Basics About Signals Systems
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Transcript of Basics About Signals Systems
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Presentation by:
Mr. S. Karthie,
Assistant Professor/ECE
SSN College of Engineering
CS2403 - Digital Signal Processing
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OUTLINE OF THIS COURSE�Introduction – Basics of Signals & Systems (Unit-I)
�Discrete Time LTI Systems – Analysis (Unit-I)
�Z-Transform (Unit-I)
�Discrete Fourier Transform & Fast Fourier Transform (Unit-II)
�Digital Filter Structures
�IIR Filter Design (Unit-III)
�FIR Filter Design (Unit-IV)
�Finite Word length Effects (Unit-IV)
�Applications of DSP (Unit-V)
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Introduction
• Signal : A physical quantity that varies with time or frequency or any other independent variables
Broad Classification of Signals:
(i) Continuous Time Signal
(ii) Discrete Time Signal
(iii) Digital Signal
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Broad Classification of Signals
•Continuous time –•Continuous amplitude
•Continuous time –•Discrete amplitude
•Discrete time –• Continuous amplitude
•Discrete time –•Discrete amplitude
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• Analog signals: continuous in time and
amplitude
– Example: voltage, current, temperature,…
• Digital signals: discrete both in time and
amplitude
– Example: attendance of this class, digitizes analog
signals,…
• Discrete-time signals: discrete in time,
continuous in amplitude
– Example: hourly change of temperature
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• System : A physical device that operates on an input signal inorder to change/modify the characteristics of that signal into a desired signal.
DT System : y(n) = T{x(n}
Broad Classification of Systems:
(i) Continuous Time System
(ii) Discrete Time System
(iii) Digital System
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Why signals should be processed?
• Signals are carriers of information
–Useful and unwanted
–Extracting, enhancing, storing and transmitting the useful information
• How signals are being processed?
– Analog Signal Processing
– Digital Signal Processing
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Block Diagram of DSP
PrF ADC DSP DAC PoFAnalog Analog
Equivalent analog signal processor
PrF: antialiasing filtering
PoF: smooth out the staircase waveform
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Comparison of DSP over ASP
-Advantages
• Developed Using Software on Computer
• Working Extremely Stable
• Easily Modified in Real Time
• Low Cost and Portable
-Disdvantages
• Lower Speed and Lower Frequency
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Basic Ways to Represent DT Signals
�Sequence Representation
�Tabular Representation
�Functional Representation
�Graphical Representation
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Discrete Time Signal -Types
(i) Unit sample Sequence
(ii) Unit step sequence
{ }LL ,0,0,1,0,0,0,0
0,1)(
↑=
≠
==
n
nnδ
{ }LL ,1,1,1,0,0,0,0
0,1)(
↑=
<
≥=
n
nnu
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Discrete Time Signal – Types (Contd…)
(iii) Ramp Sequence
r(n) = n ; n>0
0 ; n<0
(iv) Exponential Sequence
where x(n) = exp(n)
Rananxn ∈∀= ;,)(
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Classification based on Properties
• CT and DT Signals
• Deterministic and Random Signals
• Periodic and Aperiodic Signals
• Symmetric (Even) and Antisymmetric (Odd) Signals
• Energy and Power Signals
• Causal and Non-Causal Signals
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Deterministic and Random Signals
• Deterministic Signal – No uncertainity of its magnitude and phase at any given instant of time. (Ex : Sine Signal)
• Random Signal – Charcaterized by uncertainity about its actual occurrence. (Ex: Noise, Speech signal etc)
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Periodic and Aperiodic Signals
• Periodic Signal – If the DT signal satisfies the condition
x(n) = x(n+ N)
where N = Fundamental Period
* A signal which repeats itself at regular interval of time is said to be “periodic” otherwise it is “aperiodic”or “non-periodic” signal
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Symmetric (Even) and Antisymmetric (Odd) Signals
• Even Signal :
A signal which satisfies the condition x(-n) = x(n)
• Odd Signal :
A signal which satisfies the condition x(-n) = - x(n)
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Energy and Power Signals
• A signal is an energy signal if and only if the total energy of the signal is finite and the average power is zero
• A signal is a power signal if the average power of the signal is finite and the total energy is infinite
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Causal and Non-Causal Signals
• A DT signal is said to be “causal” if and only if it satisfies the condition
x(n) = 0 for n < 0
In other words, the signal should not exist in the negative part of the time axis.
* The signals which do not satisfy the above condition are “Non- Causal” or “Anti-Causal” Signals.
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Discrete Systems
• A Discrete-Time System is a mathematical operation that maps a given input sequence x[n] into an output sequence y[n]
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Classification based on Properties
• CT and DT Systems
• Linearity
• Time/Shift Invariance
• Causality
• Stability
• Invertibility
• Static and Dynamic Systems
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Linearity
• Linear Systems satisfy “Superposition principle”
Statement :
The response of the system to a weighted sum of signals is equal to the corresponding weighted sum of the outputs of the system to each of the individual input signals.
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Time (or) Shift Invariance
• A system is said to be “time/shift invariant” if it satisfies the condition
y(n,k) = y(n-k)
where,
y(n,k) = Delay in the input sequence
by ‘k’ samples
y(n-k) = Delay if the output
sequence by ‘k’ samples
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Causality
• Causal System : The response of the system at any instant of time depends only on the present input and/or the past input, but not on the future input.
• Non-Causal/AntiCausal System: Response depends on past output, present and future inputs.
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Stability
• BIBO – “Bounded Input Bounded
Output”
* In other words, the sum of the impulse response of the system must yield a finite value for a system to be stable
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Invertibility
• A system is said to be invertible if the input signal given to the system can be recovered from the output signal of the system.
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Static and Dynamic Systems
• Static System : A system which does not have any memory unit to store the past and/or future input values. In other words, the response of the system depends only on the present input value
• Dynamic System: A system which has a memory unit in it to store the past and/or future input values
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�Folding/ Time Reversal
�Time Shifting
�Scaling
- Amplitude Scaling (Constant
Multiplication)
- Time Scaling
(i) Upsampling (ii) Down Sampling
Basic Operations on Sequence
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�Signal Addition
�Signal Multiplication
Basic Operations on Sequence (Contd…)
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Interconnection of two DT-LTI Systems
• Cascade (series) - Associative Property
• Parallel - Distributive Property
• Combination of Cascade and Parallel
• Feedback
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Notes
• Natoms= total charge / electron charge (electrolysis)
• Nmoles = Natoms / Avogadros Number
• Weight (in gram) = Molecular Weight * Nmoles
• Avogadro’s Number = 6.03 * 1023
atoms/mole