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Posts tagged “Engineering

Day #22 : Parametric vs. NonParametric Statistics – 365 DoA

How Mean Meme

Technically we could call this parametric statistics part 2. However, since we are covering nonparametric statistics and more importantly the difference between parametric and nonparametric statistics, it would seem that this title makes more sense. As usual with a continuation, you probably want to start at the beginning where we define parametric statistics. Ready to get started?*

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Day #21 : Defining Parametric Statistics – 365 DoA

normal-distribution

It’s halloween time, we are talking about normally distributed data, so this fits, and I don’t want to hear otherwise!

Well my lovely readers, we’ve made it to the three week mark, 5.7% of the way through! Okay maybe that doesn’t seem like a big deal written like that, but hey it’s progress. So last post we had our independence day, or rather defined what it meant to have independent events vs. dependent events. We also said it was an important assumption in parametric statistics that our events are independent, but then we realized we never defined what parametric statistics even is, oops. So let’s stop dragging our feet and talk parametric statistics!*

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Day #20 : Independent Events – 365 DoA

correlation

By: xkcd

 

Because we introduced the central limit theorem last post, it’s time to introduce another important concept. The idea of independent events, while this may seem intuitive, it is one of the assumptions we make in parametric statistics, another concept we will define, but for now let’s jump into independence.*

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Day #19 : The Central Limit theorem – 365 DoA

 

 

CLT

Well here we are again, if you recall from our last post, we talked Bonferroni Correction. You may also recall that when the post concluded, there was no real topic for today. Well after some ruminating, before we jump into more statistics, we should talk about the central limit theorem. So let’s do a quick dive into what that is and why you should know it!*

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Day #18 : The Bonferroni Correction – 365 DoA

Keep calm and do the Bonferroni corrrection

Keep calm and do the Bonferroni corrrection

By now we are masters of statistics… right? Okay, not really, but we are getting there. So far we’ve covered two types of errors, type 1 which you can read about here, and type 2 which you can read about here. Armed with this new knowledge we can break into a way to correct for type 1 errors that come about from multiple comparisons. Sound confusing? Well, not for long, let’s break it down and talk Bonferroni.*

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Day #17 : Type 2 errors – 365 DoA

 

cat asleep

Last post we did a quick bit on type 1 errors. As with anything, there is more than one way to make an error. Today we are talking type 2 errors! They are related in the sense and we’ll go over what that means and compare the two right… now!*

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Day #16 : Type 1 errors – 365 DoA

tiny dog yawning

tiny dog yawning

We did it, we cracked the coin conundrum! We managed the money mystery! We checked the change charade! We … well you get the idea. Last post we (finally) determined if our coin was bias or not. Don’t worry, I won’t spoil it for you if you haven’t read it yet. I actually enjoyed working through a completely made up problem, so if you haven’t read it, you really should. Today we’re going to talk dogs, you’ll see what I mean, so let’s dive in.*

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Day #15 : Significance, Part 3 – 365 DoA

Standard_deviation

Where does our observation fall on the probability density function?

It looks like we’ve arrived at part 3 of what is now officially a trilogy of posts on statistical significance. There is so much more to say I don’t want to quite call this the conclusion. Instead, let’s give a quick review of where we left off and we can get back to determining if an observed value is significant.*

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Day #14 : Significance, Part 2 – 365 DoA

Bar graph showing z score across trials
Bar graph showing z score across trials

Z-score bar graph that I made just for all of you using some data I had laying around. If you’re new to statistics it may not make sense, but rest assured we will make sense of it all!

Well here we are two weeks into 365DoA, I was excited until I realized that puts us at 3.8356% of the way done. So if you remember from last post we’ve started our significance talk, as in what does it mean to have a value that is significant, what does that mean exactly, and how to do we find out? Today is the day I finally break, we’re going to have to do some math. Despite my best efforts I don’t think we can finish the significance discussion without it and still manage to make sense. With that, let’s just dive in.*

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Day #13 : Significance, Part 1 – 365 DoA

Normally distributed data shown using a histogram plot
Normally distributed data shown using a histogram plot

Histogram of normally distributed data. It looks very… nomal. No it really is normally distributed, read on to find out what that means and how we can use it.

If you’ve read my last post I hinted that today we would discuss filtering. Instead I think I want to take this a different direction. That isn’t to say we won’t go over filtering, we most definitely will. Today I want to cover something else though, significance. So you’ve recorded your signal, took an ensemble average, and now how do we tell if it actually means something, or if you are looking at an artificial or arbitrary separation in your data (IE two separate conditions lead to no difference in your data). Let’s look at significance.*

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Day #12 : Signal, cutting through the noise – 365 DoA

example data

45 separate trials of very noisy data with the average of those trials (black). Believe it or not, this is actually very useful and very real data from something I am currently working on.

Noise, it can be troublesome. Whether you are studying and someone is being loud or you are trying to record something, noise is everywhere <stern look at people who talk during movies>. Interestingly enough the concept of noise in a signal recording sense isn’t all too different from dealing with talkative movie goers, so let’s talk noise!*

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Day #11 : Why even use the spectrogram? – 365 DoA

rotated spectrogram showing all three dimensions
rotated spectrogram showing all three dimensions

A spectrogram plot rotated so we can see all three dimensions.

So you wanna use a spectrogram… but why? What does a spectrogram do that we can’t do using some other methods for signal processing? As it turns out, there is a lot of reasons you may want to use the spectrogram and today we are going to cover some of those reasons and number four may shock you! (okay not really, what do you think this is a clickbait website?)*

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Day #10 : Spectrogram vs. the banana of uncertainty – 365 DoA

banana

The banana of uncertainty (okay, it’s not a real banana)

Well ten days in and we’ve just introduced the idea of the spectrogram. While a lot of this information is just the broad strokes, I like to think that we’ve covered enough to give you a good idea about how to use these tools and what they are used for. However, we do need to discuss a limitation to the spectrogram, something called the banana of uncertainty, okay not quite the name, but you’ll see why I keep calling it that.*

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Day #9 : Reading a Spectrogram – 365 DoA

rotated spectrogram showing all three dimensions
other example

Definitely not the same spectrogram as yesterday, no really look. Now for the part where I tell you how to read this thing…

Last post we introduced a new tool in our arsenal of signal processing analysis, the spectrogram. Without knowing how to read it, it just looks sort of like a colored mess. Don’t get me wrong, it is an interesting looking colored mess, but a mess nonetheless. Well today we are going to talk about how to interpret the plot and why exactly we would ever use this seeming monstrosity.*

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Day #8 : The Spectrogram Function – 365 DoA

Spectrogram

Example spectrogram from some data I had recently processed

To (somewhat) continue with our signal processing theme that we have going on at the moment, over the next few days, let’s look at something called the spectrogram. It’s three dimensions of fun!*

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Day #7 : Small waves, or wavelets! – 365 DoA

Meyer Mother wavelet

This is the Meyer wave, a representation of a so-called mother wavelet function to use for the wavelet transform. Notice that it is finite!

Waves! We’re officially one week through 365 Days of Academia! Woo! 1 week down, 51(.142…) weeks left! Let’s wrap up this weeks theme (there wasn’t originally a theme, but it kind of ended up that way) by talking about other ways we can get to the frequency domain. Specifically, let’s stop the wave puns and let’s talk wavelets!*

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Day #6 : The fast and the Fourier – 365 DoA

Fourier_transform_time_and_frequency_domains_(small)

A good example of how the Fourier transform can approximate signals. The red signal is our input signal and the blue shows how the output of the Fourier transform.

Okay, if you’ve been keeping up with these posts, we know about Welch’s method, Thomson’s method, the things that make them different, and the things that make them similar. The thing that both of these transforms rely on is the Fourier transform. What is the Fourier transform? Well, something I probably should have covered first, but whatever this is my blog we do it in whatever order we feel like, so let’s dive in!*

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Day #5 : Whose window function is it anyway? – 365 DoA

Window function - funny

This is not how we use a window function on the computer…

One day someone looked at the windowed fourier transform and said, “Don’t be such a square!” and thus window functions were invented. If you believe that, then I have an island for sale, real cheap. But seriously, let’s do a dive into what a window function is and why the heck there are so many of them, because there ARE a LOT! So let’s get started!*

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Day #4 : Spectral leakage… embarrassing – 365 DoA

Day 4 - Leakage - arrows

Look at that leakage!

Leakage, it’s never a good thing. For today’s post we’re going to cover a very important topic. Spectral leakage, it’s a big reason why spectral density estimation is well, an estimation. The other reason it is an estimation is because the fourier transform is an approximation of the original signal, but the Fourier transform is a whole other post on its own. So let’s talk leakage!*

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Day #3 : Power Spectral Density Overview – 365 DoA

In our last post we introduced the two main characters in this story of spectrogram. On one end we have Welch’s method (pwelch) on the other end we have the Thomson multitaper method (pmtm). As promised here is a awful basic breakdown of why is more than one way to compute power spectral density (in fact there are several, far more than the two I’m talking about). So, let’s just dig right in!*

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Day #2 : Power Spectral Density (pmtm) – 365 Days of Academia

Day 2 - EKG

A example EKG signal

This is a (somewhat) continuation on what we were discussing in the previous post. We covered the pwelch MATLAB function, this time we will cover the PMTM function, this function uses the Thomson multitaper method to calculate power spectral density. We can do a deep dive into the differences between the two next time, but for now let’s talk about the command itself.*

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Back again with 365 Days of Academia

It’s been an awful time. dusts off the cobwebs around the blog Things have been rough, but I figure it’s time to try and blog regularly again.

So what’s new?

Robo legs - no trash2

Humanoid bipedal robot for balance testing, 100% designed and built by me!

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