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Chapter 1INTRODUCTION TO DIGITAL SIGNAL
PROCESSING
1.1 Introduction1.2 The Sampling Process
Copyright c© 2005- Andreas AntoniouVictoria, BC, Canada
Email: [email protected]
January 31, 2008
Frame # 1 Slide # 1 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Introduction
� Signal processing emerged soon after World War I in theform electrical filtering.
Frame # 2 Slide # 2 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Introduction
� Signal processing emerged soon after World War I in theform electrical filtering.
� With the invention of the digital computer and the rapidadvances in VLSI technology during the 1960s, a new wayof processing signals emerged: digital signal processing.
Frame # 2 Slide # 3 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Introduction
� Signal processing emerged soon after World War I in theform electrical filtering.
� With the invention of the digital computer and the rapidadvances in VLSI technology during the 1960s, a new wayof processing signals emerged: digital signal processing.
� This and the next two presentations provide a briefhistorical summary of the emergence of signal processingand its applications.
Frame # 2 Slide # 4 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Introduction
� Signal processing emerged soon after World War I in theform electrical filtering.
� With the invention of the digital computer and the rapidadvances in VLSI technology during the 1960s, a new wayof processing signals emerged: digital signal processing.
� This and the next two presentations provide a briefhistorical summary of the emergence of signal processingand its applications.
� To start with, a classification of the various types of signalsencountered in today’s technological world is provided.
Frame # 2 Slide # 5 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Introduction
� Signal processing emerged soon after World War I in theform electrical filtering.
� With the invention of the digital computer and the rapidadvances in VLSI technology during the 1960s, a new wayof processing signals emerged: digital signal processing.
� This and the next two presentations provide a briefhistorical summary of the emergence of signal processingand its applications.
� To start with, a classification of the various types of signalsencountered in today’s technological world is provided.
� Then the sampling process is described as a means ofconverting analog into digital signals.
Frame # 2 Slide # 6 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals
� Typically one assumes that a signal is an electrical signal,for example, a radio, radar, or TV signal.
Frame # 3 Slide # 7 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals
� Typically one assumes that a signal is an electrical signal,for example, a radio, radar, or TV signal.
However, in DSP a signal is any quantity that depends onone or more independent variables.
Frame # 3 Slide # 8 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals
� Typically one assumes that a signal is an electrical signal,for example, a radio, radar, or TV signal.
However, in DSP a signal is any quantity that depends onone or more independent variables.
A radio signal represents the strength of anelectromagnetic wave that depends on one independentvariable, namely, time.
Frame # 3 Slide # 9 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
� In our generalized definition of a signal, there may be morethan one independent variables and the independentvariables may be any quantity other than time.
Frame # 4 Slide # 10 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
� In our generalized definition of a signal, there may be morethan one independent variables and the independentvariables may be any quantity other than time.
For example, a digitized image may be thought of as lightintensity that depends on two independent variables, thedistances along the x and y axes; as such a digitizedimage is, in effect, a 2-dimensional signal.
Frame # 4 Slide # 11 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
� In our generalized definition of a signal, there may be morethan one independent variables and the independentvariables may be any quantity other than time.
For example, a digitized image may be thought of as lightintensity that depends on two independent variables, thedistances along the x and y axes; as such a digitizedimage is, in effect, a 2-dimensional signal.
A video signal is made up of a series of images whichchange with time; thus a video signal is light intensity thatdepends on the distances along the x and y axes and alsoon the time; in effect, a video signal is a 3-dimensionalsignal.
Frame # 4 Slide # 12 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
� In our generalized definition of a signal, there may be morethan one independent variables and the independentvariables may be any quantity other than time.
For example, a digitized image may be thought of as lightintensity that depends on two independent variables, thedistances along the x and y axes; as such a digitizedimage is, in effect, a 2-dimensional signal.
A video signal is made up of a series of images whichchange with time; thus a video signal is light intensity thatdepends on the distances along the x and y axes and alsoon the time; in effect, a video signal is a 3-dimensionalsignal.
� Some signals arise naturally, others are man-made.
Frame # 4 Slide # 13 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Natural signals are found, for example, in:� Acoustics, e.g., speech signals, sounds made by dolphins
and whales
Frame # 5 Slide # 14 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Natural signals are found, for example, in:� Acoustics, e.g., speech signals, sounds made by dolphins
and whales� Astronomy, e.g., cosmic signals originating galaxies and
pulsars, astronomical images
Frame # 5 Slide # 15 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Natural signals are found, for example, in:� Acoustics, e.g., speech signals, sounds made by dolphins
and whales� Astronomy, e.g., cosmic signals originating galaxies and
pulsars, astronomical images� Biology, e.g., signals produced by the brain and heart
Frame # 5 Slide # 16 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Natural signals are found, for example, in:� Acoustics, e.g., speech signals, sounds made by dolphins
and whales� Astronomy, e.g., cosmic signals originating galaxies and
pulsars, astronomical images� Biology, e.g., signals produced by the brain and heart� Seismology, e.g., signals produced by earthquakes and
volcanoes
Frame # 5 Slide # 17 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Natural signals are found, for example, in:� Acoustics, e.g., speech signals, sounds made by dolphins
and whales� Astronomy, e.g., cosmic signals originating galaxies and
pulsars, astronomical images� Biology, e.g., signals produced by the brain and heart� Seismology, e.g., signals produced by earthquakes and
volcanoes� Physical sciences, e.g., signals produced by lightnings, the
room temperature, the atmospheric pressure
Frame # 5 Slide # 18 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Man-made signals are found in:� Audio systems, e.g., music signals
Frame # 6 Slide # 19 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Man-made signals are found in:� Audio systems, e.g., music signals� Communications, e.g., radio, telephone, TV signals
Frame # 6 Slide # 20 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Man-made signals are found in:� Audio systems, e.g., music signals� Communications, e.g., radio, telephone, TV signals� Telemetry, e.g., signals originating from weather stations
and satellites
Frame # 6 Slide # 21 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Man-made signals are found in:� Audio systems, e.g., music signals� Communications, e.g., radio, telephone, TV signals� Telemetry, e.g., signals originating from weather stations
and satellites� Control systems, e.g., feedback control signals
Frame # 6 Slide # 22 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Man-made signals are found in:� Audio systems, e.g., music signals� Communications, e.g., radio, telephone, TV signals� Telemetry, e.g., signals originating from weather stations
and satellites� Control systems, e.g., feedback control signals� Medicine, e.g., electrocardiographs, X-rays, magnetic
resonance imaging
Frame # 6 Slide # 23 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Man-made signals are found in:� Audio systems, e.g., music signals� Communications, e.g., radio, telephone, TV signals� Telemetry, e.g., signals originating from weather stations
and satellites� Control systems, e.g., feedback control signals� Medicine, e.g., electrocardiographs, X-rays, magnetic
resonance imaging� Space technology, e.g., the velocity of a space craft
Frame # 6 Slide # 24 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Man-made signals are found in:� Audio systems, e.g., music signals� Communications, e.g., radio, telephone, TV signals� Telemetry, e.g., signals originating from weather stations
and satellites� Control systems, e.g., feedback control signals� Medicine, e.g., electrocardiographs, X-rays, magnetic
resonance imaging� Space technology, e.g., the velocity of a space craft� Politics, e.g., the popularity ratings of a political party
Frame # 6 Slide # 25 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Man-made signals are found in:� Audio systems, e.g., music signals� Communications, e.g., radio, telephone, TV signals� Telemetry, e.g., signals originating from weather stations
and satellites� Control systems, e.g., feedback control signals� Medicine, e.g., electrocardiographs, X-rays, magnetic
resonance imaging� Space technology, e.g., the velocity of a space craft� Politics, e.g., the popularity ratings of a political party� Economics, e.g., the price of a stock at the TSX, the TSX
index, the gross national product
Frame # 6 Slide # 26 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signals Cont’d
Two general classes of signals can be identified:� Continuous-time signals� Discrete-time signals
Frame # 7 Slide # 27 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Continuous-Time Signals
� A continuous-time signal is a signal that is defined at eachand every instant of time.
Frame # 8 Slide # 28 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Continuous-Time Signals
� A continuous-time signal is a signal that is defined at eachand every instant of time.
� Typical examples are:
Frame # 8 Slide # 29 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Continuous-Time Signals
� A continuous-time signal is a signal that is defined at eachand every instant of time.
� Typical examples are:– An electromagnetic wave originating from a distant galaxy
Frame # 8 Slide # 30 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Continuous-Time Signals
� A continuous-time signal is a signal that is defined at eachand every instant of time.
� Typical examples are:– An electromagnetic wave originating from a distant galaxy– The sound wave produced by a dolphin
Frame # 8 Slide # 31 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Continuous-Time Signals
� A continuous-time signal is a signal that is defined at eachand every instant of time.
� Typical examples are:– An electromagnetic wave originating from a distant galaxy– The sound wave produced by a dolphin– The ambient temperature
Frame # 8 Slide # 32 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Continuous-Time Signals
� A continuous-time signal is a signal that is defined at eachand every instant of time.
� Typical examples are:– An electromagnetic wave originating from a distant galaxy– The sound wave produced by a dolphin– The ambient temperature– The light intensity along the x and y axes in a photograph
Frame # 8 Slide # 33 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Continuous-Time Signals
� A continuous-time signal is a signal that is defined at eachand every instant of time.
� Typical examples are:– An electromagnetic wave originating from a distant galaxy– The sound wave produced by a dolphin– The ambient temperature– The light intensity along the x and y axes in a photograph
� A continuous-time signal can be represented by a function
x(t) where −∞ < t < ∞
Frame # 8 Slide # 34 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Continuous-Time Signals Cont’d
x(t)
t
Frame # 9 Slide # 35 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals
� A discrete-time signal is a signal that is defined at discreteinstants of time.
Frame # 10 Slide # 36 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals
� A discrete-time signal is a signal that is defined at discreteinstants of time.
� Typical examples are:
Frame # 10 Slide # 37 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals
� A discrete-time signal is a signal that is defined at discreteinstants of time.
� Typical examples are:– The closing price of a particular commodity on the stock
exchange
Frame # 10 Slide # 38 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals
� A discrete-time signal is a signal that is defined at discreteinstants of time.
� Typical examples are:– The closing price of a particular commodity on the stock
exchange– The daily precipitation
Frame # 10 Slide # 39 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals
� A discrete-time signal is a signal that is defined at discreteinstants of time.
� Typical examples are:– The closing price of a particular commodity on the stock
exchange– The daily precipitation– The daily temperature of a patient as recorded by a nurse
Frame # 10 Slide # 40 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals Cont’d
� A discrete-time signal can be represented as a function
x(nT ) where −∞ < n < ∞
and T is a constant.
Frame # 11 Slide # 41 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals Cont’d
� A discrete-time signal can be represented as a function
x(nT ) where −∞ < n < ∞
and T is a constant.
� The quantity x(nT ) can represent a voltage or current levelor any other quantity.
Frame # 11 Slide # 42 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals Cont’d
� A discrete-time signal can be represented as a function
x(nT ) where −∞ < n < ∞
and T is a constant.
� The quantity x(nT ) can represent a voltage or current levelor any other quantity.
� In DSP, x(nT ) always represents a series of numbers.
Frame # 11 Slide # 43 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals Cont’d
� A discrete-time signal can be represented as a function
x(nT ) where −∞ < n < ∞
and T is a constant.
� The quantity x(nT ) can represent a voltage or current levelor any other quantity.
� In DSP, x(nT ) always represents a series of numbers.
� Constant T usually represents time but it could be anyother physical quantity depending on the application.
Frame # 11 Slide # 44 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals Cont’d
x(nT)
nT
T
Frame # 12 Slide # 45 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals Cont’d
Frame # 13 Slide # 46 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals Cont’d
Frame # 14 Slide # 47 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Discrete-Time Signals Cont’d
Note:
The signals in the previous two slides are discrete-time signalssince a mutual fund or the TSX index has only one closingvalue per day.
They are plotted as if they were continuous-time signals for thesake of convenience.
Frame # 15 Slide # 48 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Nonquantized and Quantized Signals
� Signals can also be classified as:– Nonquantized– Quantized
Frame # 16 Slide # 49 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Nonquantized and Quantized Signals
� Signals can also be classified as:– Nonquantized– Quantized
� A nonquantized signal is a signal that can assume anyvalue within a given range, e.g., the ambient temperature.
Frame # 16 Slide # 50 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Nonquantized and Quantized Signals
� Signals can also be classified as:– Nonquantized– Quantized
� A nonquantized signal is a signal that can assume anyvalue within a given range, e.g., the ambient temperature.
� A quantized signal is a signal that can assume only a finitenumber of discrete values, e.g., the ambient temperatureas measured by a digital thermometer.
Frame # 16 Slide # 51 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Nonquantized and Quantized Signals Cont’d
t nT
x(nT)x(t)
x(t)
(a) Continuous-time, nonquantized (b) Discrete-time, nonquantized
nT
x(nT)
(d) Discrete-time, quantized(c) Continuous-time, quantized
t
Frame # 17 Slide # 52 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Alternative Notation
� A discrete-time signal x(nT ) is often represented in termsof the alternative notations
x(n) and xn
Frame # 18 Slide # 53 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Alternative Notation
� A discrete-time signal x(nT ) is often represented in termsof the alternative notations
x(n) and xn
� In the early presentations, x(nT ) will be used most of thetime to emphasize the fact that a discrete-time signal istypically generated by sampling a continuous-time signalx(t) at instant t = nT .
Frame # 18 Slide # 54 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Alternative Notation
� A discrete-time signal x(nT ) is often represented in termsof the alternative notations
x(n) and xn
� In the early presentations, x(nT ) will be used most of thetime to emphasize the fact that a discrete-time signal istypically generated by sampling a continuous-time signalx(t) at instant t = nT .
� In later presentations, the more economical notation x(n)
will be used where appropriate.
Frame # 18 Slide # 55 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process
To be able to process a nonquantized continuous-timesignal by a digital system, we must first sample it togenerate a discrete-time signal.
Frame # 19 Slide # 56 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process
To be able to process a nonquantized continuous-timesignal by a digital system, we must first sample it togenerate a discrete-time signal.
We must then quantize it to get a quantized discrete-timesignal.
Frame # 19 Slide # 57 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process
To be able to process a nonquantized continuous-timesignal by a digital system, we must first sample it togenerate a discrete-time signal.
We must then quantize it to get a quantized discrete-timesignal.
That way, we can generate a numerical representation ofthe signal that entails a finite amount of information.
Frame # 19 Slide # 58 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
A sampling system comprises three essential components:
– sampler
– quantizer
– encoder
Frame # 20 Slide # 59 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
Encoderx(t)x(nT) xq(nT)
Quantizer
Clock
nT
Sampler
xq(nT)'
Sampling system
Frame # 21 Slide # 60 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
A sampler in its bare essentials is a switch controlled by aclock signal which closes momentarily every T secondsthereby transmitting the level of the input signal x(t) atinstant nT , i.e., x(nT ), to its output.
Encoderx(t)x(nT) xq(nT)
Quantizer
Clock
nT
Sampler
xq(nT)'
Sampling system
Frame # 22 Slide # 61 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
A sampler in its bare essentials is a switch controlled by aclock signal which closes momentarily every T secondsthereby transmitting the level of the input signal x(t) atinstant nT , i.e., x(nT ), to its output.Parameter T is called the sampling period.
Encoderx(t)x(nT) xq(nT)
Quantizer
Clock
nT
Sampler
xq(nT)'
Sampling system
Frame # 22 Slide # 62 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
A quantizer is a device that will sense the level of its inputand produce as output the nearest available level, say,xq(nT ), from a set of allowed levels, i.e., a quantizer willproduce a quantized continuous-time signal.
Encoderx(t)x(nT) xq(nT)
Quantizer
Clock
nT
Sampler
xq(nT)'
Sampling system
Frame # 23 Slide # 63 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
An encoder is essentially a digital device that will sense thevoltage or current level of its input and produce acorresponding binary number at its output, i.e., it willconvert a quantized continuous-time signal into acorresponding discrete-time signal in binary form.
Encoderx(t)x(nT) xq(nT)
Quantizer
Clock
nT
Sampler
xq(nT)'
Sampling system
Frame # 24 Slide # 64 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
The sampling system described is essentially ananalog-to-digital converter and its implementation canassume numerous forms.
Encoderx(t)x(nT) xq(nT)
Quantizer
Clock
nT
Sampler
xq(nT)'
Frame # 25 Slide # 65 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
The sampling system described is essentially ananalog-to-digital converter and its implementation canassume numerous forms.
These devices go by the acronym of A/D converter or ADCand are available in VLSI chip form as off-the-shelf devices.
Encoderx(t)x(nT) xq(nT)
Quantizer
Clock
nT
Sampler
xq(nT)'
Frame # 25 Slide # 66 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
A quantized discrete-time signal produced by an A/Dconverter is, of course, an approximation of the originalnonquantized continuous-time signal.
Frame # 26 Slide # 67 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
A quantized discrete-time signal produced by an A/Dconverter is, of course, an approximation of the originalnonquantized continuous-time signal.
The accuracy of the representation can be improved byincreasing
– the sampling rate, and/or– the number of allowable quantization levels in the quantizer
Frame # 26 Slide # 68 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
A quantized discrete-time signal produced by an A/Dconverter is, of course, an approximation of the originalnonquantized continuous-time signal.
The accuracy of the representation can be improved byincreasing
– the sampling rate, and/or– the number of allowable quantization levels in the quantizer
The sampling rate is simply 1/T = fs in Hz or 2π/T = ωs inradians per second (rad/s).
Frame # 26 Slide # 69 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
Once a discrete-time signal is generated which is anaccurate representation of the original continuous-timesignal, any required processing can be perform by a digitalsystem.
Frame # 27 Slide # 70 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
Once a discrete-time signal is generated which is anaccurate representation of the original continuous-timesignal, any required processing can be perform by a digitalsystem.
If the processed discrete-time signal is intended for aperson, e.g., a music signal, then it must be convertedback into a continuous-time signal.
Frame # 27 Slide # 71 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
Once a discrete-time signal is generated which is anaccurate representation of the original continuous-timesignal, any required processing can be perform by a digitalsystem.
If the processed discrete-time signal is intended for aperson, e.g., a music signal, then it must be convertedback into a continuous-time signal.
Just like the sampling process, the conversion from adiscrete- to a continuous-signal requires a suitabledigital-to-analog interface.
Frame # 27 Slide # 72 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
Typically, the digital-to-analog interface requires a series oftwo cascaded modules, a digital-to-analog (or D/A)converter and a smoothing device:
Smoothing devicey(nT)
y′(nT) D/A converter
y(t)
Frame # 28 Slide # 73 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
A D/A converter will receive an encode digital signal inbinary form like that in Fig. (a) as input and produce acorresponding quantized continuous-time signal such asthat in Fig. (b).The stair-like nature of the quantized signal is, of course,undesirable and a D/A converter is normally followed bysome type of smoothing device, typically a lowpass filter,that will eliminate the uneveness in the signal.
y'(t)
(a)nT
y(nT)
(b)
t
Frame # 29 Slide # 74 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
Complete DSP system
y(nT)
Smoothing device
y′(nT)
D/A converter
y(t)
EncoderQuantizerSampler
x(t)x(nT) xq(nT)
Clock
nT
xq(nT)'
Digital system
Frame # 30 Slide # 75 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
The quality of the conversion from a continuous- to adiscrete-time signal and back to a continuous-time signalcan be improved
– by understanding the processes involved and/or– by designing the components of the sampling system
carefully.
Frame # 31 Slide # 76 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Sampling Process Cont’d
The quality of the conversion from a continuous- to adiscrete-time signal and back to a continuous-time signalcan be improved
– by understanding the processes involved and/or– by designing the components of the sampling system
carefully.
This subject will be treated at a higher level ofsophistication in Chap. 6.
Frame # 31 Slide # 77 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signal Processing
Signal processing is the science of analyzing,synthesizing, sampling, encoding, transforming, decoding,enhancing, transporting, archiving, and generallymanipulating signals in some way or another.
Frame # 32 Slide # 78 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signal Processing
Signal processing is the science of analyzing,synthesizing, sampling, encoding, transforming, decoding,enhancing, transporting, archiving, and generallymanipulating signals in some way or another.
These presentations are concerned primarily with thebranch of signal processing that entails the manipulation ofthe spectral characteristics of signals.
Frame # 32 Slide # 79 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signal Processing
Signal processing is the science of analyzing,synthesizing, sampling, encoding, transforming, decoding,enhancing, transporting, archiving, and generallymanipulating signals in some way or another.
These presentations are concerned primarily with thebranch of signal processing that entails the manipulation ofthe spectral characteristics of signals.
If the processing of a signal involves modifying, reshaping,or transforming the spectrum of the signal in some way,then the processing involved is usually referred to asfiltering.
Frame # 32 Slide # 80 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
Signal Processing
Signal processing is the science of analyzing,synthesizing, sampling, encoding, transforming, decoding,enhancing, transporting, archiving, and generallymanipulating signals in some way or another.
These presentations are concerned primarily with thebranch of signal processing that entails the manipulation ofthe spectral characteristics of signals.
If the processing of a signal involves modifying, reshaping,or transforming the spectrum of the signal in some way,then the processing involved is usually referred to asfiltering.
If the filtering is carried out by digital means, then it isreferred to as digital filtering.
Frame # 32 Slide # 81 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2
This slide concludes the presentation.Thank you for your attention.
Frame # 33 Slide # 82 A. Antoniou Digital Signal Processing – Secs. 1.1, 1.2