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MATLAB : Fourier transform

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By Nuno Nogueira, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=3912826 MATLAB has been  crucial programming language across worldwide that let us express matrix and array mathematics directly. In signal processing and communication it plays vital role in analysing and exploring time series data in time domain or frequency domain. For analysing non periodic signals in frequency domain we use Fourier transform instead of Fourier series ,which is used to express periodic signals in terms of infinite sum of sinusoidal terms .   Fourier transform can exist for :      1. Energy signals      2. Power signals       3. Impulse signals  That means absolutely integrable signals can have their Fourier transform only.  Formula for Fourier transform;   Then its come to use Fourier transform in MATLAB. So here is the code for Fourier transform of sinusoidal wave , for any other signal we ...

Voyager : Journey of the twin to interstellar space



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         Image credit: NASA/JPL-Caltech
The Voyager mission was launched by NASA in Summer of 1977 which consists of two spacecraft named Voyager 1 and Voyager 2. The main mission for the dual spacecraft was to review Jupiter and Saturn. It's been more than 40 years, they have been travelling through our solar system, unveiling the mysteries of outer planets and discovering new moons and now they have reached in interstellar space. Let's have a look on their journey.

LAUNCH

Voyager 2 was launched on August 20, 1977. After 16 days, on 5th of September, 1977 voyager 1 was launched. The Voyager missions were designed to take advantage of a special alignment of the outer planets that happens every 176 years. It would allow a spacecraft to slingshot from one planet to the next, assisted by the first planet's gravity which means it will require less propellant and time. Voyager 1 was the first man-made object to reach beyond our solar system in interstellar space, Voyager 2 is the second. 
Voyager 1 left the heliosphere behind in 2012 while voyager 2 did this in 2018.

JOURNEY

Before voyager, our knowledge of the outer planets of our solar system was very low. Voyager 2 path was designed to pass by Jupiter, Saturn, Uranus and Neptune while voyager 1 concentrated mainly on Jupiter and Saturn.

Voyager 1 

Even after starting its journey 16 days after its twin, Voyager 1 overtakes voyager 2 on 19th of December,1977 while they were in the asteroid belt. It came out of the asteroid belt in 1978 and started Jupiter's observation in January 1979. The greatest surprise revealed by the mission at Jupiter was probably the invention of active volcanoes on Jupiter’s moon Io. It was the first time active volcanoes were found on any other body of the solar system. It started Saturn's observation in August 1980. It mainly observes Saturn's largest moon Titan. After studying Saturn, Voyager 1 began a journey that one day took it outside of our solar system. Now, it is 22.2 billion Km from the earth as of March 2020. It is the foremost distant man-made object from earth.

Voyager 2

Voyager 2 reaches Jupiter in July 1979. It revealed the mystery of great red spot seen on the surface of Jupiter. It was a complex storm with a counterclockwise direction. It also closely studies the Jupiter's moon Europa. The two Voyager space probes made a variety of important discoveries about Jupiter, its satellites, its radiation belts, and its never-before-seen planetary rings. It started Saturn's observation in August 1981. It gathered much information about Saturn's atmosphere and its ring system.
After this, it's the closest approach with Uranus occurred in January 1986. Through this, we came to know about the misaligned magnetic field of Uranus and 11 new moons were also discovered. Two previously unknown Uranian rings were also discovered. Voyager's closest encounter with Neptune occurs in August 1989. It discovered six new moons of Neptune.
After this voyager 2 started an extended mission to study the outer parts of our solar system. In 2018 it reaches interstellar medium leaving behind our solar system.

FUTURE OF THE PROBES

Both the probes are now on an extended mission, voyager interstellar mission (VIM) as called by NASA. Its mission objective is to increase the NASA exploration of the system beyond the neighbourhood of the outer planets to the outer limits of the Sun's sphere of influence, and possibly beyond. We’re still receiving data from the Voyager probes as they create their epic journey through the region . Both spacecraft are now studying how the sun affects the system, even at such an excellent distance. Any of the space probes will not be able to pass by any star in about 40,000 years and scientists don't expect them to work longer than 5 years from now. Scientists have predicted that Voyager 1's extended mission will continue until about 2025, after that its radioisotope thermoelectric generators will not supply enough electric power whereas Voyager 2 is expected to send weak radio messages till the mid-2020s. But they have done their work long ago.

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