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DSB-SC vs SSB-SC



DSB-SC Modulation

Theory

Double Sideband Suppressed Carrier (DSB-SC) modulation is a type of amplitude modulation where only the sidebands are transmitted, and the carrier signal is suppressed. This method is more power-efficient compared to standard amplitude modulation (AM), as it eliminates the carrier, which does not carry useful information.

Mathematical Representation

The DSB-SC modulated signal \( S(t) \) can be expressed as:

\( S(t) = A_c m(t) \cos(2\pi f_c t) \)

Where:

  • \( A_c \) is the amplitude of the carrier signal.
  • \( m(t) \) is the baseband (modulating) signal.
  • \( f_c \) is the frequency of the carrier signal.

In DSB-SC modulation, the carrier signal \( \cos(2\pi f_c t) \) is multiplied by the modulating signal \( m(t) \), resulting in the modulated signal \( S(t) \). The key characteristic of DSB-SC is that the carrier \( A_c \cos(2\pi f_c t) \) is not transmitted. Instead, only the sidebands generated by the multiplication of \( m(t) \) and \( \cos(2\pi f_c t) \) are transmitted.


SSB-SC Modulation

Theory

The SSB-SC modulated signal \( S(t) \) can be expressed as:

\( S(t) = \frac{A_c}{2} \left[ m(t) \cos(2\pi f_c t) \pm \hat{m}(t) \sin(2\pi f_c t) \right] \)

Where:

  • \( A_c \) is the amplitude of the carrier signal.
  • \( m(t) \) is the baseband (modulating) signal.
  • \( f_c \) is the frequency of the carrier signal.
  • \( \hat{m}(t) \) is the Hilbert transform of the modulating signal \( m(t) \).

In SSB-SC modulation, either the upper sideband (USB) or the lower sideband (LSB) is transmitted by choosing the corresponding sign (plus or minus) in the equation. The carrier \( A_c \cos(2\pi f_c t) \) is suppressed, and only one sideband is transmitted. This reduces the bandwidth required for transmission to half that of DSB-SC.


Comparison of Double Sideband Suppressed Carrier (DSB-SC) and Double Side Band (DSB)


Similar to amplitude-modulated (AM) signals, double side-band full carrier (DSB-FC) signals transmit both the upper sideband and lower sideband with a carrier signal.

We transmit only the sidebands of the modulated signal when using a double sideband suppressed carrier (DSB-SC) modulation. The carrier signal itself is not transmitted. It is also possible to reconstruct the original message signal using only one sideband—either the upper or lower sideband—in the case of single sideband suppressed carrier (SSB-SC) modulation. In this case, we transmit only the upper sideband or the lower sideband.


Spectrums of Frequencies for DSB-FC and DSB-SC


The AM signal and the DSB-FC signal use the same frequency spectrum. Take a carrier frequency of 100 Hz and a message frequency of 10 Hz, for instance. You also perform modulation using DSB-FC. Then, peak frequencies that are comparable to AM modulation will be at 90 Hz (100 - 10 Hz), 100 Hz, and 110 Hz (100 + 10 Hz).

 



 Figure: Frequency Spectrums of DSB (Lower Sideband, Carrier, and Upper Sideband)


When DSB-SC modulation is used, the carrier frequency is absent from the modulated signal's spectrum. You will find peak magnitude at frequencies like 90 Hz (100 - 10 Hz) and 110 Hz (100 + 10 Hz) for the same example above with a carrier frequency of 100 Hz and a message frequency of 10 Hz. There won't be any carrier frequency in this

 

                 Figure: Frequency Spectrums of DSB-SC (Lower Sideband, and Upper Sideband)



Further Reading

  1. DSB-SC in detail
  2. SSB-SC in detail
  3. DSB-SC in MATLAB

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