Nature of Sound signals: Real or Complex

[mileoung]

how is sound waves related to complex numbers

Hi there,

Could you please tell me when a sound signal is complex valued. If possible please provide references.


Thanks,

mileoung

 

[sunderwood]

calculate complex number from sinus

My guess would be that its instantaneous value is real, but if you see it as a sine wave with varying amplitude, frequency and phase you can represent it with a complex number, like A(t) * exp(j * (w(t)*t + phi(t)))

 

[flanello]

All natural signals are real.

With a complex representation one sinus wave can be descirbed (amplitude, frequency and phase) - like sunderwood said.

The benefit of the complex representation is that you can easily calculate with the sinus waves.

A real sound singal often isn't only a singel sinus wave. However it can be speperated into single sinus waves that overlapp:
sound signal = A(t)*exp(j*(w_a(t)*t + phi_a(t))) + B(t)*exp(j*(w_b(t)*t + phi_b(t))) + ....

 

[mileoung]

I am not an expert in sound processing ,however the way I think of this problem is that a pure sound signal is a real signal however because in reality when this signals reaches our 'ears' it is disturbed by other signals. The different signals that disturb the original sound wave is impossible for all of them to have the same phase. Hence, sound signals that reach our ears are complex valued signals.

 

[mmelek1]

Of course real.
The sound signal represents the pressure of the air (compressions and rarefactions)

Have a look at this page:
**broken link removed**

 

[scintillatingstuffs]

Nothing is complex in the world. We have introduced "a theory" of complex numbers so that we can accomodate inexplicable phenomenon under that.

Like we don't define log(-1).. but it can be represented as a complex number.. Similarly asin where mod>1...

For sound signals, they reach our ear; and hence they have some real magnitude at all times. They are Real.

When we hear different sounds from 1 place:

just bcos we hear sound from diff directions, it duznt mean that they r complex. It is we who model them using their phase differences as a complex conglomeration.

 

[ashuisgolu]

All signals that we encounter in the real world are real. However for ease of computation and representation we have introduced the complex notations.
for example a sinusoidal wave 'A sin wt' can be represented in complex notation as A exp (jwt) which is a phasor of amplitude A rotating at the rate of w radians per second. for mathematical computation and system analysis this notation is very useful.

 

[m_pourfathi]

when you think of a signal which PHYSICALLY exists like sound waves or even electromagnetic waves, it's definitely REAL!! but when you need to describe and analyze it MATHEMATICALLY you can use complex numbers. but eventually, to calculate the physical signal you need to look at the real part of the equation or the number.
for instance you can define S(t) = A(t)*cos(w*t + phi) which is real as
Sc(t) = A(t)* exp(j*(w*t + phi)) in which Sc means complex representation of the signal S to which is related as Real(Sc(t)) = S(t).
It just helps you calculate more easily.