1. Human Sense

All the sense is the signal which received by different organs. After received by organs, our nerve will send all of these signal to brain waiting to be analysed.

2. What are the relationship of Sound and Signals ?

People use sound all the time. We delivers our sound through mouth and then received by ears. But actually, what we are delivering is, signal. The essential of sound is signals, signal includes all the information we want to deliver and receive.

3. Unique signal

Every creature or any stuff which could generate sound own their unique signals, and we call it "Timbre." As the figure you may see below, every sound generator has their own timbre, including human being.

4. Harmonic

In fact, every timbre can be divided into lots of partitions. It means that we can understand an abstruse signal by dividing into lots of partition, and we may call these partitions as the components of the signals or harmonic in music term.

5. Fourier Transform

Fourier Transform is a fantastic analytic method which invented by the great man, Joseph Fourier. Fourier Transform decompose a function of time into the frequencies which make it up. Fourier Transform helps us to see the world in a different way. It let us to understand the signal in frequency world. Fourier Transform facilitates us in analyzing a signal, because the presentation of signal in time domain is far more complicated than in frequency domain. In conclusion, Fourier Transform enable us to comprehend signal thoroughly and visualize it in frequency domain.

6. Music (Song)

There are different kinds of categories in music, one of them is song. Song is a complex signal since it is made by different instruments and, of course, human voice.

I'm going to manipulate both of the song below in my midterm project.

7. Music analyze

First, lets see the Doraemon in time domain. It is really a catastrophe if we analyze the song in time domain. We see nothing but only a complex wave which is made up of other infinite waves that we couldn't see.

All right, after realizing how a disaster would be in time domain, lets take a look in frequency domain. Through Fourier Transform, everything will be clean and simple as the figure below.

What the hell is going on ? There's nothing left in frequency domain. Don't worry, we'll zoom in the figure and then the truth will come out.

As you may see, we could exactly see the components which compose this song.

Let's also analyze the song, Tale as old as Time, too.

8. Filter

Filter is a device or process that removes or remains the components of what we chose in signal. Of course, I am only applying filter in process way since there are no devices. And, I'm going to implement low-pass filter and high-pass filter on Doraemon song.

Low-pass filter

A low-pass filter is the filter that only pass the signals with a frequency lower than the cutoff frequency. Let's examine the equation Y=signal*(1/1+S), and S=jw. Y will remain same as frequency is very small. And it's obvious that Y will approach zero if the frequency keep getting higher and higher and force the denominator approaches infinity. The figure below will give you a better picture of how it works.

Now, I am going to implement it on the Doraemon song. And see what it happens, the low-pass filter exactly removes the high frequency.

And let's take a closer look. The low-pass filter has removed the frequency over about 3kHz.

High-pass filter

Different with low-pass filter, high-pass filter will removes frequency which is lower than cutoff frequency. Examine the equation Y=signal*(S/1+S) as before, imagine what will happens when the frequency approaches infinitely high and infinitely small. The answer emerges simply as Y approaches zero when frequency is infinite low and remain same if frequency is infinite high.

9. Noise

The noise is always exist while the signal is transmitting. Human being eliminate noise through different methods. However, I'm going to generate the noise and add in Doraemon song purely for fun. It's not difficult to generate the noise. As its name implies, it's just a "noise." So, all I have to do is, create a same matrix with random numbers and adds it to the original signal, and it means song in here.

Look, it's totally a mess.

10. Mixture

If you have been to a night club, you will heard of DJ. DJ will mix different songs together to create a new exciting song. However, I'm not a DJ and I do not have those professional skills. So, I will only add both Doraemon and tale as old as time together. The method is not complicated, all we need is to add both matrices of the songs together.

11. Matlab GUI

I combined all the function above with a GUI. So now, we could implement all the functions we talked before in a GUI. It's convenient to manipulate all the functions just in an interface.

12. Demonstration

The only problem here is, speed 5 is over the frequency which Matlab could handle. So the error came when I give 5 to it in this video.