complex exponential signals

[Bhuvanesh123]

what makes complex exponential special.its just an addition of cosine and sine with imaginary amplitude ,isn't it?.In my book the waveform for real exponential is given and for complex exponential signal the graph given is just sinusoidal signal .so i cannot differentiate complex exponential and sinusoidal signal.Thank you in advance

 

[panda1234]

can you explain your question more clear?

 

[Bhuvanesh123]

can you explain your question more clear?

sure sir

actually i don't know the purpose of j(i).Does cos(x)+ sin(x) and cos(x)+jsin(x) same?what does j does to sin().is j just an amplitude of sin?

 

[panda1234]

cos(x)+sin(x) don't same as cos(x)+jsin(x). suppose you have a vector in x-y plane you can write it:A=x(x hat)+y(y hat)
and sure this isn't same as A=x+y because two axis are disjoint from each other you never can add two apple and three seconds
because those don't have same type.axis of complex is disjoint from real axis.did you got it?
(sorry for my bad english)

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cos(x)+sin(x) don't same as cos(x)+jsin(x). suppose you have a vector in x-y plane you can write it:A=x(x hat)+y(y hat)
and sure this isn't same as A=x+y because two axis are disjoint from each other you never can add two apple and three seconds
because those don't have same type.axis of complex is disjoint from real axis.did you got it?
(sorry for my bad english)

 

[Bhuvanesh123]

my professor stressed the line"complex exponential play big role in signals and system and it makes the things easier".i need strong reason to agree that.Thank you in advance

 

[rahdirs]

"complex exponential play big role in signals and system and it makes the things easier".i need strong reason to agree that.

1) The set of complex exponentials e^(j2*pi*f*t) where f can take values from (-inf,inf) forms a basis for a large class of signal & Fourier transform of a signal is basically its expansion w.r.t its basis.
2) Real valued sinusoids are contained in complex exponentials (Euler's theorem).

 

[Dan Mills]

Some things are very much easier in polar coordinates, which is all a complex exponential is a means of expressing.
j (in electronic engineering) is the mathematicians i, as i had already been given a meaning in electronics.

j is equal to the square root of -1 in the two dimensional vector space represented by the complex plane, in which a multiplication by j is equivalent to a rotation by 90 degrees CCW on an Argand diagram.

The exponential form of a complex number is useful as phase shifts for example are much more easily reasoned about when represented in this form then in rectangular form.

e^(j(wt + Pi/2)) * e^(j Pi/4) = e^(j(wt + 3 Pi/4) for example is a much easier way to rotate a signal thru 45 degrees then doing the equivalent in a rectangular coordinate system.

You need, I suspect to study complex numbers some more, they really are absolutely fundamental to a lot of the maths engineering uses.

Regards, Dan.

 

[Bhuvanesh123]

[Moved]imaginary and real world signals

my professor signals and system talk"we have two signals real signal and imaginary signals.WE CAN PLAY WITH IMAGINARY SIGNALS but cannot with real signals and we can always transform imaginary signals into real signals"

could anyone understand what he trying to say.Why does he say we can play with imaginary signals

 

[yavuzyaman]

That does not mean anything to me that "we can play with imaginary signals".
for the signal x= a+j b,
a-real number or signal
b-real number or signal
x-complex number or signal

if you define j b= k and say x = a + k , you cannot sum these too regularly. You need to do a vector summation, because a and k are orthogonal to each other. on the other hand, complex exponential is also a complex number like x. but now
a =cos
b=sin

These are most basic things with complex numbers with two representations namely, "cartesian form" and "polar form"
The most significant is one that @rahdirs said above:

1) The set of complex exponentials e^(j2*pi*f*t) where f can take values from (-inf,inf) forms a basis for a large class of signal & Fourier transform of a signal is basically its expansion w.r.t its basis.

 

[Bhuvanesh123]

i am sailing in boat moving 3 units in north moving 4 units in east having 3+4j as vector now i want to rotate it to 90 degree counter clockwise so i just multiply by i.Then i get the answer ,but i want to know it can be done in harder way,i mean how to do same rotation with using complex plane .THank you in advance

 

[rahdirs]

Hi,
that is simple vector algebra,you can do it by checking out its x & y axis component & the angle made by the vector w.r.t axes.