# vestigial sideband modulation [closed]

If we are given the following equation of Vestigial Side-band Modulation, what values will I put in the equation?

$$H_0(f)=\frac{1}{H_i(f+f_c)+H_i(f-f_c)}$$

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• These are frequency plots (thus are multi-valued). – analogsystemsrf Apr 7 at 14:51

Practical VSB transmitters generally haven't proper antisymmetrical output signal filtering around the carrier frequency as Harry Nyquist in his VSB modulation theory proved they should have. One sideband is transmitted nearly as is, the carrier is attenuated and the the other sideband is band limited radically. The total filtering in the transmitter is a non-ideal bandpass filtering which is presented by transfer function Hi in your formula.

The non-ideality of the VSB filtering in the transmitter can be compensated in the receiver, if we have there after the detector a correction filter which has transfer function

$$H_0(f)=\frac{1}{H_i(f+f_c)+H_i(f-f_c)}$$

The formula can be used to determine the frequency response of the correction filtering if the filtering in the transmitter is known.

VSB was common in the era of analog TV. These calculations for analog television design were unnecessary because the needed filterings were determined in TV signal norms. I believe (I haven't proven it) the formula isn't valid if the detector is a diode, synchronous detection by mixing down to 0Hz is needed to avoid unwanted new frequency components in detection. In analog TV receivers the correction filtering was in intermediate frequency stages before the detector to avoid the need of complex synchronous detection.

Warning: Your sourcebook, where you have taken this formula from, seems to assume the reader is well familiar with usual university level communication engineering math, where transfer functions are complex and negative frequencies are as meaningful as positive ones.

If you happen NOT to have any sourcebook, only the given formula titled with "VSB" and you are wondering what in the hell it exactly and precisely presents in relative to VSB, you can find more complete theoretical discussion from here: http://faculty.kfupm.edu.sa/EE/wajih/files/EE%20370/EE%20370,%20Lecture%2013.pdf

Be sure you need math knowledge worth several months of full time studies to understand the calculations.

• @ User287001 What do you think of my hypothesis that the VSB is needed to ensure the TV can extract low frequency amplitudes and thus use the vertical/horizontal sync pulses to set up a proper Automatic Level Control, so the entire NTSC signal is accurately extracted from a full-swing (but not clamped nor limited) IF signal? – analogsystemsrf Apr 8 at 4:13
• @analogsystemsrf Sync pulses aren't low freq info, they cover whole video band. SSB + a low amplitude freq&phase reference signal (=attenuated carrier) could in theory well do the job, but the the needed circuits were impossible to build industrially in the era of electron tubes. They were also otherwise impossible, for ex. steep enough filtering would have caused large phase delay errors. Today we could have as complex DSP as needed directly from I.F. signal. Consider the used VSB as the largest practically possible step from AM towards SSB. – user287001 Apr 8 at 9:34
• @analogsystemsrf (continued) Quick sag calculations show that band 0...500Hz can well be taken out of the video signal. – user287001 Apr 8 at 10:01
• @ user287001 I like that sentence "they used VSB as the largest practical step from AM to SSB" !! Notice the burden of the VSB is on the (one per city) transmitter, not in the (1,000,000 per city) receiver. – analogsystemsrf Apr 9 at 17:06

Here is frequency response (its Vestigal Sideband Response) for the NTSC Television signal

simulate this circuit – Schematic created using CircuitLab

Thus the Frame Rate and Line Rate pulses are available without needing a carrier phaselock?? Thus amplitude information is inherently available?

And a non-synchronous_local_oscillator into RF mixer is adequate to down-convert the Upper Side Band to Base Band information, which has the amplitude (video intensity), the phase (the Chroma), and a Frequency-deviation sound carrier.

• I think this text doesn't have especially much explicit information of the meaning of questioner's formula. – user287001 Apr 8 at 9:38