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I/Q is a standard method to sample radio frequency and its use is even seen in some non radio signals like sonar. But it seems that it is not used to sample acoustic frequencies.

What property of sound makes plain in-phase PCM or PDM adequate for recording and storing audio–even for high-fidelity recording?

I have an intuition as to the answer, but I think satisfying explanation would be useful to those researching this area of signal processing.

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It is because the audio signals are real and already at baseband. In contrast radio frequency signals are often represented as complex numbers once they are brought back to baseband. Real signals can be represented as a single stream of real numbers, while for complex numbers two streams of real numbers are required to represent them (as in $I+jQ$).

When the upper sideband of a radio waveform at a given carrier frequency does not match the lower sideband of the waveform in magnitude and opposite phase, then the waveform when brought to baseband must be represented with a complex signal (because at baseband the positive and negative frequencies will not be complex conjugate symmetric, which is the requirement for any real signal). A simple example of this is Quadrature Phase Shift Keying and Quadrature Amplitude Modulation where samples are mapped to locations on the complex (IQ) plane as part of the modulation.

It is helpful to have a full grasp of a complex frequency represented as $e^{j\omega t}$ vs $cos(\omega t)$ and what happens when you translate either in frequency to a real carrier: in the case of the exponential only a positive frequency exists so when translated using a real carrier frequency will be a single real tone at a higher frequency than the carrier (upper side band) and similarly $e^{-j\omega t}$ will be a single real frequency at a lower frequency than the carrier (lower side band). The sinusoid in contrast contains both exponentials (see Euler’s identify) and therefore will have both sidebands when translated. This shows how the complex form can be used to occupy half the bandwidth which is a motivation for doing so (in fact the higher modulation orders mentioned offer better spectral efficiency and are complex waveforms in order to do this.)

Similarly the audio signal could be made complex if it was to be converted to a carrier for the same reason (for example single-sided AM is one variant of an analog modulation that can be used with audio in complex form.)

But ultimately an audio signal that is going to one speaker is represented by a single stream of real signals so as explained earlier is not complex — but between the microphone and the speaker we can choose any way to encode the data including complex signals.

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  • $\begingroup$ If I understand correctly: the symmetry in an audio signal only changes from one time=t to another since at any given t the signal is simply the sum of all of the frequencies that combined at the input. But with a modulated carrier, we could have asymmetries in the sidebands at the same time=t, therefore we need to sample the complex component to preserve those possible asymmetries? $\endgroup$ – medbot Apr 1 '20 at 23:36
  • $\begingroup$ I added some more detail to my answer that will hopefully help make it clearer. It all has to do with modulating it to another carrier frequency and ultimately providing for spectral efficiency. $\endgroup$ – Dan Boschen Apr 2 '20 at 2:02
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To complement @DanBoschen's answer: a real baseband signal is a purely in-phase signal. Its quadrature component is zero, so there is no need to sample it or represent it in any way.

An interesting approach, though, would be to represent a stereo signal as quadrature. You could define the right channel as the in-phase signal, the left channel as quadrature, and store the samples as complex numbers. However, there are few, if any, practical advantages to doing so.

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PCM/PDM is used for storing audio samples, while IQ data format is used when transmission using digital communication techniques.

An audio signal (of any any real world signal) when sampled is represented by bits on a computer. The bits represent quantized values of real numbers in a standardized format (for example IEEE 754 floating point standard).

It is when you want to transmit them over a medium is where the IQ data comes into picture. The signal on the I (in phase) channel is getting modulated by carrier signal $cos(\omega_c t)$ while signal on the quadrature channel is getting modulated by $sin(\omega_c t)$. In a computer however, there is nothing called 'complex' number, so the samples would exist as 2 parallel streams $I$ and $Q$. This is efficient compared to using only one carrier (sin or cos) as you would be still able to separate them out at receiver.

Also, audio signals have bandwidth in the range of $kHz$, where all other consumer data would occupy in $MHz$ range. PCM/PDM are much simpler techniques and I think they didn't change much so far because of the storage or bandwidth needed for transmission of audio was negligible compared to other internet data. But when you want to transmit the stored audio samples, you would modify them into I/Q data to transmit over a radio channel, because almost all commercial wireless standards today format data into I and Q streams before transmission.

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IQ sampling is needed when the sampling frequency is near or at the center frequency of the desired signal or signal band. Thus a second sample is needed to discriminate between spectrum above, and spectrum below the sampling frequency.

Audio is sampled well above the center of the audible signal bandwidth, and above twice the highest audible or filter limited frequency in the audio input, thus doesn’t need the 2nd channel for a quadrature component. Because the entire audio bandwidth is well below the sampling frequency (by over a factor of 2), no indication of spectrum above the sampling frequency is required.

Audio sampling typically has a 2nd component, but uses it as a 2nd channel for stereo, instead of for quadrature.

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