CS2 S24 403 - Dig igiital Si Sign gna al Processing Presentation by: Mr. S. Karthie, Assistant Professor/ECE SSN College of Engineering
OUTLINE OF THIS COURSE Introducti uction on Introd
– Basics Basics of Sign Signals als & System Systems s
(Unit-I) Discrete e Time LTI LTI Systems Systems – Analysi Analysis s (Unit-I) (Unit-I) Discret 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)
OUTLINE OF THIS COURSE Introducti uction on Introd
– Basics Basics of Sign Signals als & System Systems s
(Unit-I) Discrete e Time LTI LTI Systems Systems – Analysi Analysis s (Unit-I) (Unit-I) Discret 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)
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
Broad Classification of Signals •Continuous time – •Continuous amplitude •Continuous time – •Discrete amplitude •Discrete time – • Continuous amplitude •Discrete time – •Discrete amplitude
• 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
• 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
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
Block Diagram of DSP Equivalent analog signal processor Analog
Analog PrF
ADC
DSP
DAC
PoF
PrF: antialiasing filtering PoF: smooth out the staircase waveform
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
Basic Ways to Represent DT Signals Sequence
Representation Tabular Representation Functional Representation Graphical Representation
Discrete Time Signal Types (i) Unit sample Sequence
1, δ ( n ) = 0,
n=0 n≠0
{
}
= L ,0,0, 1,0,0, L ↑
(ii) Unit step sequence
1, n ≥ 0 u ( n) = = L,0,0, 1,1,1, L ↑ n 0 , 0 <
{
}
Discrete Time Signal – Types (Contd…) (iii) Ramp Sequence r(n) = n ; n>0 0 ; n<0 (iv) Exponential Sequence
x ( n ) = a , ∀ n ; a ∈ R n
where x(n) = exp(n)
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
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)
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
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)
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
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.
Discrete Systems • A Discrete-Time System is a mathematical operation that maps a given input sequence x[n] into an output sequence y[n]
Classification based on Properties • • • • • • •
CT and DT Systems Linearity Time/Shift Invariance Causality Stability Invertibility Static and Dynamic Systems
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.
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
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.
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
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.
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
Basic Operations on Sequence Folding/
Time Reversal Time Shifting Scaling - Amplitude Scaling (Constant Multiplication) - Time Scaling (i) Upsampling (ii) Down Sampling
Basic Operations on Sequence (Contd…) Signal
Addition Signal Multiplication
Interconnection of two DTLTI Systems • Cascade (series) - Associative Property • Parallel - Distributive Property • Combination of Cascade and Parallel • Feedback
