DSP_2018_FOEHU - Lec 1 - Introduction to Digital Signal Processing
1. LECTURE (1)
Introduction to Digital Signal Processing
رَـدْقِـن،،،لمااننا نصدقْْقِنرَد
Amr E. Mohamed
Faculty of Engineering - Helwan University
2. Introduction
Objectives:
what is a signal
What is Signal Processing
• Analog Signal Processing System
• Digital Signal Processing System
Time and Frequency Domain Representations of Signals
Brief introduction to MATLAB.
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3. Fundamentals of Signals
Signal (flow of information):
Generally convey information about the state or behavior of a physical phenomena.
Measured quantity that varies with time (or position)
Electrical signal received from a transducer (Microphone, Thermometer,
Accelerometer, Antenna, etc.)
Electrical signal that controls a process
Signal:
Signal is defined as any physical quantity that varies with Time, Space, or any other
independent variables. For Example, the functions
Example:
𝑠1(𝑡) = 5𝑡 or 𝑠1(𝑡) = 5𝑡2 one variable
𝑆(𝑥, 𝑦) = 3𝑥 + 4𝑥𝑦 + 6𝑥2
two variables x and y
3
4. Overview of Signal Processing: Signal Classifications
4
Fig. 1.1 Signal Classifications
Signal is a representation of physical quantity or phenomenon
Deterministic Signals Random Signals
Time Domain Representation
t is the independent variable
Frequency Domain Representation
f is the independent variable
Representation
Continuous
Discrete
Continuous
Discrete
5. Continuous-Time versus Discrete-Time Signals
1) Continuous-Time signal or analog signal: are defined for every value
of time and they take on values in the continuous interval (a,b).
Analog Signal
Continuous in time.
Amplitude may take on any value in the continuous range of (-∞, ∞).
Analog Processing
Differentiation, Integration, Filtering, Amplification.
Differential Equations
Implemented via passive or active electronic circuitry.
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6. Continuous-Time versus Discrete-Time Signals
2) Discrete-Time signals: are defined only at certain specific value of
time.
Continuous in Amplitude but Discrete in Time
Only defined for certain time instances.
Can be obtained from analog signals via sampling.
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7. 3) Digital Signal: is the signal that takes on values from a finite set of
possible values.
Discrete in Amplitude & Discrete in Time.
Can be obtained from Discrete signals via quantization.
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Continuous-Time versus Discrete-Time Signals
8. Sampling Process
Discrete-time signals are often generated from corresponding continuous-time
signals through the use of an analog-to-digital (A/D) interface. An A/D
interface typically comprises three components, namely, a sampler, a
quantizer, and an encoder as depicted in Fig. 1.3(a).
Similarly, continuous-time signals can be obtained by using a digital-to-analog
(D/A) interface. The D/A interface comprises two modules, a decoder and a
smoothing device as depicted in Fig. 1.3(b).
8Fig. 1.3 Sampling system: (a) A/D interface, (b) D/A interface.
(SNR) dB= 6.02 n + 4.77
9. Deterministic versus Random Signals
1) Deterministic Signal: Any signal whose past,
present and future values are precisely
known without any uncertainty.
2) Random Signal: A signal in which cannot be
approximated by a formula to a reasonable
degree of accuracy (i.e. noise).
The ‘shhhh’ sound is a good example that is
rather easy to observe using a microphone
and oscilloscope.
Random signals are characterized by
analyzing the statistical characteristics
across an ensemble of records.
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10. Transient Signals
Transient signals may be defined as signals that exist for a finite range
of time as shown in the figure. Typical examples are hammer excitation
of systems explosion and shock loading etc.
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11. Stationary versus Nonstationary Signals
Stationary signals are those whose average properties do not change
with time Stationary signals have constant parameters to change with
time.
Nonstationary signals have time dependent parameters. In an engine
excited vibration where the engines speed varies with time; the
fundamental period changes with time as well as with the corresponding
dynamic loads that cause vibration.
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12. Finite and infinite length
1. Finite-length signal: nonzero over a finite interval tmin< t< tmax
2. Infinite-length signal: nonzero over all real numbers
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13. Multi-channel & Multidimensional Signals
A signal is described by a function of one or more independent
variables. The value of function can be real-valued Scalar, a complex-
valued, or perhaps a vector.
Real-Valued Signal
Complex-Valued Signal
Vector Signal
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3
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ts
ts
ts
tS
13
14. Multi-channel & Multidimensional Signals
1) Multi-channel Signals
Signals are generated by multiple source or multiple sensor. This signals, can
represented in vector form.
Example: ECG (Electrocardiogram) are often used 3-channel and 12-
channel.
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15. Multi-channel & Multidimensional Signals
2) Multidimensional Signals:
If the signal is a function of a single independent variable, the signal called a
one-dimensional signal.
On the other hand , a signal called M-dimensional if its value is a function of M
independent variables.
The gray picture is an example of a 2-dimensional signal, the brightness or the
intensity I(x,y) at each point is a function of 2 independent variables.
The black & white TV picture [I(x,y,t)]: is a “3-Dimensional” since the
brightness is a function of time.
The color TV picture: is a multi-channel/multidimensional signal.
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17. What is Signal Processing
Signals may have to be transformed in order to
Amplify or filter out embedded information
Detect patterns
Prepare the signal to survive a transmission channel
Undo distortions contributed by a transmission channel
Compensate for sensor deficiencies
Find information encoded in a different domain.
To do so, we also need:
Methods to measure, characterize, model, and simulate signals.
Mathematical tools that split common channels and transformations into easily
manipulated building blocks.
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19. Analog Signal Processing
ℎ(𝑡): The System Impulse Response
𝐻(𝑠): The System Transfer Function
𝐻(Ω): The System Frequency Response
Analogue signal processing is achieved by using analogue components
such as:
Resistors.
Capacitors.
Inductors.
)(tx
)(sX
)(*)()( txthty
)(.)()( sXsHsY
Analog
input
Signal
Analog
output
Signal
Analog
Signal
Processor
19
)(X )(.)()( XHY
20. 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
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21. Digital Signal Processing
ℎ(𝑛): The System Impulse Response (Weighted Sequence)
𝐻(𝑧): The System Transfer Function
𝐻 𝑝𝑓(𝑠) : Prefilter (Band-limited – Reduce noise)
𝐻𝑟𝑐(𝑠) : reconstruction filter (smoothing)
Analog/digital and digital/analog converters, CPU, DSP, ASIC, FPGA
Digital signal processing techniques are now so powerful that sometimes it is extremely
difficult, if not impossible, for analogue signal processing to achieve similar
performance.
Examples:
FIR filter with linear phase.
Adaptive filters.
)(nx
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)(sH pf )(sHrc
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Digital
Signal
Processor
ADC DAC
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22. Pros and Cons of Digital Signal Processing
Pros
It is easy to Change, Correct, or Update applications (software changes).
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
Small size.
Development time.
Power consumption.
Cost, cheaper than analog.
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23. Pros and Cons of Digital Signal Processing
Cons
Sampling causes loss of information
A/D and D/A requires mixed-signal hardware
Limited speed of processors
Quantization and round-off errors
Discrete time processing artifacts (aliasing, delay)
Dan require significantly more power (battery, cooling)
Digital clock and switching (Synchronization)
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24. 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
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25. 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,…
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26. Time and Frequency Domain Representations of Signals
Signals have so far been represented in terms of functions of time, i.e., x(t) or x(nT). In
many situations, it is useful to represent signals in terms of functions of frequency using
Fourier transform or Fourier series.
For example, a continuous-time periodic signal made up of a sum of sinusoidal
components such as:
can be fully described by two sets, say:
And
that describe the amplitudes and phase angles of the sinusoidal components present in
the signal. Sets A() and () can be referred to as the amplitude spectrum and phase
spectrum of the signal, respectively, for obvious reasons, and can be represented by
tables or graphs that give the amplitude and phase angle associated with each frequency.
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)sin()(
9
1
kk
k
k tAtx
9...,,2,1:)( kforAA kk
9...,,2,1:)( kforkk
27. Time and Frequency Domain Representations of Signals (Cont…)
For example, if Ak and k in Eq. (1.1) assume the numerical values given
by Table 1.1, then x(t) can be represented in the time domain by the
graph in Fig. 1.7(a) and in the frequency domain by Table 1.1 or by the
graphs in Fig. 1.7(b) and (c).
27Fig. 1.7(a) Time-domain representation.Table 1.1 Parameters of signal in Eq. (1.1)
28. Time and Frequency Domain Representations of Signals
(Cont…)
28Fig. 1.7 (b) Amplitude spectrum, (c) Phase spectrum.
(b) (c)
29. Filtering Process
Filtering can be used to select one or more desirable and
simultaneously reject one or more undesirable bands of frequency
components, or simply frequencies. They include different types:
1. Lowpass filters select a band of preferred low frequencies and reject a
band of undesirable high frequencies from the frequencies present in
the signal depicted in Fig. 1.7, as illustrated in Fig. 1.8.
2. Highpass filters select a band of preferred high frequencies and reject
a band of undesirable low frequencies as illustrated in Fig. 1.9.
3. Bandpass filters select a band of frequencies and reject low and high
frequencies as illustrated in Fig. 1.10.
4. Bandstop filters to reject a band of frequencies but select low
frequencies and high frequencies as illustrated in Fig. 1.11.
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30. Filtering Process: Lowpass Filter
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Fig. 1.8(a) Lowpass filtering applied to the signal depicted in Fig. 1.7: (a) Time-domain
representation, (b) amplitude spectrum, (c) phase spectrum..
(b) (c)
(a)
31. Filtering Process: Highpass Filter
31
Fig. 1.9(a) Highpass filtering applied to the signal depicted in Fig. 1.3: (a) Time-domain
representation, (b) amplitude spectrum, (c) phase spectrum..
(b)
(c)
(a)
32. Filtering Process: Bandpass Filter
32
Fig. 1.10(a) Bandpass filtering applied to the signal depicted in Fig. 1.3: (a) Time-domain
representation, (b) amplitude spectrum, (c) phase spectrum..
(b) (c)
(a)
33. Filtering Process: Bandstop Filter
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Fig. 1.11(a) Bandstop filtering applied to the signal depicted in Fig. 1.3: (a) Time-domain
representation, (b) amplitude spectrum, (c) phase spectrum..
(b) (c)
(a)