>> And a digital signal is a sequence of regular measurements of this phenomenon.

And the cool thing is that,

if we take these measurements often enough, the resulting sequence of numbers

will contain all the relevant information about the original phenomenon.

>> This is where we need a mathematical framework to talk about signal processing.

The convenient framework is linear algebra, in particular, Hilbert space.

>> Aha, did you say Dilbert space?

>> Come on.

>> [LAUGH] >> Let's say that it's very convenient

to see signals as vectors embedded it in a vector space.

>> Okay, so you said the V word, and

I thought this video was going to be all lame jokes and fun.

And now, people are going to look inside our blog and see that it is full of math

and formulas, a nd we're going to lose half of our audience, at least.

>> Let me say two things about this.

First, the book is available for free, and one doesn't look for

a gift horse in the mouth.

Second, theorems are extremely important, they're actually life or death.

>> Okay, sell it to me.

>> Take, for example, a CAT scan >> A machine takes a bunch of x-rays, and

the fancy DSP algorithm makes a three dimensional reconstruction of your brain.

>> Like this one, which is me, by the way.

>> Exactly.

Now, if a medical doctor wants to produce a diagnosis based on the reconstruction,

you want to make sure the reconstruction is correct and unique.

>> Sure, I don't want to end up with someone else's brain.

>> And signal processing theorems give you exactly this guarantee.

>> Okay, but then we can say, that all the math and the theory that we will study,

will always be at the service of practical applications.

>> Exactly. And we went through great pain and

efforts to produce a series of videos called, Signal of the Day, which present

interesting and famous signal processing sequences and relevant algorithms.

>> And remember, your PC is a fully functional signal processing lab, so

we will encourage you to write code to test the theory that we will teach you,

and also to develop some cool applications.

>> For example, you learn how to program an MP3 player.

>> Well, I guess our sales pitch is over.

>> We hope you enjoy the class.