 Hi, I am Chaitanya. And I am Ashwit. So, we are here to show you a demo of signals and systems live in action. So, in module 2, I guess we looked at Fourier analysis and this had a lot of math. And we have seen in the forums a lot of people asking where is all this math used in real life. So, Chaitanya has thought of a lot of good examples in the field of music where we can actually see all these signals and systems being used in the practical world. So, what we will do is record a musical instrument into the computer and then look into the process carefully. So, all of you heard music, we all love music and you all probably been wondering what makes different sound instruments sound different. So, we have got a violin here and a guitar. And what we are going to do right now is play a note and we play the same note on the guitar and on the violin and see how it looks on a computer, we will see the waveform and we will be able to look at some details of this and gain some insights. So, Chaitanya, you will be playing which note? I will play the E note. So, go ahead. So, I am going to record the E note right now. Here we have the waveform, let us play it back again. So, now we will look at what just happened. So, it seemed like a very trivial process but there are a lot of things going on here. So, the violin when I played it, it created an acoustic signal which is vibrations in air essentially and what happens in this violin is the vibrations of the string are transferred to the wood of the violin and what I have here is a piezoelectric pickup which will convert the vibrations into electric signals. So, essentially the acoustic signal is put into this system. So, this is essentially a system to which the input is an acoustic signal and output is electrical signal. But before going to the computer, it has to pass through another system. Let me tell you why because the computer only accepts digital inputs. So, what I have here is an audio interface which is basically an interface between the microphone or the transducer and the computer. So, this piezoelectric pickup is connected here and this has basically two systems in it. One is the preamp and another is the ADC. Now, let me explain what they are. So, what the first system does is magnify the signal so that the values are workable for the computer. So, here is a knob which we can adjust so that the magnification can be increased or decreased according to the strength of our original signal. And the second system is an analog digital converter which converts the analog signal to a digital signal which is which can be read by the computer. So, the digital signal is finally fed through a USB cable to the computer in which the software will record it. So, we have the recording here. Let me play it back once again. So, now you can see there is this 48000 hertz which is the sampling frequency about which we will talk more in module 3. So, this is a diagram which essentially sums up what happened. So, there is this sound source which will produce the acoustic signal, the transducer or the piezoelectric pickup in our case will convert the acoustic signal to an electric signal and it will go through a preamp which will amplify the signal to workable values. The signal will go through an ADC which will convert it to a digital signal which is fed to the computer. And I have written a DAC over here which is digital to analog converter which is used while playing it back to the speakers. So, now that we have listened to the E note on the violin, let us hear it on the guitar too. So, let us record it too. So, you have listened to the E note on both the violin and the guitar and they sound starkly different. Have you ever wondered why? Let us explore more about that. So, what we see here are the two recordings on the same screen and you can we have zoomed in a little bit so that you can see things better. And the top signal is the violin recording and the bottom waveform is the guitar recording. You can see that the shape of the two waveforms is quite different. And this is in time domain and in time domain we can see that the shape is different and this gives us some sense on why the two instruments sound so different. Let us zoom in a little bit. So, we have zoomed into the waveforms here and you can see that the shape is indeed quite different. However, you cannot really come to know much about this. The difference in shape is actually called timbre in music that is spelt as T-I-M-B-R-E. And this is why instruments sound different even though they are playing exactly the same note at exactly the same octave. But you can see that we cannot really come to know much from these waveforms and if you remember the introduction video, Professor Gadre also says that you know we cannot really come to know much in the natural domain. So, we need to look at things in an alternate domain. And let us look at this in the frequency domain. So, first let us look at the spectrum of the violin. So, here you can see what the spectrum of the violin looks like. You can see its frequency components plotted on this graph. Let us look at some of them. The fundamental is at E4. We just played the E4 note and you can see that it is written at the bottom of the x-axis. You can see that little E4 written over there. That is one peak. The second harmonic is at E5 and you can see that I have moved the mouse there and it is at double the frequency. The third harmonic is at B5, which is triple the frequency. And you can also see the various values of each of these components. For example, E4 is at about minus 34 dB, E5 is at about minus 37 dB and B5 is at about minus 35 dB and so on. So, this is the spectrum of the violin. Let us next move to the spectrum of the guitar. So, what you see here is the spectrum of the guitar and you can also see its components and you can see it is quite different from that of the violin. So, here you can see again E4, that is the first harmonic, E5, the second harmonic and B5, the third harmonic and you can see a big difference here. In the violin's case, the B5 was not as high as you can see here. You can see that the B5 component here is much higher than the fundamental itself. So, you can see that there are differences in the frequency domain and you can actually appreciate the differences between the guitar and the violin when you look at things in the frequency domain. In the time domain, things were not very clear. So, let us compare the two waveforms. So, we have the violin spectrum on the left and the guitar spectrum on the right. So, we played the E note on both the instruments. So, we can clearly see that both of these have the first peaks at the E4 note and they also have the harmonics present in it. So, what is different is the relative magnitudes of the peaks of the harmonics and that is what makes the sound different for each instrument, even though the bass frequency is same. So, in this demo, we have compared two instruments, the guitar and the violin. Of course, there are many more instruments out there. So, those of you who are musicians, we encourage you to record small snippets, you know, compare notes, compare different instruments and you know, plot the spectra on audacity. So, the software we use is audacity. We will put a link below the video, try to study the spectrum, post on the forums and let us know what you think. Thank you.