How Science Could have helped the F&F team to open safe in Fast and Furious 5

Hey guys, Have you ever wondered how tej picked the Locker’s passcode in Fast and Furious 5 without any clue. Most of yours would be brute force technique. What if the Locker would have had Builtin GPS system which would alert the antagonist with location when the wrong passcode entries exceed 3 tries. Then Vin diesel and his team would have had a problem, right? With some help from Science Even at this situation also they could open the safe. To get this help from science we have to know some basic terms and principles.

Time Domain:

If we analyze a signal in time domain that will tell us the change in the over the time

In this Example You can see that the time domain analysis giving the behavior of the signal over the time

Frequency domain:

In Frequency domain the Signal will be analyzed with respect to time which will tell us about the different types of frequencies present in the signal. But we can’t say that frequencies are in the right order.

In this Example, You can see that the Frequency domain analysis giving different types of frequencies present in the signal. But these Frequencies are not in same order as they occurred in the signal.

So, we can Conclude that Frequency Domain analysis can give what are the different frequencies are present in the signal but it does not give us when that particular frequency has occurred in that signal.

We can easily convert the time domain signal to Frequency domain Using Fourier transform

Time Frequency analysis:

In time frequency analysis the signal will be studied both in the time domain and Frequency domain simultaneously. This will give us the Frequency and power of signal with respect to time. So, from this we can depict when the particular frequency with respect to time. One of the methods to achieve this is Gabor transform.

Keypad tones:

I hope you all would be familiar with the keypad tones. If not, No problem. Just open the phone app in your smart phone and type some numbers. Now you will hear some tones when pressing the numbers that is keypad tones. Even though all the number’s tones may sound the same. But it’s not. All of them has a unique sound frequency and a base frequency. Now you may get a glimpse of what we are gonna do in the rest of the blog.

Now let’s see how science is helping us here in this situation.

As I said every number in the keypad has a unique frequency. So now what we can do is Plot the passcode’s sound signal in the time domain and then we can convert it to the Time frequency domain Then plotting the frequencies with respect to time we can find the numbers of the passcode,

It’s bit confusing right?

Let me explain you with the Example:

Here I have used MATLAB for analysis. If you’re good at python. That will also work.

For test purpose I am using a audio file which consists of keypad tones of Redmi note 5 Pro

For now I will analyse this file to find the frequencies of the tones with respect to numbers

Code:

Time domain Plot:

Here we can see the ten peaks in the amplitude which is related to the ten number (0-9). Since all the amplitudes are almost same it is of no use.

Let’s convert this into frequency domain using FFT algorithm

Frequency Domain Plot:

Here we can able to see the different frequencies but we are not able to see when a particular frequency has occurred in the signal. So we move to Time frequency analysis

Time-Frequency analysis:

Since I have used a stereo file, I have taken only one side. Since the other side symmetrical to this it is enough.

Here we can analyze the Frequency with respect to time and Power. The Tone signals would have the high power when compare to other signals in this audio. Since yellow color signifies the highest power we can conclude those are our tone frequencies.

You may think why there are 20 yellow color instead of 10.

As I mentioned earlier this is because every tone will have two frequencies one base frequency and its unique frequency. That's why there are 20 yellow dots in the graph.I have tabulated the frequencies of the numbers below.

Here you can see a repetitive pattern in both the Base frequency and the frequency and you may think this is not unique.

But...

When u combine both base frequency and frequency then you will recognize a unique frequency number for every number

Now I know unique frequencies corresponds to every number Now we can use this to find any passcode entered in the keypad

Now let’s move to next part of the example:

Now we will see how to use this Table to find a passcode

Here I have audio file which have my mobile pin in it. (My pin: 95682)

Now let’s start analyzing

Time domain:

From here we can see there are 5 peaks so the pin might of 5 numbers

Frequency Domain:

Here we can see 10 yellow points so the pin would be 5 because in the Time domain signals also, we saw 5 peak amplitudes. To make sure the number of pins is 5 we can check the frequencies of this yellow dots and match it with our table. I already checked frequencies with our table its perfectly matching so let's move on find the numbers

Voila! As you can see, I have reverse engineered all of pin numbers.

This how tej could have found the correct pin for the safe. He already had a dummy safe with him so he could have mapped the frequencies of the number with that safe and using his RC car he could have recorded the tone sound when the antagonist enters the Pin. With help of this spectrogram and bit of a Hardwork we could even traceback what are the keys pressed by AR Rahman in his keyboard when he composed a song. Because every key in the keyboard has a unique frequency just like keypad tones.

And This how the shazam app also working it listen to the song and extract the frequencies with respect to time and match it with its library and it will give results based on the Song which almost matches with the Time-Frequency points which is extracted but that’s an topic for another blog.