B
boki
Guest
What is modulator?
G
grahamk
Guest
boki wrote:
http://homepage.ntlworld.com/g.knott/elect92.htm
and
http://homepage.ntlworld.com/g.knott/elect95.htm
Have a look at
http://homepage.ntlworld.com/g.knott/elect92.htm
and
http://homepage.ntlworld.com/g.knott/elect95.htm
B
BananaPannaPoe-
Guest
Modulation is the addition of information (or the signal) to an electronic
or optical signal carrier. Modulation can be applied to direct current
(mainly by turning it on and off), to alternating current, and to optical
signals. One can think of blanket waving as a form of modulation used in
smoke signal transmission (the carrier being a steady stream of smoke).
Morse code, invented for telegraphy and still used in amateur radio, uses a
binary (two-state) digital code similar to the code used by modern
computers. For most of radio and telecommunication today, the carrier is
alternating current (AC) in a given range of frequencies. Common modulation
methods include:
a.. Amplitude modulation (AM), in which the voltage applied to the carrier
is varied over time
b.. Frequency modulation (FM), in which the frequency of the carrier
waveform is varied in small but meaningful amounts
c.. Phase modulation (PM), in which the natural flow of the alternating
current waveform is delayed temporarily
These are sometimes known as continuous wave modulation methods to
distinguish them from pulse code modulation (PCM), which is used to encode
both digital and analog information in a binary way. Radio and television
broadcast stations typically use AM or FM. Most two-way radios use FM,
although some employ a mode known as single sideband (SSB).
More complex forms of modulation are Phase Shift Keying (PSK) and Quadrature
Amplitude Modulation (QAM). Optical signals are modulated by applying an
electromagnetic current to vary the intensity of a laser beam.
A computer with an online or Internet connection that connects over a
regular analog phone line includes a modem. This term is derived by
combining beginning letters from the words modulator and demodulator. In a
modem, the modulation process involves the conversion of the digital
computer signals (high and low, or logic 1 and 0 states) to analog
audio-frequency (AF) tones. Digital highs are converted to a tone having a
certain constant pitch; digital lows are converted to a tone having a
different constant pitch. These states alternate so rapidly that, if you
listen to the output of a computer modem, it sounds like a hiss or roar. The
demodulation process converts the audio tones back into digital signals that
a computer can understand. directly.
More information can be conveyed in a given amount of time by dividing the
bandwidth of a signal carrier so that more than one modulated signal is sent
on the same carrier. Known as multiplexing, the carrier is sometimes
referred to as a channel and each separate signal carried on it is called a
subchannel. (In some usages, each subchannel is known as a channel.) The
device that puts the separate signals on the carrier and takes them off of
received transmissions is a multiplexer. Common types of multiplexing
include frequency-division multiplexing (FDM) and time-division multiplexing
(TDM). FDM is usually used for analog communication and divides the main
frequency of the carrier into separate subchannels, each with its own
frequency band within the overall bandwidth. TDM is used for digital
communication and divides the main signal into time-slots, with each
time-slot carrying a separate signal.
--
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"boki" <bokiteam@ms21.hinet.net> wrote in message
news:4c3c095a.0309151010.a01cf32@posting.google.com...
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or optical signal carrier. Modulation can be applied to direct current
(mainly by turning it on and off), to alternating current, and to optical
signals. One can think of blanket waving as a form of modulation used in
smoke signal transmission (the carrier being a steady stream of smoke).
Morse code, invented for telegraphy and still used in amateur radio, uses a
binary (two-state) digital code similar to the code used by modern
computers. For most of radio and telecommunication today, the carrier is
alternating current (AC) in a given range of frequencies. Common modulation
methods include:
a.. Amplitude modulation (AM), in which the voltage applied to the carrier
is varied over time
b.. Frequency modulation (FM), in which the frequency of the carrier
waveform is varied in small but meaningful amounts
c.. Phase modulation (PM), in which the natural flow of the alternating
current waveform is delayed temporarily
These are sometimes known as continuous wave modulation methods to
distinguish them from pulse code modulation (PCM), which is used to encode
both digital and analog information in a binary way. Radio and television
broadcast stations typically use AM or FM. Most two-way radios use FM,
although some employ a mode known as single sideband (SSB).
More complex forms of modulation are Phase Shift Keying (PSK) and Quadrature
Amplitude Modulation (QAM). Optical signals are modulated by applying an
electromagnetic current to vary the intensity of a laser beam.
A computer with an online or Internet connection that connects over a
regular analog phone line includes a modem. This term is derived by
combining beginning letters from the words modulator and demodulator. In a
modem, the modulation process involves the conversion of the digital
computer signals (high and low, or logic 1 and 0 states) to analog
audio-frequency (AF) tones. Digital highs are converted to a tone having a
certain constant pitch; digital lows are converted to a tone having a
different constant pitch. These states alternate so rapidly that, if you
listen to the output of a computer modem, it sounds like a hiss or roar. The
demodulation process converts the audio tones back into digital signals that
a computer can understand. directly.
More information can be conveyed in a given amount of time by dividing the
bandwidth of a signal carrier so that more than one modulated signal is sent
on the same carrier. Known as multiplexing, the carrier is sometimes
referred to as a channel and each separate signal carried on it is called a
subchannel. (In some usages, each subchannel is known as a channel.) The
device that puts the separate signals on the carrier and takes them off of
received transmissions is a multiplexer. Common types of multiplexing
include frequency-division multiplexing (FDM) and time-division multiplexing
(TDM). FDM is usually used for analog communication and divides the main
frequency of the carrier into separate subchannels, each with its own
frequency band within the overall bandwidth. TDM is used for digital
communication and divides the main signal into time-slots, with each
time-slot carrying a separate signal.
--
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http://www.onecomputerguy.com/tips.htm
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news:4c3c095a.0309151010.a01cf32@posting.google.com...
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S
Steve
Guest
The simple explanation;
A modulator "multiplys" two signals together into one. It is
sometimes called a "multiplier".
For example; When you tune into a radio station, you are tuning your
radio to receive the "carrier frequency." Mixed with this carrier is
the audio signal that you hear (music or voice). The radio extracts
the audio signal from the "modulated" carrier.
The purpose of the modulator is to combine the carrier and the audio
(message) into one signal.
In AM (amplitude modulation) the carriers AMPLITUDE varies in
proportion to the audio signal.
In FM (frequency modulation) the carriers FREQUENCY varies in
proportaion to the audio signal.
The basic reason for modulation is so that the low frequency audio
signal can be transmitted using a high frequency carrier.
There are many forms of modulation, and hence many types of modulator.
Further info might be found by searching via www.google.com.
A modulator "multiplys" two signals together into one. It is
sometimes called a "multiplier".
For example; When you tune into a radio station, you are tuning your
radio to receive the "carrier frequency." Mixed with this carrier is
the audio signal that you hear (music or voice). The radio extracts
the audio signal from the "modulated" carrier.
The purpose of the modulator is to combine the carrier and the audio
(message) into one signal.
In AM (amplitude modulation) the carriers AMPLITUDE varies in
proportion to the audio signal.
In FM (frequency modulation) the carriers FREQUENCY varies in
proportaion to the audio signal.
The basic reason for modulation is so that the low frequency audio
signal can be transmitted using a high frequency carrier.
There are many forms of modulation, and hence many types of modulator.
Further info might be found by searching via www.google.com.
K
Kevin Aylward
Guest
boki wrote:
signal into another code. It can either be digital or analogue. The main
reason for doing this is that transmission of the signal is usually more
optimum in the coded form than the non-encoded form.
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
A modulator is an object that converts the information encoded in a
signal into another code. It can either be digital or analogue. The main
reason for doing this is that transmission of the signal is usually more
optimum in the coded form than the non-encoded form.
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
D
Dbowey
Guest
niftydog posted, in part:
<< In AM (amplitude modulation) the carriers AMPLITUDE varies in
proportion to the audio signal. >>
In AM modulation, the carrier amplitude does NOT vary - it is constant. The
process of modulation produces sidebands.
To answer "what is a modulator" depends on your perspective.
A "modulator" for a class C RF amplifier is nothing more nor less a voiceband
amplifier having a suitable output transformer to match the transmitter's Class
C output stage.
An end-user Video "modulator" is a device that will accept a video signal and
output, usually, a chan 3 or 4 TV band signal.
And the list goes on......
You should try to refine your question if you want to receive the correct
answer.
Don
<< In AM (amplitude modulation) the carriers AMPLITUDE varies in
proportion to the audio signal. >>
In AM modulation, the carrier amplitude does NOT vary - it is constant. The
process of modulation produces sidebands.
To answer "what is a modulator" depends on your perspective.
A "modulator" for a class C RF amplifier is nothing more nor less a voiceband
amplifier having a suitable output transformer to match the transmitter's Class
C output stage.
An end-user Video "modulator" is a device that will accept a video signal and
output, usually, a chan 3 or 4 TV band signal.
And the list goes on......
You should try to refine your question if you want to receive the correct
answer.
Don
S
Steve
Guest
dbowey@aol.com (Dbowey) wrote in message news:<20030916191327.07457.00000619@mb-m27.aol.com>...
I understand, but given the broken english in the OPs question I was
trying to give as simple an answer as possible so they might glean the
basic concept. I can appreciate how my statement would have misled
people.
Looking at a simple AM envelope on a CRO gives a beginner the
impression that the amplitude is changing in proportion to the
message. However, when you superimpose the message on the envelope,
it's easier to 'see' what's actually happening. Having a spec. an.
would be handy too! Explaining the concepts and maths behind it all
seems to be beyond the understanding of the OP at this time.
Maybe folks would benefit from reading this;
http://www.whatis.com/definition/0,,sid9_gci214073,00.html
I understand, but given the broken english in the OPs question I was
trying to give as simple an answer as possible so they might glean the
basic concept. I can appreciate how my statement would have misled
people.
Looking at a simple AM envelope on a CRO gives a beginner the
impression that the amplitude is changing in proportion to the
message. However, when you superimpose the message on the envelope,
it's easier to 'see' what's actually happening. Having a spec. an.
would be handy too! Explaining the concepts and maths behind it all
seems to be beyond the understanding of the OP at this time.
Maybe folks would benefit from reading this;
http://www.whatis.com/definition/0,,sid9_gci214073,00.html
K
Kevin Aylward
Guest
Steve wrote:
don't call the Vpk(t) the amplitude of Sin(wt), just what do we call it?
What do we call the Sin(wt) term if not the "carrier"?
is indeed changing. Thats what AM means. Sure, you can make an argument
that the signal is composed of different components or "signals" in the
frequency domain, only some of which has changing amplitudes, but in the
time domain, there is only one "signal", i.e the one voltage/current at
any instant of time.
The main point here is a mathematical identity relating sin(x).sin
->
sin(x-y) + sin(x+y)
I don't see how it is technically any more valid, language wise, to say
that the sin(x-y) and sin(x+y) terms have amplitude terms that are
varying, rather than saying the sin term has an amplitude term that
varies. Mathematically, they are identical descriptions. For lack of any
other word, one is pretty much compelled to refer to the sin term as
the "carrier". "The frequency in absence of any modulation frequency",
seems a bit much.
From a practical point of view, one can certainly measure the average
frequency term that forms sin, and separately its Vp(t) amplitude
term, just as easily, in principle, as one can measure the amplitudes
and frequencies in the conventional descriptive. Both measurements sets
form a correct description of the signal. What is the more "real" one?
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
This is more a matter of semantics. If a signal is Vpk(t).Sin(wt), if we
don't call the Vpk(t) the amplitude of Sin(wt), just what do we call it?
What do we call the Sin(wt) term if not the "carrier"?
That's because it is. The peak to peak amplitude of the complete signal
is indeed changing. Thats what AM means. Sure, you can make an argument
that the signal is composed of different components or "signals" in the
frequency domain, only some of which has changing amplitudes, but in the
time domain, there is only one "signal", i.e the one voltage/current at
any instant of time.
The main point here is a mathematical identity relating sin(x).sin
->sin(x-y) + sin(x+y)
I don't see how it is technically any more valid, language wise, to say
that the sin(x-y) and sin(x+y) terms have amplitude terms that are
varying, rather than saying the sin
term has an amplitude term thatvaries. Mathematically, they are identical descriptions. For lack of any
other word, one is pretty much compelled to refer to the sin
term asthe "carrier". "The frequency in absence of any modulation frequency",
seems a bit much.
From a practical point of view, one can certainly measure the average
frequency term that forms sin
, and separately its Vp(t) amplitudeterm, just as easily, in principle, as one can measure the amplitudes
and frequencies in the conventional descriptive. Both measurements sets
form a correct description of the signal. What is the more "real" one?
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
D
Dbowey
Guest
Kevin posted much irrelevant STUFF, but I choose to comment on the following:
<< The peak to peak amplitude of the complete signal
is indeed changing. Thats what AM means. Sure, you can make an argument
that the signal is composed of different components or "signals" in the
frequency domain, only some of which has changing amplitudes, but in the
time domain, there is only one "signal", i.e the one voltage/current at
any instant of time.
Sure, if we ignore that a scope is essentially a not-very-smart AC voltmeter,
we might be satisfied that we have the entire answer.
That's what AM means? I believe the first guys that modulated an oscillator
and heard the result on their diode detector did think the ampltude of the
carrier varied and "Amplitude Modulation" was a descriptive term at the time.
It doesn't mean we should wear blinders and ignore the realities of the
frequency domain view.
Today there are many ways to observe that the sidebands are separate from the
carrier, and one does not require a spectrum analyzer to do this.
<< The frequency in absence of any modulation frequency",
seems a bit much. >>
What's the problem? A frequency in absence of any modulation is simply an
unmodulated signal; a "carrier" awaiting modulation or a signal waiting to be
keyed to send code.
Don
<< The peak to peak amplitude of the complete signal
is indeed changing. Thats what AM means. Sure, you can make an argument
that the signal is composed of different components or "signals" in the
frequency domain, only some of which has changing amplitudes, but in the
time domain, there is only one "signal", i.e the one voltage/current at
any instant of time.
Sure, if we ignore that a scope is essentially a not-very-smart AC voltmeter,
we might be satisfied that we have the entire answer.
That's what AM means? I believe the first guys that modulated an oscillator
and heard the result on their diode detector did think the ampltude of the
carrier varied and "Amplitude Modulation" was a descriptive term at the time.
It doesn't mean we should wear blinders and ignore the realities of the
frequency domain view.
Today there are many ways to observe that the sidebands are separate from the
carrier, and one does not require a spectrum analyzer to do this.
<< The frequency in absence of any modulation frequency",
seems a bit much. >>
What's the problem? A frequency in absence of any modulation is simply an
unmodulated signal; a "carrier" awaiting modulation or a signal waiting to be
keyed to send code.
Don
K
Kevin Aylward
Guest
Dbowey wrote:
addressing.
more *physically* valid than many other views.
to analyse a function.
is actually real, verses what is an artefact of the particular measuring
method. If I design a piece of equipment to pick out the amplitudes of
single frequency sine waves, i.e the co-efficients of a Fourier
expansion, it does not mean that they are any more real then if I design
a piece of equipment to, say, pick out Bessel co-efficients from a
signal. It also does not imply that they are not real. Its entirely
arbitrary.
There is nothing unique in deciding to resolve f(t) into an orthogonal
expansion of sine(nw) and cosine(nw) waves, and unilaterally declare
that such co-efficients of the expansion are the real truth. Its just
one way of many, to look at the problem.
For example, I could equally well decide to expand f(t) in Walsh
functions, construct an analyser that outputs Walsh function
co-efficients and declare that they represent the real truth. In fact,
for a periodic waveform, I could use any suitable set of periodic
functions, e.g a set of orthogonal elliptic functions.
Indeed, if I decide to claim that the Walsh function co-efficient
analyser are the real truth, no real experiment will contradict that
view. f(t) can be described exactly by those co-efficients just as
validly as the Fourier co-efficients can. The only real blemish is that
it is a bit more complicated because circuits with L's and C's,
preferentially pick out Fourier co-efficients, not Walsh co-efficients.
However, this does not mean that Fourier co-co-efficients have any
better validity or stronger physical meaning. As noted, a Fourier
analysis is just one of an infinite number of ways of describing f(t) by
a sum of orthogonal functions. The prejudice caused by familiarly of
using Fourier co-efficients just doesn't make it any more valid than any
other view.
In the real world we construct observations of objects to to match how
we suppose those objects to behave. Our description of such objects
turns out to be not unique. For example, the shrodinger and hiesenburg
pictures of Quantum Mechanics, are fundamentally different, yet
mathematically, they are identical in that they predict exactly the same
results.
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
Its deeper than this, and yes, I saw this answer coming.
All due respect here, this is old hat, and not the point I am
addressing.
I didn't say that. What I indicated was that a Fourier expansion is no
more *physically* valid than many other views.
Not the point. An expansion in Fourier co-efficients is not a unique way
to analyse a function.
You really missed the point here. Its much more involved. It about what
is actually real, verses what is an artefact of the particular measuring
method. If I design a piece of equipment to pick out the amplitudes of
single frequency sine waves, i.e the co-efficients of a Fourier
expansion, it does not mean that they are any more real then if I design
a piece of equipment to, say, pick out Bessel co-efficients from a
signal. It also does not imply that they are not real. Its entirely
arbitrary.
There is nothing unique in deciding to resolve f(t) into an orthogonal
expansion of sine(nw) and cosine(nw) waves, and unilaterally declare
that such co-efficients of the expansion are the real truth. Its just
one way of many, to look at the problem.
For example, I could equally well decide to expand f(t) in Walsh
functions, construct an analyser that outputs Walsh function
co-efficients and declare that they represent the real truth. In fact,
for a periodic waveform, I could use any suitable set of periodic
functions, e.g a set of orthogonal elliptic functions.
Indeed, if I decide to claim that the Walsh function co-efficient
analyser are the real truth, no real experiment will contradict that
view. f(t) can be described exactly by those co-efficients just as
validly as the Fourier co-efficients can. The only real blemish is that
it is a bit more complicated because circuits with L's and C's,
preferentially pick out Fourier co-efficients, not Walsh co-efficients.
However, this does not mean that Fourier co-co-efficients have any
better validity or stronger physical meaning. As noted, a Fourier
analysis is just one of an infinite number of ways of describing f(t) by
a sum of orthogonal functions. The prejudice caused by familiarly of
using Fourier co-efficients just doesn't make it any more valid than any
other view.
In the real world we construct observations of objects to to match how
we suppose those objects to behave. Our description of such objects
turns out to be not unique. For example, the shrodinger and hiesenburg
pictures of Quantum Mechanics, are fundamentally different, yet
mathematically, they are identical in that they predict exactly the same
results.
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
K
Kevin Aylward
Guest
Dbowey wrote:
addressing.
more *physically* valid than many other views.
to analyse a function.
is actually real, verses what is an artefact of the particular measuring
method. If I design a piece of equipment to pick out the amplitudes of
single frequency sine waves, i.e the co-efficients of a Fourier
expansion, it does not mean that they are any more real then if I design
a piece of equipment to, say, pick out Bessel co-efficients from a
signal. It also does not imply that they are not real. Its entirely
arbitrary.
There is nothing unique in deciding to resolve f(t) into an orthogonal
expansion of sine(nw) and cosine(nw) waves, and unilaterally declare
that such co-efficients of the expansion are the real truth. Its just
one way of many, to look at the problem.
For example, I could equally well decide to expand f(t) in Walsh
functions, construct an analyser that outputs Walsh function
co-efficients and declare that they represent the real truth. In fact,
for a periodic waveform, I could use any suitable set of periodic
functions, e.g a set of orthogonal elliptic functions.
Indeed, if I decide to claim that the Walsh function co-efficient
analyser are the real truth, no real experiment will contradict that
view. f(t) can be described exactly by those co-efficients just as
validly as the Fourier co-efficients can. The only real blemish is that
it is a bit more complicated because circuits with L's and C's,
preferentially pick out Fourier co-efficients, not Walsh co-efficients.
However, this does not mean that Fourier co-co-efficients have any
better validity or stronger physical meaning. As noted, a Fourier
analysis is just one of an infinite number of ways of describing f(t) by
a sum of orthogonal functions. The prejudice caused by familiarly of
using Fourier co-efficients just doesn't make it any more valid than any
other view.
In the real world we construct observations of objects to to match how
we suppose those objects to behave. Our description of such objects
turns out to be not unique. For example, the shrodinger and hiesenburg
pictures of Quantum Mechanics, are fundamentally different, yet
mathematically, they are identical in that they predict exactly the same
results.
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
Its deeper than this, and yes, I saw this answer coming.
All due respect here, this is old hat, and not the point I am
addressing.
I didn't say that. What I indicated was that a Fourier expansion is no
more *physically* valid than many other views.
Not the point. An expansion in Fourier co-efficients is not a unique way
to analyse a function.
You really missed the point here. Its much more involved. It about what
is actually real, verses what is an artefact of the particular measuring
method. If I design a piece of equipment to pick out the amplitudes of
single frequency sine waves, i.e the co-efficients of a Fourier
expansion, it does not mean that they are any more real then if I design
a piece of equipment to, say, pick out Bessel co-efficients from a
signal. It also does not imply that they are not real. Its entirely
arbitrary.
There is nothing unique in deciding to resolve f(t) into an orthogonal
expansion of sine(nw) and cosine(nw) waves, and unilaterally declare
that such co-efficients of the expansion are the real truth. Its just
one way of many, to look at the problem.
For example, I could equally well decide to expand f(t) in Walsh
functions, construct an analyser that outputs Walsh function
co-efficients and declare that they represent the real truth. In fact,
for a periodic waveform, I could use any suitable set of periodic
functions, e.g a set of orthogonal elliptic functions.
Indeed, if I decide to claim that the Walsh function co-efficient
analyser are the real truth, no real experiment will contradict that
view. f(t) can be described exactly by those co-efficients just as
validly as the Fourier co-efficients can. The only real blemish is that
it is a bit more complicated because circuits with L's and C's,
preferentially pick out Fourier co-efficients, not Walsh co-efficients.
However, this does not mean that Fourier co-co-efficients have any
better validity or stronger physical meaning. As noted, a Fourier
analysis is just one of an infinite number of ways of describing f(t) by
a sum of orthogonal functions. The prejudice caused by familiarly of
using Fourier co-efficients just doesn't make it any more valid than any
other view.
In the real world we construct observations of objects to to match how
we suppose those objects to behave. Our description of such objects
turns out to be not unique. For example, the shrodinger and hiesenburg
pictures of Quantum Mechanics, are fundamentally different, yet
mathematically, they are identical in that they predict exactly the same
results.
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
K
Kevin Aylward
Guest
Dbowey wrote:
addressing.
more *physically* valid than many other views.
to analyse a function.
is actually real, verses what is an artefact of the particular measuring
method. If I design a piece of equipment to pick out the amplitudes of
single frequency sine waves, i.e the co-efficients of a Fourier
expansion, it does not mean that they are any more real then if I design
a piece of equipment to, say, pick out Bessel co-efficients from a
signal. It also does not imply that they are not real. Its entirely
arbitrary.
There is nothing unique in deciding to resolve f(t) into an orthogonal
expansion of sine(nw) and cosine(nw) waves, and unilaterally declare
that such co-efficients of the expansion are the real truth. Its just
one way of many, to look at the problem.
For example, I could equally well decide to expand f(t) in Walsh
functions, construct an analyser that outputs Walsh function
co-efficients and declare that they represent the real truth. In fact,
for a periodic waveform, I could use any suitable set of periodic
functions, e.g a set of orthogonal elliptic functions.
Indeed, if I decide to claim that the Walsh function co-efficient
analyser are the real truth, no real experiment will contradict that
view. f(t) can be described exactly by those co-efficients just as
validly as the Fourier co-efficients can. The only real blemish is that
it is a bit more complicated because circuits with L's and C's,
preferentially pick out Fourier co-efficients, not Walsh co-efficients.
However, this does not mean that Fourier co-co-efficients have any
better validity or stronger physical meaning. As noted, a Fourier
analysis is just one of an infinite number of ways of describing f(t) by
a sum of orthogonal functions. The prejudice caused by familiarly of
using Fourier co-efficients just doesn't make it any more valid than any
other view.
In the real world we construct observations of objects to to match how
we suppose those objects to behave. Our description of such objects
turns out to be not unique. For example, the shrodinger and hiesenburg
pictures of Quantum Mechanics, are fundamentally different, yet
mathematically, they are identical in that they predict exactly the same
results.
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
Its deeper than this, and yes, I saw this answer coming.
All due respect here, this is old hat, and not the point I am
addressing.
I didn't say that. What I indicated was that a Fourier expansion is no
more *physically* valid than many other views.
Not the point. An expansion in Fourier co-efficients is not a unique way
to analyse a function.
You really missed the point here. Its much more involved. It about what
is actually real, verses what is an artefact of the particular measuring
method. If I design a piece of equipment to pick out the amplitudes of
single frequency sine waves, i.e the co-efficients of a Fourier
expansion, it does not mean that they are any more real then if I design
a piece of equipment to, say, pick out Bessel co-efficients from a
signal. It also does not imply that they are not real. Its entirely
arbitrary.
There is nothing unique in deciding to resolve f(t) into an orthogonal
expansion of sine(nw) and cosine(nw) waves, and unilaterally declare
that such co-efficients of the expansion are the real truth. Its just
one way of many, to look at the problem.
For example, I could equally well decide to expand f(t) in Walsh
functions, construct an analyser that outputs Walsh function
co-efficients and declare that they represent the real truth. In fact,
for a periodic waveform, I could use any suitable set of periodic
functions, e.g a set of orthogonal elliptic functions.
Indeed, if I decide to claim that the Walsh function co-efficient
analyser are the real truth, no real experiment will contradict that
view. f(t) can be described exactly by those co-efficients just as
validly as the Fourier co-efficients can. The only real blemish is that
it is a bit more complicated because circuits with L's and C's,
preferentially pick out Fourier co-efficients, not Walsh co-efficients.
However, this does not mean that Fourier co-co-efficients have any
better validity or stronger physical meaning. As noted, a Fourier
analysis is just one of an infinite number of ways of describing f(t) by
a sum of orthogonal functions. The prejudice caused by familiarly of
using Fourier co-efficients just doesn't make it any more valid than any
other view.
In the real world we construct observations of objects to to match how
we suppose those objects to behave. Our description of such objects
turns out to be not unique. For example, the shrodinger and hiesenburg
pictures of Quantum Mechanics, are fundamentally different, yet
mathematically, they are identical in that they predict exactly the same
results.
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
J
Jim Large
Guest
Dbowey wrote:
explanation and the frequency domain explanation are equally
valid. Let's imagine, for example, that we've got a carrier
wave of A Hz that is 100% modulated by a pure sine wave of B
Hz where B << A. The time domain explanation says that the
amplitude of the carrier wave slowly changes over time. The
instantaneous value of the signal at time t is:
COS(At)*(COS(Bt)+1)
-------------------
2
The frequency domain explanation says something different.
It says you're putting half of your power into an
unmodulated carrier wave, and the rest into two symmetric
sidebands at A+B and A-B Hz:
2 COS(At) + COS((A-B)t) + COS((A+B)t)
-------------------------------------
4
Well guess what. Both equations are equal. They both
describe the exact same signal. I don't know the proof, but
I do know that it's not exactly cutting edge science.
Joseph Fourier could have proved it a hundred years before
AM radio was invented.
-- Jim L.
Guess what guys, you're both right. The time-domain
explanation and the frequency domain explanation are equally
valid. Let's imagine, for example, that we've got a carrier
wave of A Hz that is 100% modulated by a pure sine wave of B
Hz where B << A. The time domain explanation says that the
amplitude of the carrier wave slowly changes over time. The
instantaneous value of the signal at time t is:
COS(At)*(COS(Bt)+1)
-------------------
2
The frequency domain explanation says something different.
It says you're putting half of your power into an
unmodulated carrier wave, and the rest into two symmetric
sidebands at A+B and A-B Hz:
2 COS(At) + COS((A-B)t) + COS((A+B)t)
-------------------------------------
4
Well guess what. Both equations are equal. They both
describe the exact same signal. I don't know the proof, but
I do know that it's not exactly cutting edge science.
Joseph Fourier could have proved it a hundred years before
AM radio was invented.
-- Jim L.
K
Kevin Aylward
Guest
Jim Large wrote:
Err..I know...That's exactly what I said, ho..humm....
That's right, and there's more. There is no unique way of describing the
universe. I expanded on this in a follow-up post, which, for some
reason, has appeared 3 times.
A point here is that the Fourier view of the universe in EE is so
abundant, that to see things in any other way needs a paradigm shift.
The use of the word bandwidth, implicitly implies that the Fourier view
is being used. If I chose to expand f(t) in say, an orthogonal set of
elliptic functions, bandwidth would not even be a valid term, yet the
resulting description of f(t) would still be just as correct, although
rather a bit obtuse.
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
Err..I know...That's exactly what I said, ho..humm....
That's right, and there's more. There is no unique way of describing the
universe. I expanded on this in a follow-up post, which, for some
reason, has appeared 3 times.
A point here is that the Fourier view of the universe in EE is so
abundant, that to see things in any other way needs a paradigm shift.
The use of the word bandwidth, implicitly implies that the Fourier view
is being used. If I chose to expand f(t) in say, an orthogonal set of
elliptic functions, bandwidth would not even be a valid term, yet the
resulting description of f(t) would still be just as correct, although
rather a bit obtuse.
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
J
John Fields
Guest
On 17 Sep 2003 17:43:40 GMT, dbowey@aol.com (Dbowey) wrote:
It still is, and it still describes the process. For example, let's say
we have a 1MHz carrier with an amplitude of 100VPP. Then let's say we
lower the plate voltage of the final amplifier reduce the amplitude of
the carrier to 50VPP. Then let's say we further lower the plate voltage
and reduce the amplitude of the carrier to 0VPP. Have we not modulated
the amplitude of the carrier? Of course we have!
Now let's say that our plate voltage controller (our modulator) can vary
the plate voltage of the final sinusoidally at 1000Hz. so that at the
positive peak of the sinusoid the carrier voltage is at 100VPP and at
the negative peak of the sinusoid the carrier voltage is at 0VPP. Have
we modulated the amplitude of the carrier? You bet your ass we have!
have we generated sidebands at 1MHz. +/- 1kHz? You bet your ass we
have!
Were those guys with the diode detectors detecting the amplitude
variations of the carrier? You bet your ass they were, they didn't have
filters selective enough not to!
--
John Fields
---
It still is, and it still describes the process. For example, let's say
we have a 1MHz carrier with an amplitude of 100VPP. Then let's say we
lower the plate voltage of the final amplifier reduce the amplitude of
the carrier to 50VPP. Then let's say we further lower the plate voltage
and reduce the amplitude of the carrier to 0VPP. Have we not modulated
the amplitude of the carrier? Of course we have!
Now let's say that our plate voltage controller (our modulator) can vary
the plate voltage of the final sinusoidally at 1000Hz. so that at the
positive peak of the sinusoid the carrier voltage is at 100VPP and at
the negative peak of the sinusoid the carrier voltage is at 0VPP. Have
we modulated the amplitude of the carrier? You bet your ass we have!
have we generated sidebands at 1MHz. +/- 1kHz? You bet your ass we
have!
Were those guys with the diode detectors detecting the amplitude
variations of the carrier? You bet your ass they were, they didn't have
filters selective enough not to!
--
John Fields
D
Dbowey
Guest
John Fields posted:
Never mind.... it didn't add anything to the discussion.
Don
Never mind.... it didn't add anything to the discussion.
Don
J
John Fields
Guest
On 18 Sep 2003 16:15:44 GMT, dbowey@aol.com (Dbowey) wrote:
Well, you seemed to be laboring under the misapprehension that amplitude
modulation doesn't change the amplitude of the carrier, so I thought I'd
better set you straight.
--
John Fields
---
Well, you seemed to be laboring under the misapprehension that amplitude
modulation doesn't change the amplitude of the carrier, so I thought I'd
better set you straight.
--
John Fields
D
dyson
Guest
Kevin Aylward wrote:
in character (and cannot directly describe the f(t) AM process.)
If everything is constant, then the Fourier view can make some
sense.
I agree with you that either the f(t), f(w) or whatever views
are equivalent, but f(w) becomes quite complex when the f(t)
signals aren't constant in character. It is best to keep full
understanding of the various processes, and decide when the f(w)
view is the best way of viewing things, and when the f(t) way
is good.
In the more general case, f(t) will help to solve problems that
f(w) will give LOTS of trouble -- but the f(w) is a good set of
shortcuts.
I agree with Kevin, that in the steady state, f(w) and f(t) can
be equivalent.
John
varying amplitude modulation is that the Fourier view changesJim Large wrote:
Dbowey wrote:
Kevin [wrote]
The peak to peak amplitude of the complete signal is
indeed changing. Thats what AM means. Sure, you can make
an argument that the signal is composed of different
components or "signals" in the frequency domain [...]
[...] That's what AM means? I believe the first guys that
modulated an oscillator and heard the result on their
diode detector did think the ampltude of the carrier
varied and "Amplitude Modulation" was a descriptive term
at the time. It doesn't mean we should wear blinders and
ignore the realities of the frequency domain view.
Guess what guys, you're both right.
Err..I know...That's exactly what I said, ho..humm....
The time-domain
explanation and the frequency domain explanation are equally
valid.
That's right, and there's more. There is no unique way of describing the
universe. I expanded on this in a follow-up post, which, for some
reason, has appeared 3 times.
A point here is that the Fourier view of the universe in EE is so
abundant, that to see things in any other way needs a paradigm shift.
The biggest problem with the simple 'Fourier' view of a time
in character (and cannot directly describe the f(t) AM process.)
If everything is constant, then the Fourier view can make some
sense.
I agree with you that either the f(t), f(w) or whatever views
are equivalent, but f(w) becomes quite complex when the f(t)
signals aren't constant in character. It is best to keep full
understanding of the various processes, and decide when the f(w)
view is the best way of viewing things, and when the f(t) way
is good.
In the more general case, f(t) will help to solve problems that
f(w) will give LOTS of trouble -- but the f(w) is a good set of
shortcuts.
I agree with Kevin, that in the steady state, f(w) and f(t) can
be equivalent.
John
D
Dbowey
Guest
jfields posted:
<< On 18 Sep 2003 16:15:44 GMT, dbowey@aol.com (Dbowey) wrote:
Well, you seemed to be laboring under the misapprehension that amplitude
modulation doesn't change the amplitude of the carrier, so I thought I'd
better set you straight.
I don't believe you set me straight....... Hmmmm....Nope. In my humble
opinion, you are not correct.
Yes, sidebands can be generated by turning the carrier on and off or changing
its amplitude by changing the power supply voltage, but that is not AM as it is
generally used; it's closer kin is CW, as in International Morse transmission.
Don
<< On 18 Sep 2003 16:15:44 GMT, dbowey@aol.com (Dbowey) wrote:
---
Well, you seemed to be laboring under the misapprehension that amplitude
modulation doesn't change the amplitude of the carrier, so I thought I'd
better set you straight.
I don't believe you set me straight....... Hmmmm....Nope. In my humble
opinion, you are not correct.
Yes, sidebands can be generated by turning the carrier on and off or changing
its amplitude by changing the power supply voltage, but that is not AM as it is
generally used; it's closer kin is CW, as in International Morse transmission.
Don
K
Kevin Aylward
Guest
dyson wrote:
the same details at the same time. This is due to an inherent
uncertainty of the transform pair. That is
df.dt >=1/2
That is, the standard deviation of the signals time distribution dt,
times the standard distribution of its frequency distributing df has a
minimum value. That is, knowing the frequency distribution accurately,
means you have larger uncertainty in the time distribution.
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
Technically, f(t) and its Fourier transform g(w) cannot explain all ofKevin Aylward wrote:
Jim Large wrote:
Dbowey wrote:
Kevin [wrote]
The peak to peak amplitude of the complete signal is
indeed changing. Thats what AM means. Sure, you can make
an argument that the signal is composed of different
components or "signals" in the frequency domain [...]
[...] That's what AM means? I believe the first guys that
modulated an oscillator and heard the result on their
diode detector did think the ampltude of the carrier
varied and "Amplitude Modulation" was a descriptive term
at the time. It doesn't mean we should wear blinders and
ignore the realities of the frequency domain view.
Guess what guys, you're both right.
Err..I know...That's exactly what I said, ho..humm....
The time-domain
explanation and the frequency domain explanation are equally
valid.
That's right, and there's more. There is no unique way of describing
the universe. I expanded on this in a follow-up post, which, for some
reason, has appeared 3 times.
A point here is that the Fourier view of the universe in EE is so
abundant, that to see things in any other way needs a paradigm shift.
The biggest problem with the simple 'Fourier' view of a time
varying amplitude modulation is that the Fourier view changes
in character (and cannot directly describe the f(t) AM process.)
If everything is constant, then the Fourier view can make some
sense.
I agree with you that either the f(t), f(w) or whatever views
are equivalent, but f(w) becomes quite complex when the f(t)
signals aren't constant in character. It is best to keep full
understanding of the various processes, and decide when the f(w)
view is the best way of viewing things, and when the f(t) way
is good.
In the more general case, f(t) will help to solve problems that
f(w) will give LOTS of trouble -- but the f(w) is a good set of
shortcuts.
I agree with Kevin, that in the steady state, f(w) and f(t) can
be equivalent.
the same details at the same time. This is due to an inherent
uncertainty of the transform pair. That is
df.dt >=1/2
That is, the standard deviation of the signals time distribution dt,
times the standard distribution of its frequency distributing df has a
minimum value. That is, knowing the frequency distribution accurately,
means you have larger uncertainty in the time distribution.
Kevin Aylward
salesEXTRACT@anasoft.co.uk
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.