Circuit to retain only the positive frequency components in a signal?

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Discussion Overview

The discussion revolves around methods to retain only the positive frequency components of a signal, exploring theoretical and practical implications in the context of signal processing and modulation techniques.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants inquire about the definition and significance of positive frequency components in signals.
  • One participant explains that a signal in the frequency domain has both positive and negative components, using the example of a cosine function.
  • Another participant suggests that mixing the signal with a carrier frequency can help isolate positive frequencies using a bandpass filter.
  • Some participants express a desire to eliminate negative frequency components without shifting the signal, questioning the necessity of negative frequencies in practical applications.
  • There is a discussion about the symmetry of filters in the frequency domain, with some asserting that filters cannot selectively remove negative frequencies due to their mirrored profiles.
  • One participant mentions single sideband (SSB) modulation as a method to achieve a one-sided spectrum without brute force filtering.
  • Another participant argues that negative frequencies are redundant and primarily a mathematical construct, while others challenge this view by citing literature that discusses the physical implications of negative frequencies.
  • Concerns are raised about the physical significance of negative frequencies, with references to papers that suggest they may have practical applications in communication systems.
  • Some participants express skepticism about the relevance of negative frequencies in real-world scenarios, emphasizing the mathematical nature of Fourier transforms.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the significance of negative frequencies, with some viewing them as redundant and others arguing for their potential physical relevance. The discussion remains unresolved regarding the best methods to eliminate negative frequency components from signals.

Contextual Notes

Participants note limitations in understanding the implications of negative frequencies, particularly in relation to the timing and phase definitions in Fourier transforms. The discussion also highlights the complexity of filtering techniques and their effects on frequency components.

  • #31
chroot said:
sanjaysan, the negative frequency components are redundant, in a sense. Consider your time domain signal, cos(2\pi \omega t). The angular frequency, \omega, could be either positive or negative, and the resulting wave would look the same in the time domain. That ambiguity leads to the two-sided, symmetric spectrum.

You can move to a one-sided spectrum if you wish, with no loss of generality, but that's just a mathematical trick. You don't need to design any real, physical device to discard the negative frequencies; they're all in your head from the beginning!

- Warren

Then how do you explain the recovery of baseband signal from single sided passband signal. Suppose we have only upper sideband of a signal then in recovery of message signal the mirrored band of the signal contributes to form the spectrum of the message signal. What do you think happens physically here...
 
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  • #32
Look at the block diagram of an ssb receiver. A local oscillator at the original carrier frequency will mix with the sideband and produce a baseband signal - and other mixing products, of course but they will be at non-baseband frequencies and their power level is not relevant.

If you're concerned about the SNR of the demodulated signal then it would be 3dB lower than when both sidebands are demodulated because the noise bandwidth would be half but the demodulated signal would be half the level - giving 3dB net loss. BUT there was 3dB less power transmitted for a start so there would is overall disadvantage (as long as the transmitter can be made efficient.

It is important to get the Maths and the Physical World reconciled properly. Like I said earlier. All the answers to the calculations should start off with "The real part of".
 

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