response
clc;
clear all;
close all;
%Ramp Sequence
s=input ('enter the length of Ramp sequence: ');
t=0:s;
y=t
subplot(3,1,1);
stem(t,y);
grid
input('y=');
disp(y);
title ('ramp Sequence');
xlabel ('time -->');
ylabel ('--> Amplitude');
xn=y;
N=input('enter the legth of the FFT sequence: ');
xk=fft(xn,N);
magxk=abs(xk);
angxk=angle(xk);
k=0:N-1;
subplot(3,1,2);
stem(k,magxk);
grid
xlabel('k');
ylabel('|x(k)|');
subplot(3,1,3);
stem(k,angxk);
disp(xk);
grid
xlabel('k');
ylabel('arg(x(k))');
OUTPUTS:
enter the length of Ramp sequence: 5
y= 0 1 2 3 4 5
enter the length of the FFT sequence: 10
15.0000
-7.7361 - 7.6942i
2.5000 + 3.4410i
0.8123i
-3.0000
2.5000 - 0.8123i
-3.2639 + 1.8164i
7.6942i
-3.2639 - 1.8164i
2.5000 +
2.5000 - 3.4410i
-7.7361 +
28
GRAPHS:
--> Amplitude
ramp Sequence
5
0
0
0.5
0
1
1
1.5
2
2.5
time -->
3
3.5
4
4.5
5
|x(k)|
20
10
0
2
3
4
5
6
7
8
9
5
6
7
8
9
k
arg(x(k))
5
0
-5
0
1
2
3
4
k
29
% FFT of the Exponential Sequence : magnitude and phase response
clc;
clear all;
close all;
%exponential sequence
n=input('enter the length of exponential sequence: ');
t=0:1:n;
a=input('enter "a" value: ');
y=exp(a*t);
input('y=')
disp(y);
subplot(3,1,1);
stem(t,y);
grid;
title('exponential response');
xlabel('time');
ylabel('amplitude');
disp(y);
xn=y;
N=input('enter the length of the FFT sequence: ');
xk=fft(xn,N);
magxk=abs(xk);
angxk=angle(xk);
k=0:N-1;
subplot(3,1,2);
stem(k,magxk);
grid;
xlabel('k');
ylabel('|x(k)|');
subplot(3,1,3);
stem(k,angxk);
grid;
disp(xk);
xlabel('k');
ylabel('arg(x(k))');
OUTPUTS:
enter the length of exponential sequence: 5
enter "a" value: 0.8
y= 1.0000 2.2255
4.9530 11.0232 24.5325 54.5982
enter the length of the FFT sequence: 10
98.3324
-73.5207 -30.9223i 50.9418 +24.7831i -41.7941 -16.0579i
38.8873 + 7.3387i
-37.3613
38.8873 - 7.3387i
-41.7941 +16.0579i
50.9418 -24.7831i
-73.5207 +30.9223i
30
GRAPHS :
exponential response
amplitude
100
50
0
0
0.5
0
1
4
3.5
3
2.5
time
2
1.5
1
4.5
5
|x(k)|
100
50
0
2
3
4
5
6
7
8
9
5
6
7
8
9
k
arg(x(k))
5
0
-5
0
1
2
3
4
k
INFERENCE : The FFT for impulse, step, ramp and exponential sequences is
generated using the FFT command. The magnitude plot is the absolute value of
magnitude versus the samples and the phase plot is the phase angle versus the samples
is plotted for different signals for different values. This program is very simple and
requires defining the signal and finding FFT and plotting.
RESULT : The FFT of different signals like impulse, step, ramp and exponential is
found and the magnitude and phase plots of the same is plotted.
31
32
33
8. POWER SPECTRAL DENSITY USING SQUARE MAGNITUDE AND
AUTOCORRELATION
AIM : To compute the Power Spectral Density of given signals using square
magnitude and autocorrelation
SOFTWARE REQUIRED : MAT LAB 7.0
PROGRAM DESCRIPTION : The stationary random processes do not have finite
energy and hence do not processes a Fourier Transform. Such signals have finite
average power and hence are characterized by a Power Density Spectrum or Power
Spectral Density (PSD). In this program we have used the property of PSD that it can
be calculated from its autocorrelation function by taking the time average. In the
Square magnitude method after taking the FFT by taking the absolute value we get the
PSD.
PROGRAM :
clc;
clear all;
close all;
f1=input('Enter the frequency of first sequence in Hz: ');
f2=input('Enter the frequency of the second sequence in Hz: ');
fs=input('Enter the sampling frequency in Hz: ');
t=0:1/fs:1;
x=2*sin(2*pi*f1*t)+3*sin(2*pi*f2*t)+rand(size(t));
px1=abs(fft(x).^2);
px2=abs(fft(xcorr(x),length(t)));
subplot(211)
plot(t*fs,10*log10(px1));%square magnitude
grid;
xlabel('Freq.in Hz-->');
ylabel('Magnitude in dB-->');
title('PSD using square magnitude method');
subplot(212)
plot(t*fs,10*log10(px2));%autocorrelation
grid;
xlabel('Freq.in Hz-->');
ylabel('Magnitude in dB-->');
title('PSD using auto correlation method');
OUTPUTS:
Enter the frequency of first sequence in Hz: 200
Enter the frequency of the second sequence in Hz: 400
34
Enter the sampling frequency in Hz: 1000
GRAPHS :
PSD using square magnitude method
Magnitude in dB-->
100
50
0
-50
0
100
200
0
100
200
300
400
500
600
700
Freq.in Hz-->
PSD using auto correlation method
800
900
1000
800
900
1000
Magnitude in dB-->
60
50
40
30
300
400
500
600
Freq.in Hz-->
700
INFERENCE : The only constraint is to take the two frequencies must be two time
lesser than the sampling frequencies.
RESULT : Hence the PSD is computed using the square magnitude and
Autocorrelation and graphs are plotted.
35
36
37
9. IMPLEMENTATION OF LP & HP FIR FILTER FOR A GIVEN
SEQUENCE (USING WINDOWING TECHNIQUES)
AIM: To implement the FIR filter for a given sequence by using windowing
techniques.
SOFTWARE REQUIRED: MATLAB 7.0
PROGRAM DESCRIPTION: A Finite Impulse Response (FIR) filter is a discrete
linear time-invariant system whose output is based on the weighted summation of a
finite number of past inputs.
An FIR transversal filter structure can be obtained directly from the equation for
discrete-time convolution.
N-1
y [n] =Σ X(k) h(n-k)
0< n< N-1
k=0
In this equation, x(k) and y(n) represent the input to and output from the filter at time
n. h(n-k) is the transversal filter coefficients at time n. These coefficients are
generated by using FDS (Filter Design Software or Digital filter design package).
FIR – filter is a finite impulse response filter. Order of the filter should be specified.
Infinite response is truncated to get finite impulse response. Placing a window of
finite length does this. Types of windows available are Rectangular, Barlett,
Hamming, Hanning, Blackmann window etc. This FIR filter is an all zero filter.
MATLAB CODE:
clc;
clear all;
close all;
rp=input('enter passband ripple');
rs=input('enter the stopband ripple');
fp=input('enter passband freq');
fs=input('enter stopband freq');
f=input('enter sampling freq ');
wp=2*fp/f;
ws=2*fs/f;
num=-20*log10(sqrt(rp*rs))-13;
dem=14.6*(fs-fp)/f;
n=ceil(num/dem);
n1=n+1;
if(rem(n,2)~=0)
n1=n;
n=n-1;
end
c=input('enter your choice of window function 1. rectangular 2. triangular 3.kaiser: \n
');
if(c==1)
38
y=rectwin(n1);
disp('Rectangular window filter response');
end
if (c==2)
y=triang(n1);
disp('Triangular window filter response');
end
if(c==3)
y=kaiser(n1);
disp('kaiser window filter response');
end
%LPF
b=fir1(n,wp,y);
[h,o]=freqz(b,1,256);
m=20*log10(abs(h));
subplot(2,1,1);plot(o/pi,m);
title('LPF');
ylabel('Gain in dB-->');
xlabel('(a) Normalized frequency-->');
%HPF
b=fir1(n,wp,'high',y);
[h,o]=freqz(b,1,256);
m=20*log10(abs(h));
subplot(2,1,2);plot(o/pi,m);
title('HPF');
ylabel('Gain in dB-->');
xlabel('(b) Normalized frequency-->');
39
USING RECTANGULAR WINDOW
OUTPUT:
enter passband ripple0.02
enter the stopband ripple0.01
enter passband freq1000
enter stopband freq1500
enter sampling freq 10000
enter your choice of window function 1. rectangular 2. triangular 3.kaiser:
1
Rectangular window filter response
GRAPH:
LPF
Gain in dB-->
50
0
-50
-100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(a) Normalized frequency-->
HPF
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(b) Normalized frequency-->
0.8
0.9
1
Gain in dB-->
20
0
-20
-40
-60
40
USING TRIANGULAR WINDOW
OUTPUT:
enter passband ripple0.02
enter the stopband ripple0.01
enter passband freq1000
enter stopband freq1500
enter sampling freq 10000
enter your choice of window function 1. rectangular 2. triangular 3.kaiser:
2
Triangular window filter response
GRAPH:
LPF
Gain in dB-->
0
-20
-40
-60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(a) Normalized frequency-->
HPF
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(b) Normalized frequency-->
0.8
0.9
1
Gain in dB-->
0
-10
-20
-30
41
USING KAISER WINDOW
OUTPUT:
enter passband ripple0.02
enter the stopband ripple0.01
enter passband freq1000
enter stopband freq1500
enter sampling freq 10000
enter your choice of window function 1. rectangular 2. triangular 3.kaiser:
3
kaiser window filter response
GRAPH:
LPF
Gain in dB-->
50
0
-50
-100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(a) Normalized frequency-->
HPF
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(b) Normalized frequency-->
0.8
0.9
1
Gain in dB-->
20
0
-20
-40
-60
42
INFERENCE: This program requires certain specifications about the pass band and
stop band ripple & frequencies and the sampling frequency. Here we have used a
function called ‘fir1’ in order to design a Nth order Low pass and a High pass filter.
This function returns the filter coefficients in length N+1 vector b. The cutoff
frequency ‘wp’ must be between 0 < wp < 1.0 , with 1.0 corresponding to half the
sampling rate.
Based up on the choice of available windowing functions, the filter response is
generated.
RESULT: The LP and HP FIR Filter response for the given sequence is generated
based upon the choice of the windowing function and the filter characteristics are
plotted.
43
44
45
10. IMPLEMENTATION OF IIR LP FILTER FOR A GIVEN SEQUENCE
AIM: To design and implement IIR (LPF) filters for a given sequence.
SOFTWARE REQUIRED: MATLAB 7.0
PROGRAM DESCRIPTION: The IIR filter can realize both the poles and zeroes of
a system because it has a rational transfer function, described by polynomials in z in
both the numerator and the denominator:
M
H(z) =
Σ bk z-k
k=0_________
M
Σ ak z-k
k=0
The difference equation for such a system is described by the following:
M
N
Y(n)=  bk x(n-k) ak y(n-k)
k=0
k=1
M and N are order of the two polynomials bk and ak are the filter coefficients. These
filter coefficients are generated using FDS (Filter Design software or Digital Filter
design package).
IIR filters can be expanded as infinite impulse response filters. In designing IIR
filters, cutoff frequencies of the filters should be mentioned. The order of the filter can
be estimated using butter worth polynomial. That’s why the filters are named as butter
worth filters. Filter coefficients can be found and the response can be plotted.
MATLAB CODE:
clc;
clear all;
close all;
disp('enter the IIR filter design specifications');
rp=input('enter the passband ripple');
rs=input('enter the stopband ripple');
wp=input('enter the passband freq');
ws=input('enter the stopband freq');
fs=input('enter the sampling freq');
w1=2*wp/fs; w2=2*ws/fs;
[n,wn]=buttord(w1,w2,rp,rs,'s');
disp('Frequency response of IIR LPF is:');
[b,a]=butter(n,wn,'low','s');
w=0:.01:pi;
[h,om]=freqs(b,a,w);
m=20*log10(abs(h));
an=angle(h);
figure,subplot(2,1,1);plot(om/pi,m);
46
title('magnitude response of IIR LP filter is:');
xlabel('(a) Normalized freq. -->');
ylabel('Gain in dB-->');
subplot(2,1,2);plot(om/pi,an);
title('phase response of IIR LP filter is:');
xlabel('(b) Normalized freq. -->');
ylabel('Phase in radians-->');
OUTPUT:
enter the IIR filter design specifications
enter the passband ripple0.15
enter the stopband ripple60
enter the passband freq1500
enter the stopband freq3000
enter the sampling freq7000
Frequency response of IIR LPF is:
GRAPHS:
magnitude response of IIR LP filter is:
0
-100
-200
-300
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(a) Normalized freq. -->
phase response of IIR LP filter is:
0.8
0.9
1
0
0.1
0.2
0.3
0.8
0.9
1
4
Phase in radians-->
Gain in dB-->
100
2
0
-2
-4
0.4
0.5
0.6
0.7
(b) Normalized freq. -->
47
INFERENCE: This program requires certain specifications about the pass band and
stop band ripple & frequencies and the sampling frequency. Here we have used a
function called ‘[n,wn]=buttord(w1,w2,rp,rs,'s')’ in order to find the lowest order N
of digital butterworth filter that loses no more than ‘rp’ db in the pass band and has at
least ‘rs’ db of attenuation in the stop band . w1 and w2 are the pass band and stop
band edge frequencies, normalized from 0 to 1.
The function ‘butter’ designs a Nth order low pass digital butterworth filter and
returns the filter coefficients in length N+1 vectors B(numerator) and A
(denominator).
RESULT: The HP IIR Filter response for the given sequence is generated and the
filter characteristics are plotted.
48
49
50
11. IMPLEMENTATION OF IIR HP FILTER FOR A GIVEN SEQUENCE
AIM: To design and implement IIR (HPF) filters for a given sequence.
SOFTWARE REQUIRED: MATLAB 7.0
PROGRAM DESCRIPTION: The IIR filter can realize both the poles and zeroes of
a system because it has a rational transfer function, described by polynomials in z in
both the numerator and the denominator:
M
H(z) =
Σ bk z-k
k=0_________
M
Σ ak z-k
k=0
The difference equation for such a system is described by the following:
M
N
Y(n)=  bk x(n-k) ak y(n-k)
k=0
k=1
M and N are order of the two polynomials bk and ak are the filter coefficients. These
filter coefficients are generated using FDS (Filter Design software or Digital Filter
design package).
IIR filters can be expanded as infinite impulse response filters. In designing IIR
filters, cutoff frequencies of the filters should be mentioned. The order of the filter can
be estimated using butter worth polynomial. That’s why the filters are named as butter
worth filters. Filter coefficients can be found and the response can be plotted.
MATLAB CODE:
clc;
clear all;
close all;
disp('enter the IIR filter design specifications');
rp=input('enter the passband ripple');
rs=input('enter the stopband ripple');
wp=input('enter the passband freq');
ws=input('enter the stopband freq');
fs=input('enter the sampling freq');
w1=2*wp/fs;w2=2*ws/fs;
[n,wn]=buttord(w1,w2,rp,rs,'s');
disp('Frequency response of IIR HPF is:');
[b,a]=butter(n,wn,'high','s');
w=0:.01:pi;
[h,om]=freqs(b,a,w);
m=20*log10(abs(h));
an=angle(h);
figure,subplot(2,1,1);plot(om/pi,m);
51
title('magnitude response of IIR HP filter is:');
xlabel('(a) Normalized freq. -->');
ylabel('Gain in dB-->');
subplot(2,1,2);plot(om/pi,an);
title('phase response of IIR HP filter is:');
xlabel('(b) Normalized freq. -->');
ylabel('Phase in radians-->');
OUTPUT:
enter the IIR filter design specifications
enter the passband ripple0.15
enter the stopband ripple60
enter the passband freq1500
enter the stopband freq3000
enter the sampling freq7000
Frequency response of IIR HPF is:
GRAPHS:
magnitude response of IIR HP filter is:
0
-200
-400
-600
0
0.1
0.2
0.3
0.4
0.5 0.6 0.7
(a) Normalized freq. -->
phase response of IIR HP filter is:
0.8
0.9
1
0
0.1
0.2
0.3
0.8
0.9
1
4
Phase in radians-->
Gain in dB-->
200
2
0
-2
-4
0.4
0.5 0.6 0.7
(b) Normalized freq. -->
52
INFERENCE: This program requires certain specifications about the pass band and
stop band ripple & frequencies and the sampling frequency. Here we have used a
function called ‘[n,wn]=buttord(w1,w2,rp,rs,'s')’ in order to find the lowest order N
of digital butterworth filter that loses no more than ‘rp’ db in the pass band and has at
least ‘rs’ db of attenuation in the stop band . w1 and w2 are the pass band and stop
band edge frequencies, normalized from 0 to 1.
The function ‘butter’ designs a Nth order high pass digital butterworth filter and
returns the filter coefficients in length N+1 vectors B (numerator) and A
(denominator).
RESULT: The HP IIR Filter response for the given sequence is generated and the
filter characteristics are plotted.
53
54
55
12. GENERATION OF DUAL TONE MULTIPLE FREQUENCY (DTMF)
SIGNALS
AIM: To generation of dual tone multiple frequency ( DTMF ) signals.
SOFTWARE REQUIRED: MAT LAB 7.0
PROGRAM DESCRIPTION: In this program the Dual tone multiple frequency
signal which is used in telephone systems is generated. A DTMF signal consists of a
sum of two tones, with frequencies taken from two mutually exclusive groups of
Preassigned frequencies. Each pair of such tones represents a unique number or a
symbol. Decoding of a DTMF signal thus involves identifying the two tones in that
signal and determining their corresponding number or symbol.
PROGRAM:
clc;
clear all;
close all;
number=input('enter a phone number with no spaces:','s');
fs=8192;
T=0.5;
x=2*pi*[697 770 852 941];
y=2*pi*[1209 1336 1477 1602];
t=[0:1/fs:T]';
tx=[sin(x(1)*t),sin(x(2)*t),sin(x(3)*t),sin(x(4)*t)]/2;
ty=[sin(y(1)*t),sin(y(2)*t),sin(y(3)*t),sin(y(4)*t)]/2;
for k=1:length(number)
switch number(k)
case'1'
tone=tx(:,1)+ty(:,1);
sound(tone);
plot(tone);
case'2'
tone=tx(:,1)+ty(:,2);
sound(tone);
plot(tone);
case'3'
tone=tx(:,1)+ty(:,3);
sound(tone);
plot(tone);
case'A'
tone=tx(:,1)+ty(:,4);
56
sound(tone);
plot(tone);
case'4'
tone=tx(:,2)+ty(:,1);
sound(tone);
plot(tone);
case'5'
tone=tx(:,2)+ty(:,2);
sound(tone);
plot(tone);
case'6'
tone=tx(:,2)+ty(:,3);
sound(tone);
plot(tone);
case'B'
tone=tx(:,2)+ty(:,4);
sound(tone);
plot(tone);
case'7'
tone=tx(:,3)+ty(:,1);
sound(tone);
plot(tone);
case'8'
tone=tx(:,3)+ty(:,2);
sound(tone);
plot(tone);
case'9'
tone=tx(:,3)+ty(:,3);
sound(tone);
plot(tone);
case'C'
tone=tx(:,3)+ty(:,4);
sound(tone);
plot(tone);
case'#'
tone=tx(:,4)+ty(:,1);
sound(tone);
plot(tone);
case'0'
tone=tx(:,4)+ty(:,2);
sound(tone);
plot(tone);
case'*'
tone=tx(:,4)+ty(:,3);
sound(tone);
57
plot(tone);
case'D'
tone=tx(:,4)+ty(:,4);
sound(tone);
plot(tone);
otherwise
disp('invalid number');
end;
pause(0.75);
end;
OUTPUT:
enter a phone number with no spaces: 936
GRAPHS:
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
500
1000
500
1000
1500
2000
2500
3000
3500
4000
4500
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
1500
2000
2500
3000
3500
4000
4500
58
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
500
1000
1500
2000
2500
3000
3500
4000
4500
INFERENCE: In this program the two frequencies which are going to produce the
dual tone when we press any button, that is why it is called Dual Tone Multiple
Frequency (DTMF). The only constraint is if the number we pressed is not there in the
list then it will generate the output as invalid number. But here the frequencies are
fixed. If we want to generate different tone we have to change the frequencies every
time.
RESULT: Hence Dual Tone Multiple Frequency (DTMF) signals are generated and
the output is verified.
59
60
61
13. PROGRAM TO VERIFY DECIMATION
AIM: To verify Decimation and Interpolation of a given Sequences
SOFTWARE REQUIRED: MAT LAB 7.0
PROGRAM DESCRIPTION: The sampling rate alteration that is employed to
generate a new sequence with a sampling rate lower than that of a given sequence.
Thus, if x[n] is a sequence with a sampling rate of FT Hz and it is used to generate
another sequence y[n] with a desired sampling rate of FT' Hz, then the sampling rate
alteration ratio is given by FT' / FT = R.
If R < 1, the sampling rate is decreased by a process called decimation and it results in
a sequence with a lower sampling rate.
The decimation can be carried out by using the pre-defined commands decimate.
MATLAB CODE:
% DECIMATION
clc;
clear all;
close all;
disp('Let us take a sinusoidal sequence which has to be decimated: ');
fm=input('Enter the signal frequency fm: ');
fs=input('Enetr the sampling frequnecy fs: ');
T=input('Enter the duration of the signal in seconds T: ');
dt=1/fs;
t=dt:dt:T
M=length(t);
m=cos(2*pi*fm*t);
r=input('Enter the factor by which the sampling frequency has to be reduced r: ');
md=decimate(m,r);
figure(1);
subplot(3,1,1);
plot(t,m);
grid;
xlabel('t-->');
ylabel('Amplitude-->');
title('Sinusoidal signal before sampling');
subplot(3,1,2);
stem(m);
grid;
xlabel('n-->');
ylabel('Amplitudes of m -->');
title('Sinusoidal signal after sampling before decimation');
subplot(3,1,3);
stem(md);
grid;
title('Sinusoidal after decimation');
62
xlabel('n/r-->');
ylabel('Amplitude of md-->');
OUTPUT:
Let us take a sinusoidal sequence which has to be decimated:
Enter the signal frequency fm: 2
Enetr the sampling frequnecy fs: 100
Enter the duration of the signal in seconds T: 1
Enter the factor by which the sampling frequency has to be reduced r: 2
GRAPHS:
Amplitude of md-->
Amplitudes of m -->
Amplitude-->
Sinusoidal signal before sampling
1
0
-1
0
0.1
0.2
0.3
0.4
0
0
0.5
0.6
0.7
0.8
t-->
Sinusoidal signal after sampling before decimation
10
20
30
40
5
10
15
0.9
1
80
90
100
40
45
50
1
0
-1
50
60
70
n-->
Sinusoidal after decimation
1
0
-1
20
25
n/r-->
30
35
INFERENCE : The only constraint about the program is that the factors of
decimation or interpolation should be an integers. If we want to change the sampling
frequency by a factor which is not an integer it can be done by using the command
resample by which we can change the sampling rate by a factor I / D. For this we have
to interpolate by an integer factor I and then decimate by an integer factor D
RESULT : The Decimation of given sequences is verified and graphs are plotted.
63
64
65
14. PROGRAM TO VERIFY INTERPOLATION
AIM: To verify Interpolation of a given Sequence.
SOFTWARE REQUIRED: MAT LAB 7.0
PROGRAM DESCRIPTION: The sampling rate alteration that is employed to
generate a new sequence with a sampling rate higher than that of a given sequence.
Thus, if x[n] is a sequence with a sampling rate of FT Hz and it is used to generate
another sequence y[n] with a desired sampling rate of FT' Hz, then the sampling rate
alteration ratio is given by FT' / FT = R.
If R > 1, the process is called interpolation and results in a sequence with a higher
sampling rate.
The interpolation can be carried out by using the pre-defined command interp
respectively.
MATLAB CODE:
%INTERPOLATION
clc;
clear all;
close all;
disp('Let us take a sinusoidal sequence which has to be interpolated: ');
fm=input('Enter the signal frequency fm: ');
fs=input('Enetr the sampling frequnecy fs: ');
T=input('Enter the duration of the signal in seconds T: ');
dt=1/fs;
t=dt:dt:T
M=length(t);
m=cos(2*pi*fm*t);
r=input('Enter the factor by which the sampling frequency has to be increased r: ');
md=interp(m,r);
figure(1);
subplot(3,1,1);
plot(t,m);
grid;
xlabel('t-->');
ylabel('Amplitude-->');
title('Sinusoidal signal before sampling');
subplot(3,1,2);
stem(m);
grid;
xlabel('n-->');
ylabel('Amplitudes of m -->');
title('Sinusoidal signal after sampling before interpolation');
subplot(3,1,3);
stem(md);
66
grid;
title('Sinusoidal after interpolation');
xlabel('n x r-->');
ylabel('Amplitude of md-->');
OUTPUT:
Let us take a sinusoidal sequence which has to be interpolated:
Enter the signal frequency fm: 2
Enetr the sampling frequnecy fs: 100
Enter the duration of the signal in seconds T: 1
Enter the factor by which the sampling frequency has to be increased r: 2
GRAPHS:
Amplitude of md-->
Amplitudes of m -->
Amplitude-->
Sinusoidal signal before sampling
1
0
-1
0
0.1
0.2
0.3
0.4
0
0
0.5
0.6
0.7
0.8
t-->
Sinusoidal signal after sampling before interpolation
10
20
30
40
20
40
60
80
0.9
1
80
90
100
160
180
200
1
0
-1
50
60
70
n-->
Sinusoidal after interpolation
2
0
-2
100 120
n x r-->
140
INFERENCE : The only constraint about the program is that the factors of
decimation or interpolation should be an integers. If we want to change the sampling
frequency by a factor which is not an integer it can be done by using the command
resample by which we can change the sampling rate by a factor I / D. For this we have
to interpolate by an integer factor I and then decimate by an integer factor D
RESULT : The Interpolation of given sequences is verified and graphs are plotted.
67
68
69
70