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Design >> Analog Design >> Real freq, Imaginary freq, positive freq and negative freq ???
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Message started by rajkumar palwai on Oct 25^th, 2011, 10:28pm

Title: Real freq, Imaginary freq, positive freq and negative freq ???
Post by rajkumar palwai on Oct 25^th, 2011, 10:28pm

Hi all,

Can someone explain about the real freq, complex freq, positive freq and negative freq ?

I use all of them while constructing root locus, bode plots and power spectral density's, but somehow i don't understand them intuitively.

For eg: what is the real meaning of negative freq? Is it same as positive freq with 180 def phase shift?

Thanks
rajkumar

Title: Re: Real freq, Imaginary freq, positive freq and negative freq ???
Post by buddypoor on Oct 26^th, 2011, 12:42am

rajkumar palwai wrote on Oct 25^th, 2011, 10:28pm:

For eg: what is the real meaning of negative freq? Is it same as positive freq with 180 def phase shift?

No, there is no real world "explanation" for the term "negative frequency" because they do not exist in reality.
They only are a mathematical tool with the aim to describe the frequency spectrum in a compact form (using exponential functions).

Title: Re: Real freq, Imaginary freq, positive freq and negative freq ???
Post by raja.cedt on Oct 26^th, 2011, 12:50am

hello rajkumar,

for any physicall signal only +ve frequency posb, but to represent a real signal in complex plane we use both +ve and -ve frequency, for example coswt=(e(iwt)+e(-iwt))/2, so here by using -ve frequency we represented a real signal. Otherwise think from vector point of view, any phaser can be represented by horizontal and vertical components.

Small corection to your post:
A.-ve frequency term will be used in PSD (by the way for real signals no need to use -ve frequency because PSD symmetry, just represent PSD in +ve frequency but magnitude will be increased by 3db ), in bode and root locus we dont use -ve frequency term at all.

B. what do you mean by complex frequency??

Thanks,
raj.

Title: Re: Real freq, Imaginary freq, positive freq and negative freq ???
Post by rajkumar palwai on Oct 26^th, 2011, 9:24am

@Raja and @buddypoor,

Thank you for ur explanations. Now got some sense of positive and negative frequencies.

Can u also explain the real and imaginary freq ?

For eg: In a transfer function, say we have got a zero @ -x1 + j(0). So, what is the meaning of -x1 here. Any real world sinusoid signal is represented as imaginary freq. If we do a real world ac sweep on the circuit, the o/p ac magnitude will start rising @ 20dB/dec from a real freq of mag(X1).
So why we have represented the zero as -x1 + j(0) and why not 0 + j(-x1) ?

Thanks
rajkumar

Title: Re: Real freq, Imaginary freq, positive freq and negative freq ???
Post by raja.cedt on Oct 26^th, 2011, 10:17am

hello rajkumar,
in the transfer functions we use state variable S, means σ+j*w, here σ means attenuation (neper/sec) and w is frewunecy (rad/sec) under the assumption of you are appling a signal called exp(-σ+j*w)t otherwise a sinusoidal signal with frequency w multiplied by exp(-σt). Noramally we will draw bode plot by assuming sigma=0, but you can 3d plot. So coming to your last point (x1+0*j means no frequency at all, it's DC) and if you represent 0+(i*x), it's frequency. There is no img frequency, up to my knoledge. We will consider img part of a S is called frequency.

Thanks,
raj.

Title: Re: Real freq, Imaginary freq, positive freq and negative freq ???
Post by loose-electron on Oct 26^th, 2011, 12:07pm

Complex Frequency - This is a concept that does not get used much in practice.

Most people work with constant amplitude sinusoids (the radians/sec part of complex frequency)

And don't deal with signals that have an exponential envelope coefficient ( the σ part)

"the general complex frequency, s, can be thought of in terms of its real and imaginary parts:

s = σ + jω

or in terms of its period and periodic decay rate:

s = T-1ejα.

The former is always the most appropriate way to use the complex frequency in a Laplace or Fourier transform, however the latter offers a bit more insight.

The imaginary part of s:

Im{s} = ω

is what you would normally think of as "frequency." It tells you how often the signal goes from positive to negative. The real part of s:

Re{s} = σ

is what you would normally think of as "decay rate." It tells you how quickly the amplitude of the oscillations change."

from: http://www.physicsforums.com/showthread.php?t=37945

Above is a pretty good explanation. Wikipedia could use a good write-up on this one.