# Question about signals ( sinc function )

Discussion in 'Wireless & RF Design' started by minismsm, Dec 13, 2013.

1. ### minismsm Thread Starter New Member

Dec 13, 2013
4
0
hello

My question is why the magnitude of a signal at the center frequency or carrier frequency is the greatest ? and falls down as we move away right or left ?(sinc)
I need an intuitive explanation without math.

2. ### WBahn Moderator

Mar 31, 2012
18,093
4,920
Who says that it does? There are modulation schemes that have a completely suppressed signal at the carrier frequency. So you need to be much more specific about what you are looking for.

3. ### minismsm Thread Starter New Member

Dec 13, 2013
4
0
(please give me example in such modulation scheme)

for example in ASK or FSK or i should say generally rect functions .. they have the greatest value at center frequency !?
also in FM modulation .. why values of frequency components are decreasing as we move from the center frequency ?

4. ### WBahn Moderator

Mar 31, 2012
18,093
4,920
SSBSC

How as ASK and FSK examples of "generally rect functions"? I think, but am not sure, that by "generally rect functions" you are talking about the spectrum of the information signal being modulated onto the carrier and not the modulation schemed used. Is that correct?

Otherwise, I ask again who says that they have the greatest value at the center frequency? Why wouldn't the shape depend on the details of the signal being modulated onto the carrier.

You want an intuitive explanation without math of a process that is best and most easily understood by understanding the mathematical details of the process involved? Why?

Perhaps you should come at it from the other side. We have baseband signal, say audio, that has a certain bandwidth. We want to modulate that into a certain part of the radio spectrum, say 900 MHz. There will be a peak somewhere, right? There will be upper and lower limits, at least in practice, to the frequency content of the signal, right? What intuitive reason would there be for the maximum to occur somewhere in the middle of those limits?

5. ### minismsm Thread Starter New Member

Dec 13, 2013
4
0
SSBSC

Yes , but do not understand what is the difference ?
I mean in digital we send 1 , 0 .. so Regardless of type of modulation used we represent the bits as square pulses , Right ?
as in this pic..

yes exactly that is my question , I could not think of a reason other than math ( Fourier ) !!

because the baseband signal itself is bandlimited ?

6. ### WBahn Moderator

Mar 31, 2012
18,093
4,920
Look at the diagram you posted. For ASK, the notion of "bits as square pulses" makes some sense, but look at FSK and PSK. What are the "square pulses" there? In FSK I see some time periods for which there is one frequency and other time periods for which there is a different frequency. Notice that there are never any time periods in which the signal is at the carrier frequency. So how much energy is going to be sitting at the carrier frequency in this case? In PSK I don't see any changes in frequency or amplitude at all, just shifts in phase at the boundaries, so what are the "rectangular pulses" here?

Last edited: Dec 22, 2013
7. ### vk6zgo Active Member

Jul 21, 2012
677
85
In the case of FM,there are combinations of frequency deviation & modulating frequency where the carrier disappears.

The classic method of setting FM deviation is to adjust the modulating signal level until a "carrier null" occurs.

In Double Sideband Suppressed Carrier operation,the carrier is suppressed,& only the sidebands are present.

Single Sideband Suppressed Carrier takes it one step further,suppressing the carrier & one sideband.

There are various combinations of the above,such as Compatible Single Sideband,where the carrier is retained,& one sideband suppressed.

Jul 21, 2012
677
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9. ### minismsm Thread Starter New Member

Dec 13, 2013
4
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thank you
could you tell me the name of this book?

10. ### SinewaveMan New Member

Apr 21, 2013
16
3
Well, acknowledging the foregoing, I may offer the following: many years ago I worked as a production engineer in a radio factory. Near the end of the production line we had to "tune" the AM and FM parts of each radio.

AM by definition can operate optimally at a single carrier frequency, where the AMPLITUDE varies according to the modulation. So on either side of that carrier frequency we would want to suppress other frequencies. We used a sweep generator and 'scope to give a display like attachment AM.jpg.

FM by definition varies the FREQUENCY according to the modulation. This requires that the RF response curve allows for the varying carrier frequency. So the width of the response curve is wider like in attachment FM.gif. We used a thing called a "wobbulator" and 'scope to display the image.

So the reason the "magnitude of a signal at the center frequency" is greatest is because of the tuned circuits being used - rejecting (as much as possible or required) frequencies on either side of center.

I hope this is "un-math" enough to get the picture (pun intended!).

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11. ### alfacliff Well-Known Member

Dec 13, 2013
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if you put an antenna on a spectrum analyzer and look at the tv stations, now they are a "haystack" a fairly flat topped spectrum that takes most of the allotted chanel space. several hundred carriers so they can get the bandwidth for dtv.
cliff

12. ### #12 Expert

Nov 30, 2010
16,705
7,358
I'm going to try a really crude approach. The amplitude of a signal is highest at the center of the carrier frequency because the amplitude of the signal is zero when you get far enough away from the carrier frequency.

If the carrier is 100MHz and you tune a receiver to 100 MHz, you will receive the signal. If you tune to 50KHz, you will not receive the signal. It is not practical to demand that the receiver be tuned to 100,000,000.0 Hz to receive the signal and have it fail at 100,000,001 Hz. Therefore the systems we use are designed so that you can be a bit off in your tuning and receive some of the signal. However, the carrier and its information must decrease in quality as you move away from the center frequency.

13. ### vk6zgo Active Member

Jul 21, 2012
677
85

The classic picture of "Amplitude Modulation" only gives part of the picture.
If you look at an RF envelope with an Oscilloscope,it shows the classic AM wave shape,as a 'scope is a wideband device which operates in the "time domain".

An AM signal is quite different when observed in the frequency domain.
A very selective receiver can resolve the carrier of an AM transmission & demonstrate that its amplitude does not in fact vary with the amplitude of the modulating signal.
If it is then tuned to above or below the carrier frequency,it will encounter new frequencies which do vary in amplitude with that of the modulating signal.

These "sidebands" can also be seen with a Spectrum Analyser.
If your theory was correct,you would not need a sweep generator,as you could simply peak the tuning to a single frequency.

In the FM case,the "varying carrier frequency" idea is more useful,but unfortunately still does not completely cover what really happens.

Again using a selective receiver,it can be seen that there is a signal present at the unmodulated carrier frequency which varies in amplitude,depending upon the frequency deviation present.
At some combinations of modulating frequency & frequency deviation,the amplitude of this signal reduces to zero.
This is how we calibrated "deviation monitors" back when I worked in Broadcasting.