In performing FFTs and looking at spectra for real signals (say, taken from a sensor) we ignore the negative frequencies. I understand that the negative frequencies often reflect the positive frequencies because their imaginary components are complex conjugates. Is this only the case for real signals? Would we be able to notice a difference if imaginary components of a signal did not cancel out (as in hearing an audio signal)?

  • $\begingroup$ Read up on "complex baseband" $\endgroup$ Aug 24 '16 at 14:31
  • $\begingroup$ You have Discrete Multitone Transmission (DMT) which is based on real signals and where negative frequencies have Hermitian symmetry property therefore there are not used for transmission. On the other hand, Orthogonal Frequency-Division Multiplexing (OFDM) widely used in wireless, is based on complex signals where positive and negative frequencies are mutually independent. Therefore, both positive and negative ones can be used for transmission and in reality they are used. $\endgroup$
    – Cali
    Aug 24 '16 at 14:57

A strictly real vector in one domain implies a complex conjugate mirrored vector in the other domain, and vice versa, for any FFT.

The "negative" frequency results of an FFT are very commonly used in SDR (Software Defined Radio), where the signal of interest might consist of only negative frequencies (LSB or lower sideband SSB is one obvious case) in a baseband IQ stream (after quadrature downconversion from strictly real higher frequency RF). Or the SDR software may display a wideband spectrum showing signals both above and below the IQ baseband center frequency, which are displayed from an FFTs negative frequency bins thru positive frequency bins.

Some USB SDR devices (Funcube, et.al.) communicate the complex IQ data stream as stereo audio inputs to the computer, so one might actually be able to listen to the complex IQ data as a stereo left and right pair of audio (after appropriate sample rate conversion, if needed).

  • $\begingroup$ Thanks for all the examples! I guess I was stumped by the pesky "imaginary" number concept, but from what I understand it carries phase information. So, IQ data streams are manipulated by changing the amplitude of the in-phase and quadrature signals (which have the same frequency, but are 90 degrees out-of-phase). Would it be correct to say that the IQ data streams can be represented as two out-of-phase signals OR one complex signal? $\endgroup$ Aug 24 '16 at 23:47

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