Signal Programming Lab Experiments with SCI Lab Software
Signal Processing Lab Experiments:
Front Page / Cover Page: Docx Format / PDF FormatExperiments: Docx Format / PDF Format
PROGRAM 1
AIM:
Generation of continuous and discrete elementary signals (Periodic and non
periodic) using mathematical expression.
Software
requirement: - SCI LAB
Theory: A
wave is a disturbance that transfers energy from one place to another without
requiring any net flow of mass. Waves can be broadly separated into pulses and
periodic waves. A pulse is a single disturbance while a periodic wave is a
continually oscillating motion. There is a close connection between simple
harmonic motion and periodic waves; in most periodic waves, the particles in
the medium experience simple harmonic motion.
Waves
can also be separated into transverse and longitudinal waves. In a transverse
wave, the motion of the particles of the medium is at right angles (i.e.,
transverse) to the direction the wave moves. In a longitudinal wave, such as a
sound wave, the particles oscillate along the direction of motion of the wave.
Surface
waves, such as water waves, are generally a combination of a transverse and a
longitudinal wave. The particles on the surface of the water travel in circular
paths as a wave moves across the surface.
Periodic
waves
A
periodic wave generally follows a sine wave pattern, as shown in the diagram.
Program code
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//continous
time cosine signal t=-5:0.0001:5; F=1; y1=cos(2*F*t*pi); subplot(3,2,1); plot2d3(t,y1); xlabel('Time'); ylabel('Magnitude'); title('continous
time cosine signal'); //continous
time sine signal y2=sin(2*F*t*pi); subplot(3,2,3); plot2d3(t,y2); xlabel('Time'); ylabel('Magnitude'); title('continous
time sine signal'); //continous
time aperiodic signal y3=sin(2*F*t*pi).*t; subplot(3,2,5); plot2d3(t,y3); xlabel('Time'); ylabel('Magnitude'); title('continous
time aperiodic signal');
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//discrete
time cosine signal n =
-20:1:20; f =
1/20; y4=cos(2*f*n*pi); subplot(3,2,2); plot2d3(n,y4); xlabel('Time'); ylabel('Magnitude'); title('discrete
time cosine signal'); //discrete
time sine signal y5=sin(2*f*n*pi); subplot(3,2,4); plot2d3(n,y5); xlabel('Time'); ylabel('Magnitude'); title('discrete
time sine signal'); //discrete
time aperiodic signal y6=cos(2*f*n*pi).*n; subplot(3,2,6); plot2d3(n,y6); xlabel('Time'); ylabel('Magnitude'); title('discrete
time aperiodic signal');
|
Figure (Expected output):
VIVA VOICE QUESTION:
Q1. What
is Signal?
Q2. What are
periodic signal.
Q3.What
is time period.
Q4.Unit
step is periodic signal or not.
Q5. u(t)+u(-t)
is periodic or not.
Q6. Exponential
signal is periodic or not.
Q7.
Sum of two periodic signal is always periodic signal. True or false?
PROGRAM 2
AIM:
Generation of Continuous and Discrete Unit Step Signal.
Software
requirement: - SCI LAB
Unit step: A signal with magnitude
one for time greater than zero. We can assume it as a dc signal which got
switched on at time equal to zero.
Unit step function is denoted by u (t).
It is defined as u (t) =
·
It is used as best test signal.
·
Area under unit step function is unity.
Program code
|
t=-10:0.001:10; x0=0; x1=1; y1=x1*(t>=0)+x0*(t<0); subplot(4,3,1); plot2d3(t,y1); xlabel('Time'); ylabel('Magnitude'); title('Continuous
Unit Step Function'); y2=x1*(t>=6)+x0*(t<6); subplot(4,3,2); plot2d3(t,y2); xlabel('Time'); ylabel('Magnitude'); title('Continuous
Unit Step u(t-6) Function'); y3=x1*(t>=-6)+x0*(t<-6); subplot(4,3,3); plot2d3(t,y3); xlabel('Time'); ylabel('Magnitude'); title('Continuous
Unit Step u(t+6) Function'); y4=x0*(t>=4)+x1*(t<4); subplot(4,3,4); plot2d3(t,y4); xlabel('Time'); ylabel('Magnitude'); title('Continuous
Unit Step u(-t+4) Function'); y5 =
y3 - y2; subplot(4,3,5); plot2d3(t,y5); xlabel('Time'); ylabel('Magnitude'); title('Continuous
Unit Step u(t+6)-u(t-6) Function'); y6 =
y3 + y2; subplot(4,3,6); plot2d3(t,y6); xlabel('Time'); ylabel('Magnitude'); title('Continuous
Unit Step u(t+6)+u(t-6) Function'); |
n=-10:1:10; x0=0; x1=1; y7=x1*(n>=0)+x0*(n<0); subplot(4,3,7); plot2d3(n,y7); xlabel('Time'); ylabel('Magnitude'); title('discrete
Unit Step u(n) Function'); y8=x1*(n>=6)+x0*(n<6); subplot(4,3,8); plot2d3(n,y8); xlabel('Time'); ylabel('Magnitude'); title('discrete
Unit Step u(n-6) Function'); y9=x1*(n>=-6)+x0*(n<-6); subplot(4,3,9); plot2d3(n,y9); xlabel('Time'); ylabel('Magnitude'); title('discrete
Unit Step u(n+6) Function'); y10=x0*(n>=4)+x1*(n<4); subplot(4,3,10); plot2d3(n,y10); xlabel('Time'); ylabel('Magnitude'); title('discrete
Unit Step u(-n+4) Function'); y11
= y9 - y8; subplot(4,3,11); plot2d3(n,y11); xlabel('Time'); ylabel('Magnitude'); title('discrete
Unit Step u(n+6)-u(n-6) Function'); y12
= y9 + y8; subplot(4,3,12); plot2d3(n,y12); xlabel('Time'); ylabel('Magnitude'); title('discrete
Unit Step u(n+6)+u(n-6) Function');
|
Figure (Expected output):
VIVA VOICE QUESTION:
Q1. What
is Signal?
Q2. What is unit
step signal?
Q3.Differention
of step signal is?
Q4.
Integration of step signal is?
Q5.
What is continues time signals?
Q6.
What are discrete time signals?
Q7.
What is Analog signal?
PROGRAM 3
AIM:
Generation of Exponential and Ramp signals in Continuous & Discrete domain.
Software
requirement: - SCI LAB
Ramp signal:
A signal whose magnitude increases same as time. It can be obtained by
integrating unit step.Ramp signal is denoted by r (t), and it is defined as r
(t) =
Area
under unit ramp is unity.
Exponential signal:
Exponential signal is in the form of x (t) = eαt.
The shape of exponential can be defined by α.
Case
i: if α=
0 → x(t) =e0=
1
Case ii: if α<
0 i.e. -ve then x (t) = e-αt.
The shape is called decaying exponential.
Case iii: if α>
0 i.e. +ve then x (t) = eαt .
The shape is called rising exponential.
Program code
|
t=-2:0.01:2; a=2; //continous
time increasing exponential signal y1=exp(a*t); subplot(3,2,1); plot2d3(t,y1); xlabel('time'); ylabel('amplitude'); title('continous
time increasing exponential signal'); //continous
time decreasing exponential signal y2=exp(-a*t); subplot(3,2,2); plot2d3(t,y2); xlabel('time'); ylabel('amplitude'); title('continous
time decreasing exponential signal'); |
//discrete
time increasing exponential signal n=-5:1:5; a =
1/4; y3=exp(a*n); subplot(3,2,3); plot2d3(n,y3); xlabel('time'); ylabel('amplitude'); title('discrete
time increasing exponential signal'); //discrete
time decreasing exponential signal y4=exp(-a*n); subplot(3,2,4); plot2d3(n,y4); xlabel('time'); ylabel('amplitude'); title('discrete
time decreasing exponential signal');
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//continous
ramp signal x0=0; y5=t.*(t>=0)+x0.*(t<0); subplot(3,2,5); plot2d3(t,y5); xlabel('time'); ylabel('amplitude'); title('continous
ramp signal'); //discrete
ramp signal y6=n.*(n>=0)+x0*(n<0); subplot(3,2,6); plot2d3(n,y6); xlabel('time'); ylabel('amplitude'); title('discrete
ramp signal');
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Figure (Expected output):
VIVA VOICE QUESTION:
Q1. What
is Signal?
Q2. What is ramp signal?
Q3.What
is Exponential signal.
Q4.Differention
of ramp signal is?
Q5.
Integration of ramp signal is?
Q6.
What is continues time signals?
Q7.
What are discrete time signals?
Q8.
What is Analog signal?
PROGRAM 4
AIM:
Continuous and Discrete Time Convolution (Using Basic Definition).
Software
requirement: - SCI LAB
Theory: A convolution
is an integral that expresses the amount of overlap of one function as it is
shifted over another function.It therefore "blends" one function with
another. For example, in synthesis imaging, the measured dirty map is a
convolution of the "true" CLEAN map with the dirty beam (the FOURIER TRANSFORM of
the sampling distribution). The convolution is sometimes also known by its
German name, faltung ("folding").
Abstractly,
a convolution is defined as a product of functions 
and 
that are objects in the algebra of SCHWARTZ FUNCTIONS in.
Convolution of two functions and over a finite range is given by
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|
Where the symbol 
denotes convolution of and .
Convolution is more often taken over an infinite
range,
Program code
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(4A) x=input('enter
first sequence'); b1=input('enter
the lower limit'); u1=input('enter
the upper limit'); x1=b1:1:u1; h=input('enter
second sequence'); b2=input('enter
the lower limit'); u2=input('enter
the upper limit'); h1=b2:1:u2; b=b1+b2; u=u1+u2; a=b:1:u; m=length(x); n=length(h); X=[x,zeros(1,n)]; subplot(2,2,1); disp('x(n)
is:'); disp(x); plot2d3(x1,x); xlabel('n'); ylabel('x(n)'); title('first
squence'); grid
on; H=[h,zeros(1,m)]; subplot(2,2,2); disp('h(n)
is;'); disp(h); plot2d3(h1,h); xlabel('n'); ylabel('h(n)'); title('second
sequence'); grid
on; for i=1:n+m-1 Y(i)=0; for j=1:m; if((i-j+1)>0) Y(i)=Y(i)+(X(j)*H(i-j+1)); else end end end subplot(2,2,[3 4]); disp('y(n)
is:'); disp(Y); plot2d3(a,Y); xlabel('n'); ylabel('Y(n)'); title('output
sequence'); grid
on; |
(4B)
t1=-5:1:0 t2=0:1:2; t3=2:1:5; h1=zeros(size(t1)); h2=ones(size(t2)); h3=zeros(size(t3)); t=[t1
t2 t3]; h=[h1
h2 h3]; subplot(3,1,1); plot2d3(t,h); xlabel('time'); ylabel('magnitude'); a1=-5:1:0; a2=0:1:4; a3=4:1:6; x1=zeros(size(a1)); x2=ones(size(a2)); x3=zeros(size(a3)); a=[a1
a2 a3]; x=[x1
x2 x3]; subplot(3,1,2); plot2d3(a,x); xlabel('time'); ylabel('magnitude'); c=conv(x2,h2); subplot(3,1,3); plot2d3(c); xlabel('time'); ylabel('magnitude');
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(4C) x =
input('enter the first seq'); N1 =
length(x); n1 =
0:1:N1-1; subplot(2,2,1); plot2d3(n1,x); xlabel('time'); ylabel('mag'); title('seq
of x'); h =
input('enter the second seq'); N2 =
length(h); n2 =
0:1:N2-1; subplot(2,2,2); plot2d3(n2,h); xlabel('time'); ylabel('mag'); title('seq
of h'); y=conv(x,h); n =
0:1:N1+N2-2; subplot(2,2,[3
4]); plot2d3(n,y); xlabel('time'); ylabel('mag'); title('convolution');
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Figure (Expected output):
Figure
4(c):
Input:
enter
the first seq:=[0 1 2 3]
enter the second
seq:=[2 3 4]
Output
y(n)= [0 2
7 16 17
12]
Figure
4(b):
Figure
4(a):
Input
& Output
enter
first sequence:=[-2 -4 5 6]
enter
the lower limit:=-1
enter
the upper limit:=2
enter
second sequence:=[3 4 5]
enter
the lower limit:=0
enter
the upper limit:=2
x(n)
is:
-2
-4 5 6
h(n)
is;
3
4 5
y(n)
is:
-6
-20 -11 18
49 30 38
24
Result:-I
have performed convolution on matlab successfully.
VIVA VOICE QUESTION:
Q1. What
is the importance of linear and circular convolution in signals and systems?
Q2. Write the
properties of linear convolution.
Q3.What
is formula for continuous time convolution signal?
Q4.
What is formula for discrete time convolution signal?
Q5.
What is meaning of time shifting.
Q6. What is impulse
response? Explain its significance.
Q7.
Which command we use in sci lab for performing convolution.
PROGRAM 5
AIM: Adding
and subtracting two given signals (continuous as well as discrete signals).
Software requirement:
- SCI LAB
Program
Code
|
clc; //continuous
signal t = 0:0.001:30; y1 = t; y2 = 2*t; //First Signal subplot(4,2,1); plot2d3(t,y1); xlabel('time'); ylabel('magnitude'); title('First Signal'); //Second
Signal subplot(4,2,2); plot2d3(t,y2); xlabel('time'); ylabel('magnitude'); title('Second Signal'); y3 = y1+y2; y4 = y1-y2; //Addition subplot(4,2,3); plot2d3(t,y3); xlabel('time'); ylabel('magnitude'); title('Addition'); //subtraction subplot(4,2,4); plot2d3(t,y4); xlabel('time'); ylabel('magnitude'); title('Subtraction');
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//discrete
signal n=0:1:30; a=n; b=2*n; //First Signal subplot(4,2,5); plot2d3(n,a); xlabel('time'); ylabel('magnitude'); title('First Signal'); //Second
Signal subplot(4,2,6); plot2d3(n,b); xlabel('time'); ylabel('magnitude'); title('Second Signal'); c=a+b; d=a-b; //Addition subplot(4,2,7); plot2d3(n,c); xlabel('time'); ylabel('magnitude'); title('Addition'); //subtraction subplot(4,2,8); plot2d3(n,d); xlabel('time'); ylabel('magnitude'); title('Subtraction');
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Figure (Expected output):
VIVA VOICE QUESTION:
Q1. Addition
of two periodic signals is periodic or not?
Q2. Addition of u (t) and u (-t) is …………….signals.
Q3. Subtraction of u (t) and u (-t) is …………….signals.
Q4.
Addition of two even signals is even or odd?
Q5. Addition
of two odd signals is even or odd?
Q6. Addition of even
and odd signals is ?
PROGRAM 6
AIM: To
generate uniform random numbers between (0,1).
Software requirement:
- SCI LAB
Theory:
Two Classes Signals
Signals are subdivided into two classes, namely,
(1)Deterministic signals
(2)Random
signals
Deterministic Signals & Random
Signals
Signals
that can be modelled exactly by a mathematical formula are known as
deterministic signals. Deterministic signals are not always adequate to model
real-world situations. Random signals, on the other hand, cannot be described
by a mathematical equation; they are modeled in probabilistic terms.
It’s
fairly easy to generate uncorrelated pseudo- random sequences. MATLAB has two
built-in functions to generate pseudo-random numbers, namely rand and randn.
The rand function generates pseudo-random numbers whose elements are
uniformly distributed in the interval (0,1). You can view this as tossing a
dart at a line segment from 0 to 1, with the dart being equally likely to hit
any point in the interval [0,1]. The randn function generates
pseudo-random numbers whose elements are normally distributed with mean 0 and
variance 1 (standard normal). Both functions have the same syntax. For example,
rand(n) returns a n-by- n matrix of random numbers, rand(n,m) returns a n-by-m
matrix with randomly generated entries distributed uniformly between 0 and 1.,
and rand(1) returns a single random number.
- Random Number Generation: Pseudo-random Numbers -
>> %Generate one thousand uniform
pseudo-random numbers
|
>>rand(1,1000) |
% return a row
vector of 1000 entries |
|
>>%Generate one thousand
gaussian pseudo-random numbers |
|
|
>>randn(1,1000); |
% return a row
vector of 1000 entries |
Program Code
|
clc; n=input('Enter the number
which is generated:'); y=rand(1,n); //continuous
signal subplot(2,1,1); plot2d3(n,y); xlabel('n'); ylabel('magnitude'); title('continuous
signal'); //discrete
signal subplot(2,1,2); plot2d3(n,y); xlabel('n'); ylabel('magnitude'); title('discrete signal;');
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Figure (Expected output):
VIVA VOICE QUESTION:
Q1. What
is Random Signal?
Q2. What is
probability?
.
Q3.What
is Maximum value of probability
Q4. How
many types of discrete distribution.
Q5.
What is uniform distribution?
Q6. Which
command we use to generate random signal?
PROGRAM 7
AIM: To
generate a random binary wave.
Software requirement:
- SCI LAB
Program
Code
|
n =
input('enter the total number which is generated N='); j =
0; y1
= rand(1,n); y =
round(y1); for i=
1:n if y(i) == 1; j(i) = ones; else j(i) = zeros; end end plot2d3(j); xlabel('no.
of random signal'); ylabel('amplitude'); title('plot
of random in ones and zeros 0-1');
|
Figure (Expected output):
VIVA VOICE QUESTION:
Q1. What
is Random Signal?
Q2. What are binary
signals?
.
Q3.
Binary wave generated by which command?
Q4.
What is uniform distribution?
Q5.
Which command we use to generate random signal?
Q6.
What is used of round command?
PROGRAM 8
AIM: To
generate and verify random sequences with arbitrary distributions, means and
Variances for following:
(a) Rayleigh distribution
(b) Normal distributions: N(0,1)
(c) Poisson
distributions: N(m, x)
Software requirement: - SCI LAB
Theory:
(a)The Rayleigh distribution- it
is a special case of the WEIBULL
DISTRIBUTION.
If A and B are the parameters of the Weibull distribution, then
the Rayleigh distribution with parameter b is equivalent to the Weibull
distribution with parametersA=21/2 b and B = 2.
If
the component velocities of a particle in the x and y directions
are two independent normal random variables with zero means and equal
variances, then the distance the particle travels per unit time is distributed
Rayleigh.
In
communications theory NAKAGAMI
DISTRIBUTION,
RICIAN
DISTRIBUTION,
and Rayleigh distributions are used to model scattered signals that reach a
receiver by multiple paths. Depending on the density of the scatter, the signal
will display different fading characteristics. Rayleigh and Nakagami
distributions are used to model dense scatters, while Rician distributions
model fading with a stronger line-of-sight. Nakagami distributions can be
reduced to Rayleigh distributions, but give more control over the extent of the
fading.
The Rayleigh pdf is
y= f(x)
=
(b)
The Normal distributions-
A
normal distribution in a VARIATE 
with MEAN 
and VARIANCE 
is a statistic distribution with probability
density function
|
|
(1) |
on
the domain 
. While statisticians and
mathematicians uniformly use the term "normal distribution" for this
distribution, physicists sometimes call it a Gaussian distribution and, because
of its curved flaring shape, social scientists refer to it as the "bell
curve."
The
so-called "standard normal distribution" is given by taking 
and 
in a general normal distribution.
An arbitrary normal distribution can be converted to a standard normal
distribution by changing variables to 
, so 
, yielding
|
(c) The
Poisson distributions- A Poisson random variable is
the number of successes that result from a Poisson experiment. The
probability distribution of a Poisson random variable is called a Poisson
distribution. Given the mean number of successes (μ)
that occur in a specified region, we can compute the Poisson probability
based on the following formula: Poisson Formula.
Suppose we conduct a Poisson experiment, in which the average number of
successes within a given region is μ. Then, the Poisson probability is: P(x;
μ) = (e-μ) (μx) / x! Where x is the actual number of
successes that result from the experiment and e is approximately equal
to 2.71828. The Poisson distribution has the
following properties: ·
The mean of the distribution is equal
to μ . ·
The variance is also equal to σ.
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Program code
|
//normal
distribution x =
-5:0.01:5; y1
= (normpdf(x,0,1)); y2
= (normpdf(x,0.1,2)); y3
= (normpdf(x,0,0.5)); subplot(3,1,1); plot2d3(x,y1,'.',x,y2,'-',x,y3,'*'); xlabel('value
of x'); ylabel('value
of y'); title('normal
distribution');
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//rayleigh
distribution x =
-5:1:15; y1
= (poisspdf(x,4)); y2
= (poisspdf(x,2)); y3
= (poisspdf(x,1)); subplot(3,1,2); plot2d3(x,y1,'.',x,y2,'-',x,y3,'*'); xlabel('value
of x'); ylabel('value
of y'); title('rayleigh
distribution');
|
//poission
distribution x =
-5:1:15; y1
= (raylpdf(x,4)); y2
= (raylpdf(x,2)); y3
= (raylpdf(x,1)); subplot(3,1,3); plot2d3(x,y1,'.',x,y2,'-',x,y3,'*'); xlabel('value
of x'); ylabel('value
of y'); title('poission
distribution');
|
Figure (Expected output):
VIVA VOICE QUESTION:
Q1. What
is pdf?
Q2. What is cdf.
Q3.What
are the Mean and variance of Poisson distribution?
Q4.
What are the Mean and variance of Normal distribution?
Q5.Which
command we use in scilab to plot pdf of normal distribution.
Q6.Normal
distribution is continuous or discrete?
Q7.If
value of probability is very small and number is large than which distribution
is used?
PROGRAM 9
AIM: To
plot the probability density functions. Find mean and variance for the above
Distributions
Software requirement:
- SCI LAB
Theory:
PDF:
in probability theory, a probability density function (PDF), or density
of a continous random variable, is a function, whose value at any given sample
(or point) in the sample space (the set of possible values taken by the random
variable) can be interpreted as providing a relative likelihood that the value
of the random variable would equal that sample.In other words, while the
absolute likelihood for a continuous random variable to take on any particular
value is 0 (since there are an infinite set of possible values to begin with),
the value of the PDF at two different samples can be used to infer, in any
particular draw of the random variable, how much more likely it is that the
random variable would equal one sample compared to the other sample.
In a
more precise sense, the PDF is used to specify the probability of the random
variable falling within a particular range of values, as opposed to taking on
any one value. This probability is given by the integral of this variable’s PDF
over that range—that is, it is given by the area under the density function but
above the horizontal axis and between the lowest and greatest values of the
range. The probability density function is nonnegative everywhere, and its
integral over the entire space is equal to one.
The
terms "probability distribution functions" and "probability
function" have also sometimes been used to denote the probability density
function. However, this use is not standard among probability and
statisticians. In other sources, "probability distribution function"
may be used when the probability distribution is defined as a function over
general sets of values, or it may refer to the cumulative distribution
function, or it may be a probability mass function (PMF) rather than the density.
"Density function" itself is also used for the probability mass
function, leading to further confusion. In general though, the PMF is used in
the context of discrete random variables (random variables that take values on
a discrete set), while PDF is used in the context of continuous random
variables.
CDF: (Cumulative Distribution Function)As the name
cumulative suggests, this is simply the probability up to a particular value of
the random variable, say x. Generally denoted by F, F= P (X<=x) for any value
of x in the X space. It is defined for both discrete and continuous random
variables.
Program code
|
//pdf
mu
= 100; sigma
= 15; xmin
= 70; xmax
= 130; n =
100; k =
10000; x =
linspace(xmin,xmax,n); p =
normpdf(x,mu,sigma); subplot(2,1,1); plot2d3(x,p); xlabel('x'); ylabel('pdf'); title('probability
density function');
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//cdf mu
= 100; sigma
= 15; xmin
= 70; xmax
= 130; n =
100; k =
10000; x =
linspace(xmin,xmax,n); c =
normcdf(x,mu,sigma); subplot(2,1,2); plot2d3(x,c); xlabel('x'); ylabel('pdf'); title('cumulative
distribution function');
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Figure (Expected output):
VIVA VOICE QUESTION:
Q1. What
is pdf?
Q2. What is cdf.
Q3.What
is the Mean and variance of Poisson distribution?
Q4.
What are the Mean and variance of Normal distribution?
Q5.Which
command we use in matlab to plot pdf of normal distribution.
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