Digital Identity is Under Attack: FIDO Paris Seminar.pptx
Dsp
1. EXPERT SYSTEMS AND SOLUTIONS
Email: expertsyssol@gmail.com
expertsyssol@yahoo.com
Cell: 9952749533
www.researchprojects.info
PAIYANOOR, OMR, CHENNAI
Call For Research Projects Final
year students of B.E in EEE, ECE,
EI, M.E (Power Systems), M.E
(Applied Electronics), M.E (Power
Electronics)
Ph.D Electrical and Electronics.
Students can assemble their hardware in our
Research labs. Experts will be guiding the
projects.
3. WHAT IS DSP?
Converting a continuously changing waveform
(analog) into a series of discrete levels (digital)
4. WHAT IS DSP?
The analog waveform is sliced into equal
segments and the waveform amplitude is
measured in the middle of each segment
The collection of measurements make up the
digital representation of the waveform
6. DSP IS EVERYWHERE
Sound applications
Compression, enhancement, special effects, synthesis, recognition,
echo cancellation,…
Cell Phones, MP3 Players, Movies, Dictation, Text-to-speech,…
Communication
Modulation, coding, detection, equalization, echo cancellation,…
Cell Phones, dial-up modem, DSL modem, Satellite Receiver,…
Automotive
ABS, GPS, Active Noise Cancellation, Cruise Control, Parking,…
Medical
Magnetic Resonance, Tomography, Electrocardiogram,…
Military
Radar, Sonar, Space photographs, remote sensing,…
Image and Video Applications
DVD, JPEG, Movie special effects, video conferencing,…
Mechanical
Motor control, process control, oil and mineral prospecting,…
7. SIGNAL PROCESSING
Humans are the most advanced signal processors
speech and pattern recognition, speech synthesis,…
We encounter many types of signals in various
applications
Electrical signals: voltage, current, magnetic and electric
fields,…
Mechanical signals: velocity, force, displacement,…
Acoustic signals: sound, vibration,…
Other signals: pressure, temperature,…
Most real-world signals are analog
They are continuous in time and amplitude
Convert to voltage or currents using sensors and transducers
Analog circuits process these signals using
Resistors, Capacitors, Inductors, Amplifiers,…
Analog signal processing examples
Audio processing in FM radios
Video processing in traditional TV sets
8. LIMITATIONS OF ANALOG SIGNAL
PROCESSING
Accuracy limitations due to
Component tolerances
Undesired nonlinearities
Limited repeatability due to
Tolerances
Changes in environmental conditions
Temperature
Vibration
Sensitivity to electrical noise
Limited dynamic range for voltage and currents
Inflexibility to changes
Difficulty of implementing certain operations
Nonlinear operations
Time-varying operations
Difficulty of storing information
9. DIGITAL SIGNAL PROCESSING
Represent signals by a sequence of numbers
Sampling or analog-to-digital conversions
Perform processing on these numbers with a digital processor
Digital signal processing
Reconstruct analog signal from processed numbers
Reconstruction or digital-to-analog conversion
digital digital
signal signal
analog analog
signal A/D DSP D/A signal
• Analog input – analog output
– Digital recording of music
• Analog input – digital output
– Touch tone phone dialing
• Digital input – analog output
– Text to speech
• Digital input – digital output
– Compression of a file on computer
9
10. PROS AND CONS OF DIGITAL
SIGNAL PROCESSING
Pros
Accuracy can be controlled by choosing word length
Repeatable
Sensitivity to electrical noise is minimal
Dynamic range can be controlled using floating point numbers
Flexibility can be achieved with software implementations
Non-linear and time-varying operations are easier to
implement
Digital storage is cheap
Digital information can be encrypted for security
Price/performance and reduced time-to-market
Cons
Sampling causes loss of information
A/D and D/A requires mixed-signal hardware
Limited speed of processors
Quantization and round-off errors
11. DSP APPLICATIONS
Image Processing – Robotic vision, FAX, satellite
weather
Instrumentation – Spectrum analysis, noise
reduction
Speech & Audio – Speech recognition,
equilization
Military – Radar processing, missile guidance
Telecommunications – Echo cancellation, video
conferencing, VoIP
Biomedical – ECG analysis, patient monitoring
Consumer Electronics – Cell phones, set top box,
video cameras
13. ANOTHER LOOK AT DSP
APPLICATIONS
High-end
Wireless Base Station - TMS320C6000
Increasing
Cable modem
gateways
Cost
Mid-end
Cellular phone - TMS320C540
Fax/ voice server
Low end
Storage products - TMS320C27
volume
Increasing
Digital camera - TMS320C5000
Portable phones
Wireless headsets
Consumer audio
Automobiles, toasters, thermostats, ...
14. ADVANTAGES OF DSP
Guaranteed Accuracy – Accuracy only
limited by bit length
Perfect Reproducibility – No component
tolerances, no component drift due to
temperature or age
Greater Flexibility – Functions and
algorithms can be changed through
software
Superior Performance – Adaptive
filtering, linear phase response
Some Data Naturally Digital – Images,
computer files
15. DISADVANTAGES OF DSP
Speed and Cost – ADC/DAC, uProc
Design Time – Can be tricky
Finite Word Length Issues
17. CONVOLUTION
Many uses but a common use is
determining a system’s output if system
input and system impulse response is
known. For continuous system:
x( t ) h( t ) y ( t ) = x ( t ) ∗ h( t )
∞ ∞
y (t ) = x(t ) ∗ h(t ) = ∫ x(τ ) h( t − τ ) dτ = ∫ x( t − τ ) h(τ ) dτ
−∞ −∞
18. DISCRETE CONVOLUTION
We may however have a computer sampling a
signal so that we have discrete data.
So instead of continuous integration process we
have discrete summation.
∞
y ( n ) = x ( n ) ∗ h( n ) = ∑ h( k ) x ( n − k ) n = 0,±1,±2,
k = −∞
Practically speaking though we would have finite
sequences x(n) and h(n) of lengths N1 and N2
respectively, so this is then:
M −1
y ( n ) = x( n ) ∗ h( n ) = ∑ h( k ) x( n − k ) n = 0,1, , ( M − 1)
k =0
with M = N1 + N 2 − 1
19. CORRELATION
Correlation is essentially the same as convolution
(from a computational standpoint). You just
don’t “flip” anything.
Instead of describing system output, correlation
tells us information about the signals.
Cross-correlation function
Tellsyou a measure of similarities between two signals.
Application: Identifying radar return signals
20. Signals
• What is a signal?
– A signal is a function of independent
variables such as time, distance, position,
temperature, pressure, etc.
– Most signals are generated naturally but a
signal can also be generated artificially
using a computer
– Can be in any number of dimensions (1D,
2D or 3D)
21. CLASSIFICATION OF SIGNALS
Signals can be classified into various types by
Nature of the independent variables
Value of the function defining the signals
Examples:
Discrete/continuous function
Discrete/continuous independent variable
Real/complex valued function
Scalar (single channel)/Vector (multi-channels)
Single/Multi-trial (repeated recordings)
Dimensionality based on the number of independent variables
(1D/2D/3D)
Deterministic/random
Periodic/aperiodic
Even/odd
Many more….
Lecture 1 CE804 Autumn 2007/8 (copyright R. Palaniappan,
2008)
22. CLASSIFICATION - DISCRETE/CONTINUOUS
SIGNALS
Normally, the independent variable is time
Continuous time signal
Time is continuous
Defined at every instant of time
Discrete time signal
Time is discrete
Defined at discrete instants of time - it is a sequence of numbers
Four classifications based on time/amplitude -
continuous/discrete:
Analogue, digital, sampled, quantised boxcar
Lecture 1 CE804 Autumn 2007/8 (copyright R. Palaniappan,
2008)
23. CONTINUOUS AND DISCRETE
SIGNALS
Continous signal
xa(t)
Discrete signal
(sequence)
x[n]
T : sampling period
x[n] = xa(nT) fs = 1/T : sampling rate
25. RANDOM VS DETERMINISTIC SIGNAL
Deterministic signal
A signal that can be predicted using some methods like a
mathematical expression or look-up table
Easier to analyse
Random (stochastic)
A signal that is generated randomly and cannot be predicted
ahead of time
Most biological signals fall in this category
More difficult to analyse
25
26. CLASSIFICATION –
PERIOD/APERIODIC
Periodic
Continuous time-signal is
periodic if it exhibits
periodicity, i.e. x(t+T)=x(t),
-∝<t<∝ where T=period of the
signal
The smallest value of T is
Periodic signal (continuous-time)
called the fundamental
period, T0
A periodic signal has a
definite pattern that repeats
over and over with a
repetition period of T0
Periodic signal (discrete-time)
For discrete-time signals,
x(n+N0)=x(n),-∝<n<∝
A signal, which does not have
a repetitive pattern is
Lecture 1 CE804 Autumn 2007/8 (copyright R. Palaniappan,
aperiodic 2008)
27. SINGULAR FUNCTIONS
Singular functions
Important non-periodic signals
Delta/unit-impulse function is the most basic and all other singular functions can
be derived from it
0, t < 0 0, n < 0
∞ 1, n = 0 r (t ) = { r(n ) = {
δ (n ) = { t, t > 0 n, n ≥ 0
δ (t ) = 0, t ≠ 0; ∫ δ (t )dt = 1 0, n ≠ 0
−∞
Unit impulse functions Unit ramp functions
0, t < 0 0, n < 0 1 1
u(t ) = { u(n ) = { Π(t ) = u t + − u t −
1, t > 0 1, n > 0 2 2
Unit step functions Unit pulse function
Lecture 1 CE804 Autumn 2007/8 (copyright R. Palaniappan,
2008)
28. CLASSIFICATION –EVEN/ODD
Even signal
Signal exhibit symmetry in the
time domain
x(t)=x(-t) or x(n)=x(-n)
Odd signal
Signal exhibit anti-symmetry
in the time domain
x(t)=-x(-t) or x(n)=-x(-n)
A signal can be expressed as a sum of its even and
odd components
x(t)=xeven(t)+xodd(t)
where xeven(t)=1/2[x(t)+x(-t)], xodd(t)=1/2[x(t)-x(-t)]
29. CLASSIFICATION OF SIGNALS
DIMENSIONALITY
SIGNAL DESCRIPTION EXAMPLE
1–D Signal is a function of Speech
a single independent
variable
2-D Signal is a function of Image
2 independent
variables
M-D Signal has more than 2 Video signal
independent variables
30. CLASSIFICATION OF SIGNALS
Continuous-time signals
The signal is defined
for every instant of
time in a defined
range
Discrete-time signal
The independent
variable (time) is
discrete. The signal is
defined at discrete
instants of time
31. CLASSIFICATION OF SIGNALS
Analog signal
x(t)
A continuous-time
t
and a continuous
amplitude
A Quantized Signal
discrete in
xq(t) t
amplitude but
continuous in time
32. CLASSIFICATION OF SIGNALS
Sampled data signal
has a continuous
amplitude.
Amplitude can take
any value within a
specified range.
• Digital signal is a
discrete-time signal
with discrete-valued
amplitudes
33. CLASSIFICATION OF SIGNALS
A deterministic Signal
is one that is uniquely
determined by a well
defined process such
as a mathematical
expression or a look-
up table
• A random signal is
one that is generated
in a random fashion
and cannot be
predicted or
reproduced
36. DISCRETE-TIME SIGNALS:
TIME-DOMAIN REPRESENTATION
•In some applications, a discrete-time sequence
{x[n]} may be generated by sampling a continuous-
time signal xa (t ) at uniform intervals of time
37. DISCRETE-TIME SIGNALS:
TIME-DOMAIN REPRESENTATION
Here, n-th sample is given by
x[n] = xa (t ) t = nT = xa (nT ), n = , − 2, − 1,0,1,
The spacing T between two consecutive samples is
called the sampling interval or sampling period
Reciprocal of sampling interval T, denoted as FT , is
called the sampling frequency:
1
FT =
T
38. DISCRETE-TIME SIGNALS:
TIME-DOMAIN REPRESENTATION
Unit of sampling frequency is cycles per second, or
hertz (Hz), if T is in seconds
Whether or not the sequence {x[n]} has been
obtained by sampling, the quantity x[n] is called
the n-th sample of the sequence
{x[n]} is a real sequence, if the n-th sample x[n] is
real for all values of n
Otherwise, {x[n]} is a complex sequence
39. DISCRETE-TIME SIGNALS:
TIME-DOMAIN REPRESENTATION
A complex sequence {x[n]} can be written as
{x[n]} = {xre [n]} + j{xim [n]} where xre [n] and
xim [n]
are the real and imaginary parts of x[n]
The complex x * [ n]} = {xre [ n]} of {x[n]} is given by
{ conjugate sequence − j{xim [n]}
Often the braces are ignored to denote a sequence if
there is no ambiguity
40. DISCRETE-TIME SIGNALS:
TIME-DOMAIN REPRESENTATION
Two types of discrete-time signals:
- Sampled-data signals in which samples are
continuous-valued
- Digital signals in which samples are discrete-
valued
Signals in a practical digital signal processing
system are digital signals obtained by quantizing
the sample values either by rounding or
truncation
41. DISCRETE-TIME SIGNALS:
TIME-DOMAIN REPRESENTATION
A discrete-time signal may be a finite-length or
an infinite-length sequence
Finite-length (also called finite-duration or
finite-extent) sequence is defined only for a
finite time interval: N ≤ n ≤ N
1 2
where − ∞ < N1 and N 2 < ∞ with N1 ≤ N 2
Length or duration of the above finite-length
sequence is N = N − N + 1
2 1
42. DISCRETE-TIME SIGNALS:
TIME-DOMAIN REPRESENTATION
A length-N sequence is often referred to as an
N-point sequence
The length of a finite-length sequence can be
increased by zero-padding, i.e., by appending it
with zeros
A right-sided sequence x[n] has zero-valued
samples for n < N1
If N ≥ 0, a right-sided sequence is called a
1
causal sequence
43. DISCRETE-TIME SIGNALS:
TIME-DOMAIN REPRESENTATION
A left-sided sequence x[n] has zero-valued
samples for n > N 2
If
N 2 ≤ 0,a left-sided sequence is called a anti-
causal sequence
A right-sided sequence
n
N1
A left-sided sequence
N2
n
44. OPERATIONS ON SEQUENCES:
BASIC OPERATIONS
Product (modulation) operation:
Modulator x[n] × y[n]
w[n] y[n] = x[n] ⋅ w[n]
An application is in forming a finite-length
sequence from an infinite-length sequence by
multiplying the latter with a finite-length sequence
called a window sequence
Process called windowing
46. BASIC OPERATIONS
Time-shifting operation: y[n] = x[n − N ]
where N is an integer
(i)If N > 0, it is delaying operation
Unit delay x[n]
z −1 y[n] y[n] = x[n − 1]
(ii)If N < 0, it is an advance operation
Unit advance x[n] z y[n] y[n] = x[n + 1]
47. BASIC OPERATIONS
Time-reversal (folding) operation:
y[n] = x[−n]
Branching operation:
Used to provide multiple copies of a sequence
x[n] x[n]
x[n]
48. ALIASING
Aliasing:
If you sample too slow, the high frequency components will
become irregular noise at the sampling frequency
They are noises that are in the same frequency range of your
signal!!!
• Look at the samples
alone
• Can you tell which of
the two frequencies
the sampled series
represents?
• Either of the two
signals could produce
the samples, i.e., the
signals are “aliases”
of each other
49. CLASSIFICATION OF SEQUENCES:
ENERGY AND POWER SIGNALS
Power Signal
An infinite energy signal with finite average power
is called a power signal
Example - A periodic sequence which has a finite
average power but infinite energy
50. Energy Signals
A finite energy signal with zero average
power is called an energy signal
Example - a finite-length sequence which has
finite energy but zero average power
3(−1) n ,
others
x[n] =
0,
n < 0, n ≥ 10
51. OTHER TYPES OF CLASSIFICATIONS
A sequence x[n] is said to be bounded if
x[n] ≤ Bx < ∞
A sequence x[n] is said to be absolutely summable if
∞
∑ x[n] < ∞
n = −∞
A sequence x[n] is said to be square-summable if
∞ 2
∑ x[n] < ∞
n = −∞
52. BASIC SEQUENCES
Unit impulse Unit step
Sinusoidal
Exponential
Periodic Random
53. BASIC SEQUENCES
Unit sample sequence - 1, n = 0
δ [ n] =
1
0, n ≠ 0
n
–4 –3 –2 –1 0 1 2 3 4 5 6
Unit step sequence - 1, n ≥ 0
µ[ n] =
0, n < 0
1
n
–4 –3 –2 –1 0 1 2 3 4 5 6
54. BASIC SEQUENCES
Real sinusoidal sequence -
x[n] = A cos(ω o n + φ )
where A is the amplitude,ω o is the angular
frequency, and φ is the phase of x[n]
Example -
ωo = 0.1
2
1
Amplitude
0
-1
-2
0 10 20 30 40
Time index n
55. DISCRETE-TIME SYSTEMS
INTRO. TO DISCRETE-TIME SYSTEMS
The difference equation, the impulse response and the
system function are equivalent characterization of the
input/output relation of a LTI Discrete-time systems.
LTI system can be modeled using :
1. A Difference/Differential equation, y(n) = x[n] + x[n-1] + …
2. Impulse Response, h(n)
3. Transfer Function, H(z)
The systems that described by the difference equations can
be represented by structures consisting of an
interconnection of the basic operations of addition,
multiplication by a constant or signal multiplication, delay
and advance.
56. DISCRETE-TIME SYSTEMS
The Adder, Multiplier, Delay & Advance is shown
below:
1. Adder :
2. Multiplier : Modulator:
59. Aliasing
Unable to distinguish two continuous signals with
different frequencies based on samples
Frequencies higher than Nyquist frequency
Anti-aliasing
Low-pass filter the frequencies above Nyquist
frequency
60. DISCRETE-TIME SYSTEM
Discrete-time system has discrete-time
input and output signals
61. DIGITAL SYSTEM
A discrete-time system is digital if it
operates on discrete-time signals whose
amplitudes are quantized
Quantization maps each continuous
amplitude level into a number
The digital system employs digital
hardware
1. explicitly in the form of logic circuits
2. implicitly when the operations on the signals
are executed by writing a computer
program
62. Discrete-time (DT) system is `sampled data’
system:
Input signal u[k] is a sequence of samples (=numbers)
..,u[-2],u[-1],u[0],u[1],u[2],…
System then produces a sequence of output samples y[k]
..,y[-2],y[-1],y[0],y[1],y[2],…
Will consider linear time-invariant (LTI) DT
systems:
Linear :
input u1[k] -> output y1[k] u[k] y[k]
input u2[k] -> output y2[k]
hence a.u1[k]+b.u2[k]-> a.y1[k]+b.y2[k]
Time-invariant (shift-invariant)
input u[k] -> output y[k], hence input u[k-T] -> output
y[k-T]
65. Z-Transform:
∆ ∆ ∆
H ( z ) = ∑ h[i ]. z −i
U ( z ) = ∑ u[i ]. z −i
Y ( z ) = ∑ y[i ]. z −i
i i i
y[0] h[0] 0 0 0
y[1] h[1] h[0] 0 0 u[0]
y[2] h[2] h[1] h[0] 0 u[1]
[
1 z −1
z −2
z −3
z −4 −5
z . ] =1 z
−1
[z −2
z −3
z −4 −5
z . ] .
h[2] h[1] h[0] u[2]
y[3] 0
y[4] 0
0 h[2] h[1] u[3]
y[5] 0 0 0 h[2]
Y ( z) H ( z).1 z−1 z−2 z−3
⇒ Y ( z ) = H ( z ).U ( z ) H(z) is `transfer function’
66. Z-Transform :
input-output relation
Y ( z ) = H ( z ).U ( z )
may be viewed as `shorthand’ notation
(for convolution operation/Toeplitz-vector
product)
stability
bounded input u[k] -> bounded output y[k]
∑ h[k ] ∞
--iff
k
--iff poles of H(z) inside the unit circle
(for causal,rational systems)
67. Example-1 : `Delay operator’
u[k] y[k]=u[k-1]
Impulse response is …,0,0,0, 1,0,0,0,…
Transfer function is ∆
−1
H ( z) = z
Example-2 : Delay + feedback u[k] y[k]
Impulse response is …,0,0,0, 1,a,a^2,a^3… + ∆
Transfer function is
H ( z ) = z −1 + a. z −2 + a 2 . z −3 + a 3. z −4 + ... a
x
⇒ H ( z ) − a. z −1H ( z ) = z −1
z −1
⇒ H ( z) =
1 − a. z −1
68. LINEAR TIME-INVARIANT
(LTI) SYSTEM
Discrete-time system is LTI if its
input-output relationship can be described by the
linear constant coefficients difference equation
The output sample y(ν) might depend on all input samples
that can be represented as
y (ν ) = Φ ( x(k ))
