....on real world applications of calculus, specifically one that covers Fourier
and Laplace transforms.

I've managed to squeak by in my class, but our text is theory-only, and our
instructor is... not very helpful.

What I'd really like is something that explains the theory briefly (more as a
recap), then shows real world situations where the theory can be applied.
Hopefully something at least mildly entertaining to read, but that might be
asking for a bit much :/

Does anyone have some suggestions?

....Chambers

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Chambers wrote:
> ....on real world applications of calculus, specifically one that covers Fourier
> and Laplace transforms.
> 
> Does anyone have some suggestions?

The DSP Guide covers the Fourier and Laplace transforms, and how you use 
them for digital filter design or signal analysis. It'll be of 
absolutely no help with differential or integral calculus though.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On 2/20/2010 3:11 PM, Chambers wrote:
> ....on real world applications of calculus, specifically one that covers Fourier
> and Laplace transforms.
>
> I've managed to squeak by in my class, but our text is theory-only, and our
> instructor is... not very helpful.
>
> What I'd really like is something that explains the theory briefly (more as a
> recap), then shows real world situations where the theory can be applied.
> Hopefully something at least mildly entertaining to read, but that might be
> asking for a bit much :/
>
> Does anyone have some suggestions?
>
> ....Chambers
>
>

Just like what I had in school - professor was a brain on feet, but no 
practicable applications really shown or taught.

As you probably already know, DSP systems use the transforms a lot and 
can actually be quite fun.

We did type a few transforms into MATLAB and get to hear what it did to 
a sound file, but little more.

What I really wanted was to be able to do it on a chip and then have it 
process sound real-time.  That would have helped me see the application 
much more clearly.

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Tom Austin wrote:

> Just like what I had in school - professor was a brain on feet, but no 
> practicable applications really shown or taught.

Our brain on feet was called Zimin Wu. His English was... minimal. Which 
is kind of an impediment to teaching, actually. (Fortunately, this was a 
lecture in HCI, not mathematics.)

> As you probably already know, DSP systems use the transforms a lot and 
> can actually be quite fun.
> 
> We did type a few transforms into MATLAB and get to hear what it did to 
> a sound file, but little more.
> 
> What I really wanted was to be able to do it on a chip and then have it 
> process sound real-time.  That would have helped me see the application 
> much more clearly.

Go here:

http://www.falstad.com/mathphysics.html

Scroll down to "signal processing".

They have two applets. One lets you draw an arbitrary waveform and see 
its Fourier series, draw an arbitrary Fourier series and let you see its 
waveform, and listen to the result in either case.

They also have a little DSP applet which will let you play [literally!] 
with any kind of FIR or IIR filter known to mankind - not just the usual 
type-I Chebyshev filter, but also type-II, for example. See and hear in 
realtime, tweak the parameters, and so forth.

That single page also has links to a ridiculous number of other 
addictive applets, like wavetank simulators, circuit simulators, and God 
only knows what else. You might not leave for several hours.

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On 2/22/2010 8:16 AM, Invisible wrote:
> Go here:
>
> http://www.falstad.com/mathphysics.html
>

Something that should be on any geek's bookmarks list!

> Scroll down to "signal processing".
>
> They have two applets. One lets you draw an arbitrary waveform and see
> its Fourier series, draw an arbitrary Fourier series and let you see its
> waveform, and listen to the result in either case.
>
> They also have a little DSP applet which will let you play [literally!]
> with any kind of FIR or IIR filter known to mankind - not just the usual
> type-I Chebyshev filter, but also type-II, for example. See and hear in
> realtime, tweak the parameters, and so forth.

Yep! These applets are quite fun indeed! I've burned many hours playing 
with them.

> That single page also has links to a ridiculous number of other
> addictive applets, like wavetank simulators, circuit simulators, and God
> only knows what else. You might not leave for several hours.

I've actually begun poking around in the source code of the circuit 
sim.... Generally well-written stuff, very organized and easy to 
understand. Not a whole lot of comments though.

I've had a couple of e-mail exchanges with the author. All around nice guy!

-- 
~Mike

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> What I really wanted was to be able to do it on a chip and then have it 
> process sound real-time.  That would have helped me see the application 
> much more clearly.

If you have a fast enough computer and use a fast enough language you should 
be able to do some pretty funky stuff on your home PC with the line/mic 
input and the speaker output of your sound card.  I would recommend using 
C++ and the ASIO driver/protocol - it's really fast (very low latency) and 
easy to code for.

As an aside, I looked into this recently because my transmitter for a radio 
controlled helicopter outputs a PWM signal that can be connected to the PC's 
audio input.  I tried to process this data using the standard Windows API 
calls for recording audio and then DirectSound, but they were *way* too slow 
(when trying to control a helicopter, even a 200 ms delay on the controls 
makes it very hard to control, I was seeing more like 500 ms).  I found the 
ASIO drivers and it worked perfectly with seemingly instant response time, 
now I can use the RC simulator with my own controller!

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scott wrote:
>> What I really wanted was to be able to do it on a chip and then have 
>> it process sound real-time.  That would have helped me see the 
>> application much more clearly.
> 
> If you have a fast enough computer and use a fast enough language you 
> should be able to do some pretty funky stuff on your home PC with the 
> line/mic input and the speaker output of your sound card.  I would 
> recommend using C++ and the ASIO driver/protocol - it's really fast 
> (very low latency) and easy to code for.

Yeah, ASIO is especially designed for low latency. The reason I spent 

produced sane latency. (Try playing keyboard when there's a 500ms delay 
between pressing a key and hearing something!)

Of course, I use Reaktor for my DSP programming, but that's just a *tad* 
expensive...

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>> What I really wanted was to be able to do it on a chip and then have 
>> it process sound real-time.  That would have helped me see the 
>> application much more clearly.
> 
> If you have a fast enough computer and use a fast enough language you 
> should be able to do some pretty funky stuff on your home PC with the 
> line/mic input and the speaker output of your sound card.  I would 
> recommend using C++ and the ASIO driver/protocol - it's really fast 
> (very low latency) and easy to code for.

Perhaps I didn't make this very clear...

A modern PC is already easily fast enough to do realtime DSP even in 
quite low-powered languages. Falstad is doing it in mere Java, for 
example. You don't need to do anything special if you're just doing a 
simple digital filter implementation, for example.

Now, if you want something that you could use for serious studio work, 
or you want to do really complex processing, you're going to need 
specialist tools. But if you just want to play around with basic DSP 
algorithms, you really don't need chips. Just a programming language 
with access to sound hardware. It's really not computationally 
challenging any more.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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> on a new sound card was because it provided ASIO drivers and produced sane 
> latency.

I just have on-board sound but downloaded this:

http://www.asio4all.com/

Works a treat.

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scott wrote:
>> Yeah, ASIO is especially designed for low latency. The reason I spent 

>> produced sane latency.
> 
> I just have on-board sound but downloaded this:
> 
> http://www.asio4all.com/
> 
> Works a treat.

Mmm, nice. (Not quite sure how adding more processing can make it do 
*faster*, but anyway...)

Presumably this doesn't improve the sound quality in quite the same way 

for music-making either. ;-)

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