The presentation covers sampling theorem, ideal sampling, flat top sampling, natural sampling, reconstruction of signals from samples, aliasing effect, zero order hold, upsampling, downsampling, and discrete time processing of continuous time signals.
Classification of signals and systems as well as their properties are given in the PPT .Examples related to types of signals and systems are also given .
Sampling is a Simple method to convert analog signal into discrete Signal by using any one of its three methods
if the sampling frequency is twice or greater than twice then sampled signal can be convert back into analog signal easily......
Classification of signals and systems as well as their properties are given in the PPT .Examples related to types of signals and systems are also given .
Sampling is a Simple method to convert analog signal into discrete Signal by using any one of its three methods
if the sampling frequency is twice or greater than twice then sampled signal can be convert back into analog signal easily......
z-Transform is for the analysis and synthesis of discrete-time control systems.The z transform in discrete-time systems play a similar role as the Laplace transform in continuous-time systems
A Brief Knowledge about Differential Pulse Code Modulation.
It contains the basics of Pulse Code modulation and why we all switching to Differential Pulse Code Modulation.
All the things about the Differential Pulse Code Modulation is given in a good understandable way
Using Chebyshev filter design, there are two sub groups,
Type-I Chebyshev Filter
Type-II Chebyshev Filter
The major difference between butterworth and chebyshev filter is that the poles of butterworth filter lie on the circle while the poles of chebyshev filter lie on ellipse.
z-Transform is for the analysis and synthesis of discrete-time control systems.The z transform in discrete-time systems play a similar role as the Laplace transform in continuous-time systems
A Brief Knowledge about Differential Pulse Code Modulation.
It contains the basics of Pulse Code modulation and why we all switching to Differential Pulse Code Modulation.
All the things about the Differential Pulse Code Modulation is given in a good understandable way
Using Chebyshev filter design, there are two sub groups,
Type-I Chebyshev Filter
Type-II Chebyshev Filter
The major difference between butterworth and chebyshev filter is that the poles of butterworth filter lie on the circle while the poles of chebyshev filter lie on ellipse.
Digital Signal Processing[ECEG-3171]-Ch1_L05Rediet Moges
This Digital Signal Processing Lecture material is the property of the author (Rediet M.) . It is not for publication,nor is it to be sold or reproduced.
#Africa#Ethiopia
Digital Signal Processing[ECEG-3171]-Ch1_L06Rediet Moges
This Digital Signal Processing Lecture material is the property of the author (Rediet M.) . It is not for publication,nor is it to be sold or reproduced.
#Africa#Ethiopia
A Simple Design to Mitigate Problems of Conventional Digital Phase Locked LoopCSCJournals
This paper presents a method which can estimate frequency, phase and power of received signal corrupted with additive white Gaussian noise (AWGN) in large frequency offset environment. Proposed method consists of two loops, each loop is similar to a phase–locked loop (PLL) structure. The proposed structure solves the problems of conventional PLL such as limited estimation range, long settling time, overshoot, high frequency ripples and instability. Traditional inability of PLL to synchronize signals with large frequency offset is also removed in this method. Furthermore, proposed architecture along with providing stability, ensures fast tracking of any changes in input frequency. Proposed method is also implemented using field programmable gate array (FPGA), it consumes 201 mW and works at 197 MHz.
Instrumentation Engineering : Signals & systems, THE GATE ACADEMYklirantga
THE GATE ACADEMY's GATE Correspondence Materials consist of complete GATE syllabus in the form of booklets with theory, solved examples, model tests, formulae and questions in various levels of difficulty in all the topics of the syllabus. The material is designed in such a way that it has proven to be an ideal material in-terms of an accurate and efficient preparation for GATE.
Quick Refresher Guide : is especially developed for the students, for their quick revision of concepts preparing for GATE examination. Also get 1 All India Mock Tests with results including Rank,Percentile,detailed performance analysis and with video solutions
GATE QUESTION BANK : is a topic-wise and subject wise collection of previous year GATE questions ( 2001 – 2013). Also get 1 All India Mock Tests with results including Rank,Percentile,detailed performance analysis and with video solutions
Bangalore Head Office:
THE GATE ACADEMY
# 74, Keshava Krupa(Third floor), 30th Cross,
10th Main, Jayanagar 4th block, Bangalore- 560011
E-Mail: info@thegateacademy.com
Ph: 080-61766222
On The Fundamental Aspects of DemodulationCSCJournals
When the instantaneous amplitude, phase and frequency of a carrier wave are modulated with the information signal for transmission, it is known that the receiver works on the basis of the received signal and a knowledge of the carrier frequency. The question is: If the receiver does not have the a priori information about the carrier frequency, is it possible to carry out the demodulation process? This tutorial lecture answers this question by looking into the very fundamental process by which the modulated wave is generated. It critically looks into the energy separation algorithm for signal analysis and suggests modification for distortionless demodulation of an FM signal, and recovery of sub-carrier signals
The presentation covers asynchronous sequential circuit analysis; Map, transition table, flow table. It also covers asynchronous circuit design process and race conditions
synchronous Sequential circuit counters and registersDr Naim R Kidwai
The presentation covers, synchronous sequential circuits; registers and counters. design of registers, shift registers are explained. Design of counter, synchronous and ripple counter is demostrated.
The presentation covers clocked sequential circuit analysis and design process demonstrated with example. State reduction and state assignment is design is also described.
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The presentation covers infrastructure project financing, typical configurations, key project parties, project contracts, It explains financing of a power project, security mechanism, SPV payment hierarchy and risk mitigation mechanism
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The presentation explains concept of Probability, random variable, statistical averages, correlation, sum of random Variables, Central Limit Theorem,
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The presentation describes Measures of Information, entropy, source coding, source coding theorem, huffman coding, shanon fano coding, channel capacity theorem, capacity of a discrete and continuous memoryless channel, Error Free Communication over a Noisy Channel
Rec101 unit ii (part 2) bjt biasing and re modelDr Naim R Kidwai
The presentation covers BJT Biasing: Operating Point or Q point, Fixed-Bias, Emitter Bias, Voltage-Divider Bias, Collector Feedback bias, Emitter-Follower bias, common base bias, bias Stabilization and re model of CB/ CE/ CC configuration
The presentation covers, Field Effect Transistor: Construction and Characteristic of JFETs, dc biasing of CS, ac analysis of CS amplifier, MOSFET (Depletion and Enhancement)Type, Transfer Characteristic
The presentation covers Bipolar Junction Transistor: Construction, Operation, Transistor configurations and input / output characteristics; Common Base, Common Emitter, and Common Collector
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The presentation covers digital Voltmeter, RAMP Techniques, digital Multi-meters. It also covers Oscilloscope; Introduction and Basic Principle, CRT, Measurement of voltage, current, phase and frequency using CRO, Introduction of Digital Storage Oscilloscope and its comparison over analogue CRO
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
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When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
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Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
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Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
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(C) 2024 Robbie E. Sayers
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Top 10 Oil and Gas Projects in Saudi Arabia 2024.pdf
Sampling Theorem
1. Sampling
3/11/2019 1
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
Sampling theorem, Ideal sampling, Flat top sampling, Natural sampling,
reconstruction of signals from samples, aliasing effect, up sampling and down
sampling, discrete time processing of continuous time signals
2. Sampling Theorem
3/11/2019 2
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
A continuous time band limited signal can be represented by its samples, and can
be recovered from its samples,
provided that Sampling frequency s≥2m, (mmaximum frequency of signal)
The condition is referred as Nyquist criterion
Sampling
Continuous time
signal g(t)
Discrete time
signal g(t)
Sampling frequency S
t tTs0
3. Ideal Sampling
3/11/2019 3
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
Let continuous time band limited signal be
0)(..)()( m
GtsGtg
Let periodic impulse train be
)(
1
)(or
])([*)(
2
1
)]([)(
)()()(signalSampledThen
2where;)()()(
n
s
s
n
ss
p
s
s
n
ss
k
sp
nG
T
G
nGtgFG
ttgtg
T
nTtt
Discrete time signal g(t)
Ideal
SamplingContinuous time signal g(t)
Sampling
frequency S
t tTs0
p(t)
tTs0
1
Using linearity property of FT and convolution property of impulse
n
s
s
nG
T
tg )(
1
)(Thus
Using multiplication property of FT
4. Ideal Sampling
3/11/2019 4
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
g(t) Signal
t
g(t) Sampled signal
tTs 2Ts0 3Ts
p(t) Impulse train
tTs 2Ts0 3Ts
1
p()
s 2s0
s
-s-2s
G()
m-m
A
F[g(t)]
s 2s0
A/Ts
-s-2s
s> 2m
In Time domain:
Sampling results in conversion of
continuous time signal into discrete time
signal
In Frequency domain:
Sampling results in multiple translation of
signal spectrum (linear combination of
shifted signal spectrum at integer
multiples of sampling frequency.
5. Ideal Sampling: Reconstruction
3/11/2019 5
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
Low Pass filter
Cut-off m
n
s
s
nG
T
tg )(
1
)( )(
1
G
Ts
Amplifier
with gain Ts
otherwise
H m
L
0
1
)(
)(G
Reconstruction Filter
Sampled signal
tTs0
g(t)
g(t)
t
)(
1
tg
Ts
6. Sampling Example: Musical CD
3/11/2019 6
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
Audio frequency range is 20Hz-20KHz.
Musical CD consists of two channels of music (for stereo sound) sampled at 44.1 KHz
(oversampling satisfying Nyquist criterion) and quantized to 16 bit. Compute the data size of CD
for 70 minutes music.
CD data= 2 x (44.1 x 103) x 16 x 60 x70 bits = 740.88 MB
7. Aliasing
3/11/2019 7
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
g(t) Signal
t
g(t) Sampled signal
tTs 2Ts0 3Ts
G()
m-m
A
F[g(t)]
s 2s0
As
-s-2s
s> 2m
In case of under sampling (s<2m),
shifted versions of signal spectrum shall
overlap resulting in spectral distortions.
In such case, signal can not be recovered
from its samples. This effect is known as
ALIASING.
To avoid aliasing effect due to spurious
frequencies, a pre alias filter is applied
before sampling
F[g(t)]
s 2s0
As
-s-2s
s= 2m
s <2m
F[g(t)]
s 2s0
As
-s-2s
g(t) Sampled signal
tTs 2Ts0 3Ts
g(t) Sampled signal
tTs 2Ts0 3Ts
8. Flat Top Sampling
3/11/2019 8
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
As ideal impulse can’t be generated, practical sampling pulse will exist for a duration.
In Flat top sampling, for each sample, the value is hold for a duration T.
Flat top sampling may be thought of as output of a system with impulse response h(t) shown
in figure to the input of ideal samples.
Ideal
SamplingContinuous time
signal g(t)
Sampling
frequency S
t
g(t)
tTs0
p(t)
tTs0
1
System with
impulse response
h(t)
tT
1
Ideal samples g(t) Flat top samples gF(t)
gF(t)
tTs0 T
9. Flat Top Sampling
3/11/2019 9
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
22
exp)(
0
22
12)(responseInput
T
Sa
Tj
TH
otherwise
T
t
T
T
Tt
rectth
)(
22
exp)(
)()()(
n
s
s
F
F
nG
T
Sa
Tj
T
T
tG
tGHtG
)(
22
exp2
1
)(Thus
n
s
ss
s
n
sF nG
T
Sa
Tj
T
T
T
Tnt
rectnTgtg
FTofpropertyshifttimeand
2
pairFTUsing
T
SaT
T
t
rect
10. Flat Top Sampling
3/11/2019 10
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
g(t) Signal
t
g(t) Sampled signal
tTs 2Ts0 3Ts
p(t) Impulse train
tTs 2Ts0 3Ts
1
p()
s 2s0
s
-s-2s
G()
m-m
A
F[g(t)]
s 2s0
As
-s-2s
s> 2m
F[gF(t)]
s 2s0
As
-s-2s
s> 2m
gF(t)
tTs0 T
Flat top sampling, introduces aperture effect as per sample function
11. Flat Top Sampling: Reconstruction
3/11/2019 11
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
Low Pass filter
Cut-off m
Equalizer
otherwise
H m
L
0
1
)(
)(G
Reconstruction Filter g(t)
t
m
s
T
Sa
T
T
H
2
1
)(
)(
22
exp)(
n
s
s
F nG
T
Sa
Tj
T
T
tg
gF(t)
tT
s
0 T
H()
t
-m m
2
1
T
Sa
T
Ts
12. Natural Sampling
3/11/2019 12
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
In Natural sampling, each sample is pulse of duration T with amplitude varying in accordance
to signal value.
Natural sampling may be thought of multiplication of signal with pulse train.
Natural
SamplingContinuous time
signal g(t)
Sampling
frequency S
t
Natural samples gN(t)
gN(t)
tTs0 T
tTs0 T
13. Natural Sampling
3/11/2019 13
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
s
n
s
s
n
s
n
TjTn
SaT
T
TnTt
rect
2
exp
2
2trainpulse
)(
22
exp)(
2
exp
2
*)(
2
1
)(
2)()(
n
s
s
s
N
s
n
s
sN
n
s
N
nG
Tn
Sa
T
T
T
tG
n
TjTn
SaTGtG
T
TnTt
recttgtg
)(
22
exp)(Thus
n
s
s
s
F nG
Tn
Sa
T
T
T
tg
14. Natural Sampling
3/11/2019 14
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
g(t) Signal
t
s 2s0
sT
-s-2s
G()
m-m
A
F[gN(t)]
s 2s0
As
-s-2s
s> 2m
tTs0 T
Pulse Train
Natural sampling, introduces amplitude scaling as per sample function at every shifted version
of G(), and not the aperture effect as in Flat top sampling.
gN(t) Natural Sampling
tTs0 T
15. Natural Sampling: Reconstruction
3/11/2019 15
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
)(G
Low Pass filter
Cut-off m
Amplifier with
gain T/Ts
otherwise
H m
L
0
1
)(
Reconstruction Filter g(t)
t
)(
22
exp)(
n
s
s
s
N nG
Tn
Sa
T
T
T
tg
gN(t) Natural Sampling
tTs0 T
16. Zero Order Hold Reconstruction of Signals
3/11/2019 16
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
g(t) Signal
tg(t) Sampled signal
tTs 2Ts0 3Ts
gZ(t) Zero order hold reconstruction
tTs 2Ts0 3Ts
Zero order hold reconstruction involve holding the
sampling value till next sample. It makes a staircase
approximation of the signal.
i.e. Zero order hold is special case of flat top sampling
with pulse width equal to sampling period gz(t)gF(t)TTs
)(
22
exp)(g
2
1
)()()(g
n
s
ss
z
n s
s
sTTFz
nG
T
Sa
Tj
t
T
Tnt
rectnTgtgt
s
Exponential term in Spectrum of Zero order hold reflects delay by Ts/2, while sample
function term results in aperture effect causing distortion.
17. Zero Order Hold Reconstruction of Signals
3/11/2019 17
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
Zero order hold can be achieved by simple holding circuit which holds sample value till next
sample
Low Pass filter
Cut-off m
Equalizer
otherwise
H m
L
0
1
)(
)(G
Reconstruction Filter g(t)
t
m
sT
Sa
H
2
1
)(
H()
t
-m m
2
1
sT
Sa
gZ(t) Zero order hold
tTs 2Ts0 3Ts
)(
22
exp)(g
n
s
ss
z nG
T
Sa
Tj
t
18. Up Sampling and Down sampling
3/11/2019 18
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
Up-sampling: introducing zeros between
samples to create a longer signal
Down-sampling (decimation): sub-sampling a
discrete signal
g(t) Signal
t
g(t) Sampled signal
tTs 2Ts0 3Ts
gd(t) down sampling g(t) by 2
tTs 2Ts0 3Ts
g(t) up-sampling gd(t) by 2
tTs 2Ts0 3Ts
19. Discrete Time Processing of Continuous time Signals
3/11/2019 19
Dr Naim R Kidwai, Professor, Integral University, Lucknow
www.nrkidwai.wordpress.com
Continuous time signals can be converted into discrete time using sampling and quantized to
make it digital. These discrete time signals can be processed using computer based discrete
time systems and output can be reconstructed as continuous time signal.
g(t) A/D converter
(Sampling/
Quantization)
Discrete time
system
D/A converter
(Reconstruction)
g(nTs)
=g[n]
y(nTs)
=y[n] y(t)