Editing Single-sideband modulation (section)

==Demodulation==
{{Main|Demodulation}}

The front end of an SSB receiver is similar to that of an [[Amplitude modulation|AM]] or [[Frequency modulation|FM]] receiver, consisting of a [[superheterodyne]] [[radio frequency|RF]] front end that produces a frequency-shifted version of the radio frequency (RF) signal within a standard [[intermediate frequency]] (IF) band.

To recover the original signal from the IF SSB signal, the single sideband must be frequency-shifted down to its original range of [[baseband]] frequencies, by using a [[product detector]] which mixes it with the output of a [[beat frequency oscillator]] (BFO). In other words, it is just another stage of heterodyning. For this to work, the BFO frequency must be exactly adjusted. 
If the BFO frequency is off, the output signal will be frequency-shifted (up or down), making speech sound strange and "[[Donald Duck]]"-like, or unintelligible.

For audio communications, there is a common agreement about the BFO oscillator shift of 1.7&nbsp;kHz. A voice signal is sensitive to about 50&nbsp;Hz shift, with up to 100&nbsp;Hz still bearable. Some receivers use a [[carrier recovery]] system, which attempts to automatically lock on to the exact IF frequency. The carrier recovery doesn't solve the frequency shift. It gives better S/N ratio on the detector output.{{Citation needed|reason="...doesn't solve..." and "...gives better..." sound like editorial comments; it also makes an isolated claim about S/N. For both these reasons, a citation is needed.|date=June 2020}}

As an example, consider an IF SSB signal centered at frequency <math>F_{\text{if}}\,</math> = 45000&nbsp;Hz. The baseband frequency it needs to be shifted to is <math>F_b\,</math> = 2000&nbsp;Hz. The BFO output waveform is <math>\cos\left(2\pi \cdot F_{\text{bfo}} \cdot t\right)</math>. When the signal is multiplied by (aka ''[[heterodyne]]d with'') the BFO waveform, it shifts the signal to &nbsp;<math>\left(F_{\text{if}} + F_{\text{bfo}}\right)</math>,&nbsp;''and'' to&nbsp;<math>\left|F_{\text{if}} - F_{\text{bfo}}\right|</math>, which is known as the ''beat frequency'' or ''image frequency''. The objective is to choose an <math>F_{\text{bfo}}</math> that results in &nbsp;<math>\left|F_{\text{if}} - F_{\text{bfo}}\right| = F_b\,</math> = 2000&nbsp;Hz. (The unwanted components at <math>\left(F_{\text{if}} + F_{\text{bfo}}\right)\,</math> can be removed by a [[lowpass filter]]; for which an output transducer or the human [[ear]] may serve).

There are two choices for <math>F_{\text{bfo}}</math>: 43000&nbsp;Hz and 47000&nbsp;Hz, called  ''low-side'' and ''high-side'' injection. With high-side injection, the spectral components that were distributed around 45000&nbsp;Hz will be distributed around 2000&nbsp;Hz in the reverse order, also known as an inverted spectrum. That is in fact desirable when the IF spectrum is also inverted, because the BFO inversion restores the proper relationships. One reason for that is when the IF spectrum is the output of an inverting stage in the receiver. Another reason is when the SSB signal is actually a lower sideband, instead of an upper sideband. But if both reasons are true, then the IF spectrum is not inverted, and the non-inverting BFO (43000&nbsp;Hz) should be used.

If <math>F_{\text{bfo}}\,</math> is off by a small amount, then the beat frequency is not exactly <math>F_b\,</math>, which can lead to the speech distortion mentioned earlier.