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https://designers-guide.org/forum/YaBB.pl Design >> Analog Design >> Real freq, Imaginary freq, positive freq and negative freq ??? https://designers-guide.org/forum/YaBB.pl?num=1319606934 Message started by rajkumar palwai on Oct 25th, 2011, 10:28pm |
Title: Real freq, Imaginary freq, positive freq and negative freq ??? Post by rajkumar palwai on Oct 25th, 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 26th, 2011, 12:42am rajkumar palwai wrote on Oct 25th, 2011, 10:28pm:
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 26th, 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 26th, 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 26th, 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 26th, 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. |
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