[portej05]

Which book is this?
Can you post the whole question - I think there's something missing from the problem statement as-is

[CP5670]

My final year project is in Signal Processing.
It's an application of Successive Mean Quantisation Transforms to audio processing and a study of its performance for the case we've got (we're still nutting out the proposal, so I'll keep things hazy for now) - I'll post more details when the proposal has been finalised with my supervisor (the deadline is about 2 months from now, but I'm doing some prereading)

Mr Nyquist, we meet again.

The funny thing is that Nyquist had little to do with the sampling theorem, but his name somehow became attached to it and many related concepts later on.

Which book is this?
Can you post the whole question - I think there's something missing from the problem statement as-is

I agree, the problem makes no sense as you have stated it. What is the "length of y" supposed to mean?

[Rian]

Wait, is it a curve length problem? As in, the length of the curve defined by that integral? Something like this?

[Mika]

I'm only familiar with Optical signal processing, it doesn't involve anything of those functions. Instead of being temporally bounded, it is usually spatially bounded by limiting apertures and detector sizes. Though we usually think of spot sizes (the image of a point source) and modulation transfer function values at certain spatial frequencies.

Mika

[Mika]

And they had the lectures at 8am...

Yes they did. Los Bastardos.

Mr Nyquist, we meet again.

Shouldn't that be more like:
[Brannigan]
You win again, Mr Nyquist!
[/Brannigan]

My approach to questions regarding whether the system is accurate enough or not was simply making sure that it was accurate enough. Meaning that I compute the Nyquist limit and multiply it by a random constant between 3 and 10, depending on the possibilities. (3-10 times oversampling). At least there is some room for error, since accuracy can be lost ridiculously easily (by other human factors excluding, of course, me), but cannot be gained back by any means.

Mika

[portej05]

And they had the lectures at 8am...

Yes they did. Los Bastardos.

Mr Nyquist, we meet again.

Shouldn't that be more like:
[Brannigan]
You win again, Mr Nyquist!
[/Brannigan]

I was thinking 'MR ANDERSON, good to see you!'

[Kosh]

Which book is this?
Can you post the whole question - I think there's something missing from the problem statement as-is

Yeah, sorry I forgot to put in the curvature part. Find the length of the curve y= integral of sqrt(cost) dt from -pi/2 to x.

The book is this

[portej05]

I still don't think we've got all the information.
Can you post a picture of the question?
Also, we don't have the value of 'x'

[portej05]

Turns out that you don't need to evaluate the integral of sqrt(cos(x)).
I've had a quick chat with a mate of mine (transcipt below) who has a solution and gets the same answer
Hope this helps.

WB: Actually, that integral comes out quite nice. The indefinite integral turns out to be 2*Sqrt(1+Cos(x))*Tan(x/2)
portej05: How come integrals.wolfram.com throughs out something hideous?
WB: Probably because you didn't enter exactly what I was evaluating. Note that in the previous expression, I had a y'(x) ... where y(x) is the integral from the forum.
portej05: http://integrals.wolfram.com/index.jsp?expr=Sqrt(Cos(x))
WB: Exactly, and then you take the derivative of that (Sqrt(Cos[x))), square it (Cos(x)) and you're left with Integrate(Sqrt(1+Cos(x)),{x,x_1,x_2}), which evaluates nicely.
portej05:ah, I see
WB: Actually, I may have just figured out the last bit of that question. The integral is complex if x isn't in (-pi/2,pi/2)...

[Mika]

First, I really have hard time in buying that. Second, I think the x-value should be specified if one wants to get a numerical answer.

Numerically integrating sqrt(cos(x)) from -pi/2 to pi/2 with 2000 intervals yields 2.3963, nothing close to 4.0000.
Anything above (or below!) that will include a complex part which can't be made to vanish.

For integrating sqrt(cos(x)), from -pi/2 to pi/2, it is not even theoretically possible to obtain value larger than pi. Why? The x-axis is defined with radians (3.14) and no matter how many square roots one takes from the cosine function value, one cannot get its value above 1 since the cosine is restricted to be equal or less than 1!

That is unless your friend can explain a little bit carefully why he arrived in the conclusion. Moments like these make me wish I could include some nifty MATLAB figures here that would make it a lot easier to visualize. I can provide the MATLAB function to do this, though.

Mika

[General Battuta]

Are you sure it's not a curve length problem?

[CP5670]

Okay, I see what's going on here. Kosh stated the question in a really roundabout way. The problem is to find the arc length of the antiderivative of sqrt(cos(x)) over (-pi/2,pi/2). In other words, you don't need the actual antiderivative of that thing at all, since whatever it is, you would just be differentiating it again. The reasoning portej05's friend gave is correct.

Are you sure it's not a curve length problem?

It is. That explains where the answer of 4 comes from, and also why this is presumably appearing in a calculus class. I've never seen a calculus level problem that requires special functions.

[Mika]

OK, if that is the actual question then his friend is correct.

It is. That explains where the answer of 4 comes from, and also why this is presumably appearing in a calculus class. I've never seen a calculus level problem that requires special functions.

[Cough] Bessel function [/Cough]
[Cough] Fresnel integrals [/Cough]
...and some other came across while still being in the calculus level...

Mika

[Mika]

By the way Kosh, why are you using Chinese book if you are from US? What is that book about?

Mika

[General Battuta]

Wait, is it a curve length problem? As in, the length of the curve defined by that integral? Something like this?

That might be of some help, then.

[CP5670]

[Cough] Bessel function [/Cough]
[Cough] Fresnel integrals [/Cough]
...and some other came across while still being in the calculus level...

By calculus level, I meant the basic, first semester stuff (which is about the only time you encounter problems like this). At least I haven't seen special functions in any standard textbooks on calculus. They might be covered in physics or engineering oriented "methods" classes, although those are typically more advanced.

[Mika]

Yeah, when they teach basics, they usually don't want to include any special functions. Unfortunately, the basics took about 2 months and after that it was pretty much anything was supposed to go (but of course didn't). We were a kind of a class that got special treatment since they decided that Physicists from that year on do not read basic courses. The course material was made more easy in the next year.

I remember cursing - so did the assitants - quite a long time about one capacitor related assignment, it had something to do with a metallic sheet coated on both sides by material whose dielectric coefficient was on upper side e1 and e2 on the lower. Compute the capacitance of the capacitor formed by rolling the metallic sheet (after rolling, the sheet looks like a spiral if viewed from above)... mind you, this was actually on the first year and in an introductory course of electromagnetism.

Mika

[Kosh]

By the way Kosh, why are you using Chinese book if you are from US? What is that book about?

Mika

Because I am not IN the US. That book is about math.

[portej05]

 

Where are you? (HLP)

[Mika]

Because I am not IN the US. That book is about math.

In that case, do you have any possibility of not using a Chinese study book?

Mika