SlideShare una empresa de Scribd logo
1 de 14
Descargar para leer sin conexión
Convolution and
Correlation of discrete time
Signals
By
Md. Fazle Rabbi
16CSE057
4.2
What is Convolution?
Convolution: Convolution is a mathematical way of combining two signals to form a
third signal.
◆ It is equivalent to finite impulse response (FIR) filtering.
◆ It is important in digital signal processing because convolving two sequences in
time domain is equivalent to multiplying the sequences in frequency domain.
◆ It relates input, output and impulse response of an LTI system as
y(t) = x(t) ∗ h(t)
Where, y(t) = output of LTI, x(t) = input of LTI, h(t) = impulse response of LTI
And * denotes the Convolution Operation.
4.3
Property of Convolution
4.4
Discrete Convolution
• For a linear time invariant system, if the input sequence
x(n) and the impulse response h(n) are given, the output
sequence y(n) can be found.
• This is known as convolution sum and is represented as
• y(n) = x(n) * h(n) = h(n) *x(n)
T
Input Output
x(n) y(n)=x(n)*h(n)
4.5
Example of Discrete Linear Convolution
To calculate Discrete Linear Convolution
Convolute two sequences x[n] = {a,b,c} & h[n] = [e,f,g]
Convoluted output = [ ea, eb+fa, ec+fb+ga, fc+gb, gc]
If any two sequences have m, n number of samples
respectively, then the resulting convoluted sequence will have
[m+n-1] samples.
4.6
Example of Discrete Linear Convolution
Convolute two sequences x[n] = {1,2,3} & h[n] = {-1,2,2}
Convoluted output
y[n] = [ -1, -2+2, -3+4+2, 6+4, 6]
= [-1, 0, 3, 10, 6]
Here x[n] contains 3 samples and h[n] is also having 3
samples so the resulting sequence having 3+3-1 = 5
samples.
4.7
Periodic Convolution
 Periodic convolution is valid for discrete Fourier transform.
To calculate periodic convolution all the samples must be
real. Periodic or circular convolution is also called as fast
convolution.
 If two sequences of length m, n respectively are convoluted
using circular convolution then resulting sequence having
max [m,n] samples.
4.8
Example of Periodic Convolution
Convolute two sequences x[n] = {1,2,3} & h[n] = {-1,2,2} using circular convolution
Normal Convolution output y[n] = [ -1, -2+2, -3+4+2, 6+4, 6]
= [-1, 0, 3, 10, 6]
Here x[n] contains 3 samples & h[n] also has 3 samples.
Hence the resulting sequence obtained by circular
convolution must have max[3,3]= 3 samples.
Now to get periodic convolution result, 1st 3 samples [as the period is 3] of normal convolution is same
next two samples are added to 1st samples as shown below:
Circular convolution result y[n] = [9 6 3]
4.9
Correlation
• It is a measure of similarity between signals and is found using a
process similar to convolution.
• Correlation is used to compare two signals.
• It is used in radar and sonar systems to find the location of a
target by comparing the transmitted and reflected signals.
• Other applications of correlation are in image processing, control
engineering etc.
• The correlation is of two types:
(i) Cross correlation (ii) Auto-correlation
4.10
Cross Correlation
• Cross correlation: The cross correlation between a pair of
sequences x(n) and y(n) is given by
𝑅𝑥𝑦(n)= 𝑘=−∞
∞
𝑥 𝑘 𝑦[−(𝑛-k)]
= x(n) * y(-n)
• Observing the above equation for Rxy(n), we can conclude
that the correlation of two sequences is essentially the
convolution of two sequences in which one of the
sequence has been reversed.
4.11
Example of Cross Correlation
Find the cross correlation of two finite length sequences:
x(n) = {2, 3, 1, 4} and y(n) = {1, 3, 2, 1}
Here,
y(–n) = {1, 2, 3, 1}
Rxy(n) = x(n) * y(–n)
The cross correlation is computed as given below:
R(n) = {2, 3 + 4, 1 + 6 + 6, 4 + 2 + 9 + 2, 8 + 3 + 3, 12 + 1, 4}
= {2, 7, 13, 17, 14, 13, 4}
4.12
Auto Correlation
• The autocorrelation of a sequence is correlation of a
sequence with itself.
• It gives a measure of similarity between a sequence
and its shifted version.
• The autocorrelation of a sequence x(n) is defined as:
𝑅𝑥𝑥(n) = 𝑘=−∞
∞
𝑥 𝑘 𝑥(𝑘 − 𝑛)
𝑅𝑥𝑥 𝑛 = 𝑥 𝑘 ∗ 𝑥(−𝑘)
4.13
Example of Auto Correlation
Find the autocorrelation of the finite length sequence x(n) = {2, 3, 1, 4}.
Here,
x(n) = {2, 3, 1, 4}
x(–n) = {4, 1, 3, 2}
R(n) = x(n) * x(–n)
The auto correlation is computed as given below:
R(n) = {8, 12 + 2, 4 + 3 + 6, 16 + 1 + 9 + 4, 4 + 3 + 6, 12 + 2, 8}
= {8, 14, 13, 30, 13, 14, 8}
4.14
Thank You

Más contenido relacionado

La actualidad más candente

Dsp U Lec04 Discrete Time Signals & Systems
Dsp U   Lec04 Discrete Time Signals & SystemsDsp U   Lec04 Discrete Time Signals & Systems
Dsp U Lec04 Discrete Time Signals & Systemstaha25
 
Computing DFT using Matrix method
Computing DFT using Matrix methodComputing DFT using Matrix method
Computing DFT using Matrix methodSarang Joshi
 
DSP_2018_FOEHU - Lec 02 - Sampling of Continuous Time Signals
DSP_2018_FOEHU - Lec 02 - Sampling of Continuous Time SignalsDSP_2018_FOEHU - Lec 02 - Sampling of Continuous Time Signals
DSP_2018_FOEHU - Lec 02 - Sampling of Continuous Time SignalsAmr E. Mohamed
 
PULSE CODE MODULATION (PCM)
PULSE CODE MODULATION (PCM)PULSE CODE MODULATION (PCM)
PULSE CODE MODULATION (PCM)vishnudharan11
 
Dsp 2018 foehu - lec 10 - multi-rate digital signal processing
Dsp 2018 foehu - lec 10 - multi-rate digital signal processingDsp 2018 foehu - lec 10 - multi-rate digital signal processing
Dsp 2018 foehu - lec 10 - multi-rate digital signal processingAmr E. Mohamed
 
Circular Convolution
Circular ConvolutionCircular Convolution
Circular ConvolutionSarang Joshi
 
Digital Signal Processing
Digital Signal ProcessingDigital Signal Processing
Digital Signal ProcessingSandip Ladi
 
Auto correlation and cross-correlation
Auto correlation and cross-correlationAuto correlation and cross-correlation
Auto correlation and cross-correlationMrinmoy Majumder
 
Optimum Receiver corrupted by AWGN Channel
Optimum Receiver corrupted by AWGN ChannelOptimum Receiver corrupted by AWGN Channel
Optimum Receiver corrupted by AWGN ChannelAWANISHKUMAR84
 
PSK (PHASE SHIFT KEYING )
PSK (PHASE SHIFT KEYING )PSK (PHASE SHIFT KEYING )
PSK (PHASE SHIFT KEYING )vijidhivi
 
Equalization
EqualizationEqualization
Equalizationbhabendu
 
Basics of Digital Filters
Basics of Digital FiltersBasics of Digital Filters
Basics of Digital Filtersop205
 

La actualidad más candente (20)

quantization
quantizationquantization
quantization
 
Dsp U Lec04 Discrete Time Signals & Systems
Dsp U   Lec04 Discrete Time Signals & SystemsDsp U   Lec04 Discrete Time Signals & Systems
Dsp U Lec04 Discrete Time Signals & Systems
 
Sampling Theorem
Sampling TheoremSampling Theorem
Sampling Theorem
 
Computing DFT using Matrix method
Computing DFT using Matrix methodComputing DFT using Matrix method
Computing DFT using Matrix method
 
Discrete Time Systems & its classifications
Discrete Time Systems & its classificationsDiscrete Time Systems & its classifications
Discrete Time Systems & its classifications
 
Multirate DSP
Multirate DSPMultirate DSP
Multirate DSP
 
DSP_2018_FOEHU - Lec 02 - Sampling of Continuous Time Signals
DSP_2018_FOEHU - Lec 02 - Sampling of Continuous Time SignalsDSP_2018_FOEHU - Lec 02 - Sampling of Continuous Time Signals
DSP_2018_FOEHU - Lec 02 - Sampling of Continuous Time Signals
 
PULSE CODE MODULATION (PCM)
PULSE CODE MODULATION (PCM)PULSE CODE MODULATION (PCM)
PULSE CODE MODULATION (PCM)
 
Matched filter
Matched filterMatched filter
Matched filter
 
Dsp 2018 foehu - lec 10 - multi-rate digital signal processing
Dsp 2018 foehu - lec 10 - multi-rate digital signal processingDsp 2018 foehu - lec 10 - multi-rate digital signal processing
Dsp 2018 foehu - lec 10 - multi-rate digital signal processing
 
Sampling theorem
Sampling theoremSampling theorem
Sampling theorem
 
Circular Convolution
Circular ConvolutionCircular Convolution
Circular Convolution
 
Digital Signal Processing
Digital Signal ProcessingDigital Signal Processing
Digital Signal Processing
 
Auto correlation and cross-correlation
Auto correlation and cross-correlationAuto correlation and cross-correlation
Auto correlation and cross-correlation
 
Optimum Receiver corrupted by AWGN Channel
Optimum Receiver corrupted by AWGN ChannelOptimum Receiver corrupted by AWGN Channel
Optimum Receiver corrupted by AWGN Channel
 
PSK (PHASE SHIFT KEYING )
PSK (PHASE SHIFT KEYING )PSK (PHASE SHIFT KEYING )
PSK (PHASE SHIFT KEYING )
 
Sampling
SamplingSampling
Sampling
 
Equalization
EqualizationEqualization
Equalization
 
Dsp lecture vol 7 adaptive filter
Dsp lecture vol 7 adaptive filterDsp lecture vol 7 adaptive filter
Dsp lecture vol 7 adaptive filter
 
Basics of Digital Filters
Basics of Digital FiltersBasics of Digital Filters
Basics of Digital Filters
 

Similar a 5. convolution and correlation of discrete time signals

A novel approach for high speed convolution of finite
A novel approach for high speed convolution of finiteA novel approach for high speed convolution of finite
A novel approach for high speed convolution of finiteeSAT Publishing House
 
A novel approach for high speed convolution of finite and infinite length seq...
A novel approach for high speed convolution of finite and infinite length seq...A novel approach for high speed convolution of finite and infinite length seq...
A novel approach for high speed convolution of finite and infinite length seq...eSAT Journals
 
DSP_FOEHU - MATLAB 02 - The Discrete-time Fourier Analysis
DSP_FOEHU - MATLAB 02 - The Discrete-time Fourier AnalysisDSP_FOEHU - MATLAB 02 - The Discrete-time Fourier Analysis
DSP_FOEHU - MATLAB 02 - The Discrete-time Fourier AnalysisAmr E. Mohamed
 
4. operations of signals
4. operations of signals 4. operations of signals
4. operations of signals MdFazleRabbi18
 
Digital Signal Processing
Digital Signal ProcessingDigital Signal Processing
Digital Signal ProcessingPRABHAHARAN429
 
Convolution problems
Convolution problemsConvolution problems
Convolution problemsPatrickMumba7
 
DSP_FOEHU - MATLAB 01 - Discrete Time Signals and Systems
DSP_FOEHU - MATLAB 01 - Discrete Time Signals and SystemsDSP_FOEHU - MATLAB 01 - Discrete Time Signals and Systems
DSP_FOEHU - MATLAB 01 - Discrete Time Signals and SystemsAmr E. Mohamed
 
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORMNEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORMmathsjournal
 
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORMNEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORMmathsjournal
 
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORMNEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORMmathsjournal
 
Iterative procedure for uniform continuous mapping.
Iterative procedure for uniform continuous mapping.Iterative procedure for uniform continuous mapping.
Iterative procedure for uniform continuous mapping.Alexander Decker
 
Numarical values
Numarical valuesNumarical values
Numarical valuesAmanSaeed11
 
Numarical values highlighted
Numarical values highlightedNumarical values highlighted
Numarical values highlightedAmanSaeed11
 
Fourier supplementals
Fourier supplementalsFourier supplementals
Fourier supplementalsPartha_bappa
 
EC8553 Discrete time signal processing
EC8553 Discrete time signal processing EC8553 Discrete time signal processing
EC8553 Discrete time signal processing ssuser2797e4
 

Similar a 5. convolution and correlation of discrete time signals (20)

A novel approach for high speed convolution of finite
A novel approach for high speed convolution of finiteA novel approach for high speed convolution of finite
A novel approach for high speed convolution of finite
 
A novel approach for high speed convolution of finite and infinite length seq...
A novel approach for high speed convolution of finite and infinite length seq...A novel approach for high speed convolution of finite and infinite length seq...
A novel approach for high speed convolution of finite and infinite length seq...
 
DSP_FOEHU - MATLAB 02 - The Discrete-time Fourier Analysis
DSP_FOEHU - MATLAB 02 - The Discrete-time Fourier AnalysisDSP_FOEHU - MATLAB 02 - The Discrete-time Fourier Analysis
DSP_FOEHU - MATLAB 02 - The Discrete-time Fourier Analysis
 
4. operations of signals
4. operations of signals 4. operations of signals
4. operations of signals
 
Digital Signal Processing
Digital Signal ProcessingDigital Signal Processing
Digital Signal Processing
 
Convolution problems
Convolution problemsConvolution problems
Convolution problems
 
Unit 8
Unit 8Unit 8
Unit 8
 
lec07_DFT.pdf
lec07_DFT.pdflec07_DFT.pdf
lec07_DFT.pdf
 
DSP_FOEHU - MATLAB 01 - Discrete Time Signals and Systems
DSP_FOEHU - MATLAB 01 - Discrete Time Signals and SystemsDSP_FOEHU - MATLAB 01 - Discrete Time Signals and Systems
DSP_FOEHU - MATLAB 01 - Discrete Time Signals and Systems
 
Signal Processing Assignment Help
Signal Processing Assignment HelpSignal Processing Assignment Help
Signal Processing Assignment Help
 
Digital signal processing
Digital signal processingDigital signal processing
Digital signal processing
 
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORMNEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
 
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORMNEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
 
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORMNEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
NEW METHOD OF SIGNAL DENOISING BY THE PAIRED TRANSFORM
 
Iterative procedure for uniform continuous mapping.
Iterative procedure for uniform continuous mapping.Iterative procedure for uniform continuous mapping.
Iterative procedure for uniform continuous mapping.
 
Numarical values
Numarical valuesNumarical values
Numarical values
 
Numarical values highlighted
Numarical values highlightedNumarical values highlighted
Numarical values highlighted
 
Fourier supplementals
Fourier supplementalsFourier supplementals
Fourier supplementals
 
EC8553 Discrete time signal processing
EC8553 Discrete time signal processing EC8553 Discrete time signal processing
EC8553 Discrete time signal processing
 
z transforms
z transformsz transforms
z transforms
 

Más de MdFazleRabbi18

5.programmable interval timer 8253
5.programmable interval timer 82535.programmable interval timer 8253
5.programmable interval timer 8253MdFazleRabbi18
 
4.programmable dma controller 8257
4.programmable dma controller 82574.programmable dma controller 8257
4.programmable dma controller 8257MdFazleRabbi18
 
3.programmable interrupt controller 8259
3.programmable interrupt controller 82593.programmable interrupt controller 8259
3.programmable interrupt controller 8259MdFazleRabbi18
 
Topic4 data encryption standard(des)
Topic4 data encryption standard(des)Topic4 data encryption standard(des)
Topic4 data encryption standard(des)MdFazleRabbi18
 
Topic2 caser hill_cripto
Topic2 caser hill_criptoTopic2 caser hill_cripto
Topic2 caser hill_criptoMdFazleRabbi18
 
Topic5 advanced encryption standard (aes)
Topic5 advanced encryption standard (aes)Topic5 advanced encryption standard (aes)
Topic5 advanced encryption standard (aes)MdFazleRabbi18
 
Topic1 substitution transposition-techniques
Topic1 substitution transposition-techniquesTopic1 substitution transposition-techniques
Topic1 substitution transposition-techniquesMdFazleRabbi18
 
9. hofman coding in DIP
9. hofman coding in DIP9. hofman coding in DIP
9. hofman coding in DIPMdFazleRabbi18
 
7. image enhancement using spatial filtering
7. image enhancement using spatial filtering7. image enhancement using spatial filtering
7. image enhancement using spatial filteringMdFazleRabbi18
 
5. gray level transformation
5. gray level transformation5. gray level transformation
5. gray level transformationMdFazleRabbi18
 
1. steps in image processing
1. steps in image processing1. steps in image processing
1. steps in image processingMdFazleRabbi18
 
2. classification of signals
2. classification of signals 2. classification of signals
2. classification of signals MdFazleRabbi18
 
1. elementary signals
1. elementary signals 1. elementary signals
1. elementary signals MdFazleRabbi18
 
4. random number and it's generating techniques
4. random number and it's generating techniques 4. random number and it's generating techniques
4. random number and it's generating techniques MdFazleRabbi18
 
3. different types of simulations for appropriate systems
3. different types of simulations for appropriate systems 3. different types of simulations for appropriate systems
3. different types of simulations for appropriate systems MdFazleRabbi18
 
2. steps in a simulation study
2. steps in a simulation study 2. steps in a simulation study
2. steps in a simulation study MdFazleRabbi18
 

Más de MdFazleRabbi18 (20)

5.programmable interval timer 8253
5.programmable interval timer 82535.programmable interval timer 8253
5.programmable interval timer 8253
 
4.programmable dma controller 8257
4.programmable dma controller 82574.programmable dma controller 8257
4.programmable dma controller 8257
 
3.programmable interrupt controller 8259
3.programmable interrupt controller 82593.programmable interrupt controller 8259
3.programmable interrupt controller 8259
 
1.ppi 8255
1.ppi 8255 1.ppi 8255
1.ppi 8255
 
Topic4 data encryption standard(des)
Topic4 data encryption standard(des)Topic4 data encryption standard(des)
Topic4 data encryption standard(des)
 
Topic3 playfain
Topic3 playfainTopic3 playfain
Topic3 playfain
 
Topic2 caser hill_cripto
Topic2 caser hill_criptoTopic2 caser hill_cripto
Topic2 caser hill_cripto
 
Topic5 advanced encryption standard (aes)
Topic5 advanced encryption standard (aes)Topic5 advanced encryption standard (aes)
Topic5 advanced encryption standard (aes)
 
Topic1 substitution transposition-techniques
Topic1 substitution transposition-techniquesTopic1 substitution transposition-techniques
Topic1 substitution transposition-techniques
 
11. lzw coding
11. lzw coding11. lzw coding
11. lzw coding
 
9. hofman coding in DIP
9. hofman coding in DIP9. hofman coding in DIP
9. hofman coding in DIP
 
7. image enhancement using spatial filtering
7. image enhancement using spatial filtering7. image enhancement using spatial filtering
7. image enhancement using spatial filtering
 
5. gray level transformation
5. gray level transformation5. gray level transformation
5. gray level transformation
 
1. steps in image processing
1. steps in image processing1. steps in image processing
1. steps in image processing
 
3. systems
3. systems 3. systems
3. systems
 
2. classification of signals
2. classification of signals 2. classification of signals
2. classification of signals
 
1. elementary signals
1. elementary signals 1. elementary signals
1. elementary signals
 
4. random number and it's generating techniques
4. random number and it's generating techniques 4. random number and it's generating techniques
4. random number and it's generating techniques
 
3. different types of simulations for appropriate systems
3. different types of simulations for appropriate systems 3. different types of simulations for appropriate systems
3. different types of simulations for appropriate systems
 
2. steps in a simulation study
2. steps in a simulation study 2. steps in a simulation study
2. steps in a simulation study
 

Último

Human-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming ClassesHuman-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming ClassesMohammad Hassany
 
Prescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxPrescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxraviapr7
 
Education and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxEducation and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxraviapr7
 
How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17Celine George
 
Quality Assurance_GOOD LABORATORY PRACTICE
Quality Assurance_GOOD LABORATORY PRACTICEQuality Assurance_GOOD LABORATORY PRACTICE
Quality Assurance_GOOD LABORATORY PRACTICESayali Powar
 
General views of Histopathology and step
General views of Histopathology and stepGeneral views of Histopathology and step
General views of Histopathology and stepobaje godwin sunday
 
CAULIFLOWER BREEDING 1 Parmar pptx
CAULIFLOWER BREEDING 1 Parmar pptxCAULIFLOWER BREEDING 1 Parmar pptx
CAULIFLOWER BREEDING 1 Parmar pptxSaurabhParmar42
 
How to Use api.constrains ( ) in Odoo 17
How to Use api.constrains ( ) in Odoo 17How to Use api.constrains ( ) in Odoo 17
How to Use api.constrains ( ) in Odoo 17Celine George
 
How to Print Employee Resume in the Odoo 17
How to Print Employee Resume in the Odoo 17How to Print Employee Resume in the Odoo 17
How to Print Employee Resume in the Odoo 17Celine George
 
The Singapore Teaching Practice document
The Singapore Teaching Practice documentThe Singapore Teaching Practice document
The Singapore Teaching Practice documentXsasf Sfdfasd
 
How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17Celine George
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxDr. Santhosh Kumar. N
 
Practical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxPractical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxKatherine Villaluna
 
In - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptxIn - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptxAditiChauhan701637
 
The Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsThe Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsEugene Lysak
 
CapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapitolTechU
 
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdfP4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdfYu Kanazawa / Osaka University
 
Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.raviapr7
 

Último (20)

Human-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming ClassesHuman-AI Co-Creation of Worked Examples for Programming Classes
Human-AI Co-Creation of Worked Examples for Programming Classes
 
Prescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptxPrescribed medication order and communication skills.pptx
Prescribed medication order and communication skills.pptx
 
Education and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxEducation and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptx
 
How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17
 
Quality Assurance_GOOD LABORATORY PRACTICE
Quality Assurance_GOOD LABORATORY PRACTICEQuality Assurance_GOOD LABORATORY PRACTICE
Quality Assurance_GOOD LABORATORY PRACTICE
 
General views of Histopathology and step
General views of Histopathology and stepGeneral views of Histopathology and step
General views of Histopathology and step
 
CAULIFLOWER BREEDING 1 Parmar pptx
CAULIFLOWER BREEDING 1 Parmar pptxCAULIFLOWER BREEDING 1 Parmar pptx
CAULIFLOWER BREEDING 1 Parmar pptx
 
How to Use api.constrains ( ) in Odoo 17
How to Use api.constrains ( ) in Odoo 17How to Use api.constrains ( ) in Odoo 17
How to Use api.constrains ( ) in Odoo 17
 
Personal Resilience in Project Management 2 - TV Edit 1a.pdf
Personal Resilience in Project Management 2 - TV Edit 1a.pdfPersonal Resilience in Project Management 2 - TV Edit 1a.pdf
Personal Resilience in Project Management 2 - TV Edit 1a.pdf
 
How to Print Employee Resume in the Odoo 17
How to Print Employee Resume in the Odoo 17How to Print Employee Resume in the Odoo 17
How to Print Employee Resume in the Odoo 17
 
The Singapore Teaching Practice document
The Singapore Teaching Practice documentThe Singapore Teaching Practice document
The Singapore Teaching Practice document
 
How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptx
 
Practical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxPractical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptx
 
In - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptxIn - Vivo and In - Vitro Correlation.pptx
In - Vivo and In - Vitro Correlation.pptx
 
The Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George WellsThe Stolen Bacillus by Herbert George Wells
The Stolen Bacillus by Herbert George Wells
 
Finals of Kant get Marx 2.0 : a general politics quiz
Finals of Kant get Marx 2.0 : a general politics quizFinals of Kant get Marx 2.0 : a general politics quiz
Finals of Kant get Marx 2.0 : a general politics quiz
 
CapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptx
 
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdfP4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
P4C x ELT = P4ELT: Its Theoretical Background (Kanazawa, 2024 March).pdf
 
Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.Drug Information Services- DIC and Sources.
Drug Information Services- DIC and Sources.
 

5. convolution and correlation of discrete time signals

  • 1. Convolution and Correlation of discrete time Signals By Md. Fazle Rabbi 16CSE057
  • 2. 4.2 What is Convolution? Convolution: Convolution is a mathematical way of combining two signals to form a third signal. ◆ It is equivalent to finite impulse response (FIR) filtering. ◆ It is important in digital signal processing because convolving two sequences in time domain is equivalent to multiplying the sequences in frequency domain. ◆ It relates input, output and impulse response of an LTI system as y(t) = x(t) ∗ h(t) Where, y(t) = output of LTI, x(t) = input of LTI, h(t) = impulse response of LTI And * denotes the Convolution Operation.
  • 4. 4.4 Discrete Convolution • For a linear time invariant system, if the input sequence x(n) and the impulse response h(n) are given, the output sequence y(n) can be found. • This is known as convolution sum and is represented as • y(n) = x(n) * h(n) = h(n) *x(n) T Input Output x(n) y(n)=x(n)*h(n)
  • 5. 4.5 Example of Discrete Linear Convolution To calculate Discrete Linear Convolution Convolute two sequences x[n] = {a,b,c} & h[n] = [e,f,g] Convoluted output = [ ea, eb+fa, ec+fb+ga, fc+gb, gc] If any two sequences have m, n number of samples respectively, then the resulting convoluted sequence will have [m+n-1] samples.
  • 6. 4.6 Example of Discrete Linear Convolution Convolute two sequences x[n] = {1,2,3} & h[n] = {-1,2,2} Convoluted output y[n] = [ -1, -2+2, -3+4+2, 6+4, 6] = [-1, 0, 3, 10, 6] Here x[n] contains 3 samples and h[n] is also having 3 samples so the resulting sequence having 3+3-1 = 5 samples.
  • 7. 4.7 Periodic Convolution  Periodic convolution is valid for discrete Fourier transform. To calculate periodic convolution all the samples must be real. Periodic or circular convolution is also called as fast convolution.  If two sequences of length m, n respectively are convoluted using circular convolution then resulting sequence having max [m,n] samples.
  • 8. 4.8 Example of Periodic Convolution Convolute two sequences x[n] = {1,2,3} & h[n] = {-1,2,2} using circular convolution Normal Convolution output y[n] = [ -1, -2+2, -3+4+2, 6+4, 6] = [-1, 0, 3, 10, 6] Here x[n] contains 3 samples & h[n] also has 3 samples. Hence the resulting sequence obtained by circular convolution must have max[3,3]= 3 samples. Now to get periodic convolution result, 1st 3 samples [as the period is 3] of normal convolution is same next two samples are added to 1st samples as shown below: Circular convolution result y[n] = [9 6 3]
  • 9. 4.9 Correlation • It is a measure of similarity between signals and is found using a process similar to convolution. • Correlation is used to compare two signals. • It is used in radar and sonar systems to find the location of a target by comparing the transmitted and reflected signals. • Other applications of correlation are in image processing, control engineering etc. • The correlation is of two types: (i) Cross correlation (ii) Auto-correlation
  • 10. 4.10 Cross Correlation • Cross correlation: The cross correlation between a pair of sequences x(n) and y(n) is given by 𝑅𝑥𝑦(n)= 𝑘=−∞ ∞ 𝑥 𝑘 𝑦[−(𝑛-k)] = x(n) * y(-n) • Observing the above equation for Rxy(n), we can conclude that the correlation of two sequences is essentially the convolution of two sequences in which one of the sequence has been reversed.
  • 11. 4.11 Example of Cross Correlation Find the cross correlation of two finite length sequences: x(n) = {2, 3, 1, 4} and y(n) = {1, 3, 2, 1} Here, y(–n) = {1, 2, 3, 1} Rxy(n) = x(n) * y(–n) The cross correlation is computed as given below: R(n) = {2, 3 + 4, 1 + 6 + 6, 4 + 2 + 9 + 2, 8 + 3 + 3, 12 + 1, 4} = {2, 7, 13, 17, 14, 13, 4}
  • 12. 4.12 Auto Correlation • The autocorrelation of a sequence is correlation of a sequence with itself. • It gives a measure of similarity between a sequence and its shifted version. • The autocorrelation of a sequence x(n) is defined as: 𝑅𝑥𝑥(n) = 𝑘=−∞ ∞ 𝑥 𝑘 𝑥(𝑘 − 𝑛) 𝑅𝑥𝑥 𝑛 = 𝑥 𝑘 ∗ 𝑥(−𝑘)
  • 13. 4.13 Example of Auto Correlation Find the autocorrelation of the finite length sequence x(n) = {2, 3, 1, 4}. Here, x(n) = {2, 3, 1, 4} x(–n) = {4, 1, 3, 2} R(n) = x(n) * x(–n) The auto correlation is computed as given below: R(n) = {8, 12 + 2, 4 + 3 + 6, 16 + 1 + 9 + 4, 4 + 3 + 6, 12 + 2, 8} = {8, 14, 13, 30, 13, 14, 8}