Convolution Tutorial

>On Sun, 27 Dec 2009 10:01:07 +0000, invalid wrote:
>
>> "brent" <bulegoge@columbus.rr.com> wrote in message
>> news:0fd6f825-e7ad-4642-
>a5fe-83de8ff8f7f6@x18g2000vbd.googlegroups.com...
>>>I have created a tutorial on the convolution integral. It uses an
>>> interactive flash program with embedded audio files. It is located
>>> here:
>>> http://www.fourier-series.com/Convolution/index.html
>> 
>> You start off by saying that convolution is a mathematical operation,
at
>> which point I switched off.
>> 
>> Convolution is the way that real systems in the real world (such as
>> pianoforte strings)
>> respond to stimuli that are continuous (such as a sine wave from a
>> loudspeaker in close proximity) 
>
>Convolution is _not_ the way that real systems in the real world respond

>to stimuli of any sort.  Convolution is just a _mathematical operation_ 
>that _approximates_ what real systems do.  Sometimes it even does it
well.

Convolution *is* the way many real systems behave. Its not some arcane
mathematical trick. Its the direct mathematical representation of the
underlying physical process. How well it fits reality is generally a matter
of how much the system is affected by second order effects. This is pretty
much like any other area of science and engineering.

>All real systems are nonlinear.  The convolution operation is one way to

>implement a linear model of a system.  Thus, the convolution operation 
>does not model any real system with 100% accuracy.  As a model, the 
>convolution operation is only as good as the fit between its bedrock 
>assumption of linearity and the system's actual conformity to linear 
>behavior.

You must absolutely loath the entire scientific education system. Almost
everything is taught as if it obeys relatively simple relationships, and
that's pretty much always a first order approximation. Often the higher
order elements are so small you can largely ignore them. If you want
accuracy, you'd better scrap Newton's laws of motion.

If you really want to complain about people being taught about stuff like
its an real accurate model, look at the real villans, like how capacitors
are taught. The number of engineers who treat them like they are linear
devices is truly sad. They demand that the latest silicon can do A/D
conversion at high speed with >16 bits precision, and then surround them
with tiny surface mount capacitors who's characteristics are bizarrely
funky.

Steve

>On Sun, 27 Dec 2009 10:01:07 +0000, invalid wrote:
>
>> "brent" <bulegoge@columbus.rr.com> wrote in message
>> news:0fd6f825-e7ad-4642-
>a5fe-83de8ff8f7f6@x18g2000vbd.googlegroups.com...
>>>I have created a tutorial on the convolution integral. It uses an
>>> interactive flash program with embedded audio files. It is located
>>> here:
>>> http://www.fourier-series.com/Convolution/index.html
>> 
>> You start off by saying that convolution is a mathematical operation,
at
>> which point I switched off.
>> 
>> Convolution is the way that real systems in the real world (such as
>> pianoforte strings)
>> respond to stimuli that are continuous (such as a sine wave from a
>> loudspeaker in close proximity) 
>
>Convolution is _not_ the way that real systems in the real world respond

>to stimuli of any sort.  Convolution is just a _mathematical operation_ 
>that _approximates_ what real systems do.  Sometimes it even does it
well.

Convolution *is* the way many real systems behave. Its not some arcane
mathematical trick. Its the direct mathematical representation of the
underlying physical process. How well it fits reality is generally a matter
of how much the system is affected by second order effects. This is pretty
much like any other area of science and engineering.

>All real systems are nonlinear.  The convolution operation is one way to

>implement a linear model of a system.  Thus, the convolution operation 
>does not model any real system with 100% accuracy.  As a model, the 
>convolution operation is only as good as the fit between its bedrock 
>assumption of linearity and the system's actual conformity to linear 
>behavior.

You must absolutely loath the entire scientific education system. Almost
everything is taught as if it obeys relatively simple relationships, and
that's pretty much always a first order approximation. Often the higher
order elements are so small you can largely ignore them. If you want
accuracy, you'd better scrap Newton's laws of motion.

If you really want to complain about people being taught about stuff like
its an real accurate model, look at the real villans, like how capacitors
are taught. The number of engineers who treat them like they are linear
devices is truly sad. They demand that the latest silicon can do A/D
conversion at high speed with >16 bits precision, and then surround them
with tiny surface mount capacitors who's characteristics are bizarrely
funky.

Steve

>On Sun, 27 Dec 2009 10:01:07 +0000, invalid wrote:
>
>> "brent" <bulegoge@columbus.rr.com> wrote in message
>> news:0fd6f825-e7ad-4642-
>a5fe-83de8ff8f7f6@x18g2000vbd.googlegroups.com...
>>>I have created a tutorial on the convolution integral. It uses an
>>> interactive flash program with embedded audio files. It is located
>>> here:
>>> http://www.fourier-series.com/Convolution/index.html
>> 
>> You start off by saying that convolution is a mathematical operation,
at
>> which point I switched off.
>> 
>> Convolution is the way that real systems in the real world (such as
>> pianoforte strings)
>> respond to stimuli that are continuous (such as a sine wave from a
>> loudspeaker in close proximity) 
>
>Convolution is _not_ the way that real systems in the real world respond

>to stimuli of any sort.  Convolution is just a _mathematical operation_ 
>that _approximates_ what real systems do.  Sometimes it even does it
well.

Convolution *is* the way many real systems behave. Its not some arcane
mathematical trick. Its the direct mathematical representation of the
underlying physical process. How well it fits reality is generally a matter
of how much the system is affected by second order effects. This is pretty
much like any other area of science and engineering.

>All real systems are nonlinear.  The convolution operation is one way to

>implement a linear model of a system.  Thus, the convolution operation 
>does not model any real system with 100% accuracy.  As a model, the 
>convolution operation is only as good as the fit between its bedrock 
>assumption of linearity and the system's actual conformity to linear 
>behavior.

You must absolutely loath the entire scientific education system. Almost
everything is taught as if it obeys relatively simple relationships, and
that's pretty much always a first order approximation. Often the higher
order elements are so small you can largely ignore them. If you want
accuracy, you'd better scrap Newton's laws of motion.

If you really want to complain about people being taught about stuff like
its an real accurate model, look at the real villans, like how capacitors
are taught. The number of engineers who treat them like they are linear
devices is truly sad. They demand that the latest silicon can do A/D
conversion at high speed with >16 bits precision, and then surround them
with tiny surface mount capacitors who's characteristics are bizarrely
funky.

Steve

>On Sun, 27 Dec 2009 10:01:07 +0000, invalid wrote:
>
>> "brent" <bulegoge@columbus.rr.com> wrote in message
>> news:0fd6f825-e7ad-4642-
>a5fe-83de8ff8f7f6@x18g2000vbd.googlegroups.com...
>>>I have created a tutorial on the convolution integral. It uses an
>>> interactive flash program with embedded audio files. It is located
>>> here:
>>> http://www.fourier-series.com/Convolution/index.html
>> 
>> You start off by saying that convolution is a mathematical operation,
at
>> which point I switched off.
>> 
>> Convolution is the way that real systems in the real world (such as
>> pianoforte strings)
>> respond to stimuli that are continuous (such as a sine wave from a
>> loudspeaker in close proximity) 
>
>Convolution is _not_ the way that real systems in the real world respond

>to stimuli of any sort.  Convolution is just a _mathematical operation_ 
>that _approximates_ what real systems do.  Sometimes it even does it
well.

Convolution *is* the way many real systems behave. Its not some arcane
mathematical trick. Its the direct mathematical representation of the
underlying physical process. How well it fits reality is generally a matter
of how much the system is affected by second order effects. This is pretty
much like any other area of science and engineering.

>All real systems are nonlinear.  The convolution operation is one way to

>implement a linear model of a system.  Thus, the convolution operation 
>does not model any real system with 100% accuracy.  As a model, the 
>convolution operation is only as good as the fit between its bedrock 
>assumption of linearity and the system's actual conformity to linear 
>behavior.

You must absolutely loath the entire scientific education system. Almost
everything is taught as if it obeys relatively simple relationships, and
that's pretty much always a first order approximation. Often the higher
order elements are so small you can largely ignore them. If you want
accuracy, you'd better scrap Newton's laws of motion.

If you really want to complain about people being taught about stuff like
its an real accurate model, look at the real villans, like how capacitors
are taught. The number of engineers who treat them like they are linear
devices is truly sad. They demand that the latest silicon can do A/D
conversion at high speed with >16 bits precision, and then surround them
with tiny surface mount capacitors who's characteristics are bizarrely
funky.

Steve

>On Sun, 27 Dec 2009 10:01:07 +0000, invalid wrote:
>
>> "brent" <bulegoge@columbus.rr.com> wrote in message
>> news:0fd6f825-e7ad-4642-
>a5fe-83de8ff8f7f6@x18g2000vbd.googlegroups.com...
>>>I have created a tutorial on the convolution integral. It uses an
>>> interactive flash program with embedded audio files. It is located
>>> here:
>>> http://www.fourier-series.com/Convolution/index.html
>> 
>> You start off by saying that convolution is a mathematical operation,
at
>> which point I switched off.
>> 
>> Convolution is the way that real systems in the real world (such as
>> pianoforte strings)
>> respond to stimuli that are continuous (such as a sine wave from a
>> loudspeaker in close proximity) 
>
>Convolution is _not_ the way that real systems in the real world respond

>to stimuli of any sort.  Convolution is just a _mathematical operation_ 
>that _approximates_ what real systems do.  Sometimes it even does it
well.

Convolution *is* the way many real systems behave. Its not some arcane
mathematical trick. Its the direct mathematical representation of the
underlying physical process. How well it fits reality is generally a matter
of how much the system is affected by second order effects. This is pretty
much like any other area of science and engineering.

>All real systems are nonlinear.  The convolution operation is one way to

>implement a linear model of a system.  Thus, the convolution operation 
>does not model any real system with 100% accuracy.  As a model, the 
>convolution operation is only as good as the fit between its bedrock 
>assumption of linearity and the system's actual conformity to linear 
>behavior.

You must absolutely loath the entire scientific education system. Almost
everything is taught as if it obeys relatively simple relationships, and
that's pretty much always a first order approximation. Often the higher
order elements are so small you can largely ignore them. If you want
accuracy, you'd better scrap Newton's laws of motion.

If you really want to complain about people being taught about stuff like
its an real accurate model, look at the real villans, like how capacitors
are taught. The number of engineers who treat them like they are linear
devices is truly sad. They demand that the latest silicon can do A/D
conversion at high speed with >16 bits precision, and then surround them
with tiny surface mount capacitors who's characteristics are bizarrely
funky.

Steve

>On Sun, 27 Dec 2009 10:01:07 +0000, invalid wrote:
>
>> "brent" <bulegoge@columbus.rr.com> wrote in message
>> news:0fd6f825-e7ad-4642-
>a5fe-83de8ff8f7f6@x18g2000vbd.googlegroups.com...
>>>I have created a tutorial on the convolution integral. It uses an
>>> interactive flash program with embedded audio files. It is located
>>> here:
>>> http://www.fourier-series.com/Convolution/index.html
>> 
>> You start off by saying that convolution is a mathematical operation,
at
>> which point I switched off.
>> 
>> Convolution is the way that real systems in the real world (such as
>> pianoforte strings)
>> respond to stimuli that are continuous (such as a sine wave from a
>> loudspeaker in close proximity) 
>
>Convolution is _not_ the way that real systems in the real world respond

>to stimuli of any sort.  Convolution is just a _mathematical operation_ 
>that _approximates_ what real systems do.  Sometimes it even does it
well.

Convolution *is* the way many real systems behave. Its not some arcane
mathematical trick. Its the direct mathematical representation of the
underlying physical process. How well it fits reality is generally a matter
of how much the system is affected by second order effects. This is pretty
much like any other area of science and engineering.

>All real systems are nonlinear.  The convolution operation is one way to

>implement a linear model of a system.  Thus, the convolution operation 
>does not model any real system with 100% accuracy.  As a model, the 
>convolution operation is only as good as the fit between its bedrock 
>assumption of linearity and the system's actual conformity to linear 
>behavior.

You must absolutely loath the entire scientific education system. Almost
everything is taught as if it obeys relatively simple relationships, and
that's pretty much always a first order approximation. Often the higher
order elements are so small you can largely ignore them. If you want
accuracy, you'd better scrap Newton's laws of motion.

If you really want to complain about people being taught about stuff like
its an real accurate model, look at the real villans, like how capacitors
are taught. The number of engineers who treat them like they are linear
devices is truly sad. They demand that the latest silicon can do A/D
conversion at high speed with >16 bits precision, and then surround them
with tiny surface mount capacitors who's characteristics are bizarrely
funky.

Steve

>On Sun, 27 Dec 2009 10:01:07 +0000, invalid wrote:
>
>> "brent" <bulegoge@columbus.rr.com> wrote in message
>> news:0fd6f825-e7ad-4642-
>a5fe-83de8ff8f7f6@x18g2000vbd.googlegroups.com...
>>>I have created a tutorial on the convolution integral. It uses an
>>> interactive flash program with embedded audio files. It is located
>>> here:
>>> http://www.fourier-series.com/Convolution/index.html
>> 
>> You start off by saying that convolution is a mathematical operation,
at
>> which point I switched off.
>> 
>> Convolution is the way that real systems in the real world (such as
>> pianoforte strings)
>> respond to stimuli that are continuous (such as a sine wave from a
>> loudspeaker in close proximity) 
>
>Convolution is _not_ the way that real systems in the real world respond

>to stimuli of any sort.  Convolution is just a _mathematical operation_ 
>that _approximates_ what real systems do.  Sometimes it even does it
well.

Convolution *is* the way many real systems behave. Its not some arcane
mathematical trick. Its the direct mathematical representation of the
underlying physical process. How well it fits reality is generally a matter
of how much the system is affected by second order effects. This is pretty
much like any other area of science and engineering.

>All real systems are nonlinear.  The convolution operation is one way to

>implement a linear model of a system.  Thus, the convolution operation 
>does not model any real system with 100% accuracy.  As a model, the 
>convolution operation is only as good as the fit between its bedrock 
>assumption of linearity and the system's actual conformity to linear 
>behavior.

You must absolutely loath the entire scientific education system. Almost
everything is taught as if it obeys relatively simple relationships, and
that's pretty much always a first order approximation. Often the higher
order elements are so small you can largely ignore them. If you want
accuracy, you'd better scrap Newton's laws of motion.

If you really want to complain about people being taught about stuff like
its an real accurate model, look at the real villans, like how capacitors
are taught. The number of engineers who treat them like they are linear
devices is truly sad. They demand that the latest silicon can do A/D
conversion at high speed with >16 bits precision, and then surround them
with tiny surface mount capacitors who's characteristics are bizarrely
funky.

Steve

>On Sun, 27 Dec 2009 10:01:07 +0000, invalid wrote:
>
>> "brent" <bulegoge@columbus.rr.com> wrote in message
>> news:0fd6f825-e7ad-4642-
>a5fe-83de8ff8f7f6@x18g2000vbd.googlegroups.com...
>>>I have created a tutorial on the convolution integral. It uses an
>>> interactive flash program with embedded audio files. It is located
>>> here:
>>> http://www.fourier-series.com/Convolution/index.html
>> 
>> You start off by saying that convolution is a mathematical operation,
at
>> which point I switched off.
>> 
>> Convolution is the way that real systems in the real world (such as
>> pianoforte strings)
>> respond to stimuli that are continuous (such as a sine wave from a
>> loudspeaker in close proximity) 
>
>Convolution is _not_ the way that real systems in the real world respond

>to stimuli of any sort.  Convolution is just a _mathematical operation_ 
>that _approximates_ what real systems do.  Sometimes it even does it
well.

Convolution *is* the way many real systems behave. Its not some arcane
mathematical trick. Its the direct mathematical representation of the
underlying physical process. How well it fits reality is generally a matter
of how much the system is affected by second order effects. This is pretty
much like any other area of science and engineering.

>All real systems are nonlinear.  The convolution operation is one way to

>implement a linear model of a system.  Thus, the convolution operation 
>does not model any real system with 100% accuracy.  As a model, the 
>convolution operation is only as good as the fit between its bedrock 
>assumption of linearity and the system's actual conformity to linear 
>behavior.

You must absolutely loath the entire scientific education system. Almost
everything is taught as if it obeys relatively simple relationships, and
that's pretty much always a first order approximation. Often the higher
order elements are so small you can largely ignore them. If you want
accuracy, you'd better scrap Newton's laws of motion.

If you really want to complain about people being taught about stuff like
its an real accurate model, look at the real villans, like how capacitors
are taught. The number of engineers who treat them like they are linear
devices is truly sad. They demand that the latest silicon can do A/D
conversion at high speed with >16 bits precision, and then surround them
with tiny surface mount capacitors who's characteristics are bizarrely
funky.

Steve

>On Sun, 27 Dec 2009 10:01:07 +0000, invalid wrote:
>
>> "brent" <bulegoge@columbus.rr.com> wrote in message
>> news:0fd6f825-e7ad-4642-
>a5fe-83de8ff8f7f6@x18g2000vbd.googlegroups.com...
>>>I have created a tutorial on the convolution integral. It uses an
>>> interactive flash program with embedded audio files. It is located
>>> here:
>>> http://www.fourier-series.com/Convolution/index.html
>> 
>> You start off by saying that convolution is a mathematical operation,
at
>> which point I switched off.
>> 
>> Convolution is the way that real systems in the real world (such as
>> pianoforte strings)
>> respond to stimuli that are continuous (such as a sine wave from a
>> loudspeaker in close proximity) 
>
>Convolution is _not_ the way that real systems in the real world respond

>to stimuli of any sort.  Convolution is just a _mathematical operation_ 
>that _approximates_ what real systems do.  Sometimes it even does it
well.

Convolution *is* the way many real systems behave. Its not some arcane
mathematical trick. Its the direct mathematical representation of the
underlying physical process. How well it fits reality is generally a matter
of how much the system is affected by second order effects. This is pretty
much like any other area of science and engineering.

>All real systems are nonlinear.  The convolution operation is one way to

>implement a linear model of a system.  Thus, the convolution operation 
>does not model any real system with 100% accuracy.  As a model, the 
>convolution operation is only as good as the fit between its bedrock 
>assumption of linearity and the system's actual conformity to linear 
>behavior.

You must absolutely loath the entire scientific education system. Almost
everything is taught as if it obeys relatively simple relationships, and
that's pretty much always a first order approximation. Often the higher
order elements are so small you can largely ignore them. If you want
accuracy, you'd better scrap Newton's laws of motion.

If you really want to complain about people being taught about stuff like
its an real accurate model, look at the real villans, like how capacitors
are taught. The number of engineers who treat them like they are linear
devices is truly sad. They demand that the latest silicon can do A/D
conversion at high speed with >16 bits precision, and then surround them
with tiny surface mount capacitors who's characteristics are bizarrely
funky.

Steve

>On Sun, 27 Dec 2009 10:01:07 +0000, invalid wrote:
>
>> "brent" <bulegoge@columbus.rr.com> wrote in message
>> news:0fd6f825-e7ad-4642-
>a5fe-83de8ff8f7f6@x18g2000vbd.googlegroups.com...
>>>I have created a tutorial on the convolution integral. It uses an
>>> interactive flash program with embedded audio files. It is located
>>> here:
>>> http://www.fourier-series.com/Convolution/index.html
>> 
>> You start off by saying that convolution is a mathematical operation,
at
>> which point I switched off.
>> 
>> Convolution is the way that real systems in the real world (such as
>> pianoforte strings)
>> respond to stimuli that are continuous (such as a sine wave from a
>> loudspeaker in close proximity) 
>
>Convolution is _not_ the way that real systems in the real world respond

>to stimuli of any sort.  Convolution is just a _mathematical operation_ 
>that _approximates_ what real systems do.  Sometimes it even does it
well.

Convolution *is* the way many real systems behave. Its not some arcane
mathematical trick. Its the direct mathematical representation of the
underlying physical process. How well it fits reality is generally a matter
of how much the system is affected by second order effects. This is pretty
much like any other area of science and engineering.

>All real systems are nonlinear.  The convolution operation is one way to

>implement a linear model of a system.  Thus, the convolution operation 
>does not model any real system with 100% accuracy.  As a model, the 
>convolution operation is only as good as the fit between its bedrock 
>assumption of linearity and the system's actual conformity to linear 
>behavior.

You must absolutely loath the entire scientific education system. Almost
everything is taught as if it obeys relatively simple relationships, and
that's pretty much always a first order approximation. Often the higher
order elements are so small you can largely ignore them. If you want
accuracy, you'd better scrap Newton's laws of motion.

If you really want to complain about people being taught about stuff like
its an real accurate model, look at the real villans, like how capacitors
are taught. The number of engineers who treat them like they are linear
devices is truly sad. They demand that the latest silicon can do A/D
conversion at high speed with >16 bits precision, and then surround them
with tiny surface mount capacitors who's characteristics are bizarrely
funky.

Steve