# Why can a single sine wave signal be used to send digital data but a composite signal is needed to send human talk,etc.?

I can understand the following text (Data Communications and Networking: 4th Edition, Berhouz Forouzan, Ch.5, page 179) which says that a property of a single sine wave carrier signal (phase, frequency or amplitude) can be changed to represent the pattern in digital data:

But I fail to understand why something like human voice (as in a telephonic conversation) can't be similarly mapped onto a single sine wave signal by changing one of the characteristics of the wave (Frequency for example). Doesn't at any instant of time, human voice has a particular frequency and amplitude. Why can't that be represented by modulating a single sine wave? I am asking this because the same book says that in order to transfer human voice etc, we need a composite signal having many constituent sine waves of many frequencies:

Please explain this to me in simple terms why it is so. What's different between transmitting something like human voice on one hand and a digital data pattern on the other?And what are other "stuff" like human talk which necessitates use of a composite signal?

NB: I will appreciate if you can also tell IF human talk can be sampled, converted to a digital pattern, and THEN transmitted over a SINGLE sine wave signal. Thank you.

• As soon as you change things about your sine wave, it's not a 'simple sine wave' any more. You could think of ordinary AM radio as being a single sine wave (the carrier frequency) amplitude modulated by the voice audio signal. Whether that's 'a simple sine wave which has just been amplitude modulated' or a 'composite signal' is a distinction without a difference. Sounds like the best thing you could do with that book is hang it on the wall next to the lavatory. Anybody who thinks a sine wave sounds like 'a buzz' is worth ignoring anyway. – user1844 Oct 17 '15 at 15:10
• @WillDean :-) I am afraid bro that the author is a renowned professor from De Anza college. Leaving that aside, can one conclude that if once we alter any attribute of a single and simple carrier sine wave, it becomes a composite signal? – Meathead Oct 17 '15 at 15:13
• One of the most useful things I was told at university was that the expectation in (particularly) American academia was that everyone should publish text books, and that the author being an eminent professor at somewhere or other was no guarantee that they'd written a great book. – user1844 Oct 17 '15 at 15:56
• You realize that De Anza College is a community college, right? A professor there could be a great teacher who just isn't interested in research, or they could be not qualified to teach at a 4-year school. – The Photon Oct 17 '15 at 20:59
• Sine waves of higher, audible frequencies do sound like a buzz @willdean – Passerby Oct 18 '15 at 5:16

## 5 Answers

There are several confusions going on here. I can see what the text you cite is trying to say, but also how it can be easily misinterpreted.

The first section is talking about how to modulate a single sine wave (let's call that the "carrier"), to carry another signal. In the text's example, this other signal is digital, but it doesn't need to be.

AM radio is a great example of modulating a carrier using amplitude to carry a audio signal. FM radio is the same except it modulates the frequency. Phase modulation is also used elsewhere, so that part of the first quote is all true.

The misleading part is giving the impression the result is still just a "single sine wave". It's not. As soon as you change something about a sine wave, you no longer have a single sine wave. This may sound unintuitive, but a AM radio carrier of 1 MHz modulated with a 1 kHz audio signal is actually the combination of three sine waves, at 999 kHz, 1.000 MHz, and 1.001 MHz. Getting into why that is true is beyond the scope of this answer. You'll either have to learn a bunch of Fourier analysis or trust me on this.

The second part correctly points out that a true "single sine wave" can't carry any dynamic information. This is again part of the semantics of "single sine". A true single sine doesn't vary in frequency, amplitude, or phase. If it did, you can show by Fourier analysis that it's not really a single sine anymore, just like the AM carrier modulated with 1 kHz wasn't a single sine anymore.

Basically, a periodically changing sine wave can be mathematically decomposed into a set of separate single sines, each with their own amplitude, frequency, and phase. There is therefore no such thing as a changing single sine. This is why a true single sine doesn't carry any dynamic information.

• This was my first question on this forum and I appreciate that you took the time to answer a question that you must have found trivial. You have clearly delineated beyond which part of the answer one needs stuff like Fourier analysis to grasp it all. Thanks for your time sir. – Meathead Oct 17 '15 at 17:18
• Whoever downvoted this: It would be useful to know what you think is wrong, misleading, or badly written. Silent downvotes without obvious cause do this site a disservice. – Olin Lathrop Oct 18 '15 at 12:42

You can't send data or voice over a SINGLE sine wave signal. You have to modulate it by changing the frequency or amplitude (or phase).

A single sine wave contains a single frequency and amplitude that doesn't vary with time, correct? In the frequency domain it's a single line with no width.

Therefore you have 2 pieces of information that don't vary with time. Voice and data must vary with time to transmit information.

By modulating the sine wave's amplitude or frequency or phase with time you can transmit that information. But at that point it is no longer a single sine wave, it's a time varying composite of the information you are trying to send with the "carrier" sine wave.

So no, you can't sample human voice and send it over a single sine wave. Of course you could use a single sine wave as a carrier and modulate it however you want to carry the digital data, but then it's no longer a single sine wave.

• Referring to your first two lines, does it mean that once we modulate a single sine wave signal, it becomes a composite signal(theoretically one composed of many sine waves)? I am not from an electrical/electronics engineering domain and hence missing out the finer details. – Meathead Oct 17 '15 at 15:18
• Thanks a lot, you have already answered the above. I have understood what you said. Thanks a ton. – Meathead Oct 17 '15 at 15:21

As other answers said, neither voice nor digital data can be sent over a "single sine wave".

Either one can be transmitted over a modulated sine wave.

I fail to understand why something like human voice (as in a telephonic conversation) can't be similarly mapped onto a single sine wave signal by changing one of the characteristics of the wave (Frequency for example).

Of course a voice can be transmitted by frequency modulation. Whenever you listen to FM radio, that's exactly how the announcers' voices are transmitted to you. Whenever you made a long-distance telephone call before 1980 or so, it was likely your voice was transmitted this way also.

will appreciate if you can also tell IF human talk can be sampled, converted to a digital pattern, and THEN transmitted over a SINGLE sine wave signal.

Yes, this is also possible. For example, compact discs store sounds including voices in digital form, and when they are read back the pattern of bits on the disc is used to modulate a laser beam (an example of an electromagnetic sine wave) before they are converted back to audio signals. Also, whenever you make a long-distance telephone call nowadays, your voice is almost certainly digitized and modulated onto a carrier (and combined with 1000's of other voice signals) to be transmitted over the trunk lines.

• Thanks for taking the time to give a detailed answer. Further clarified my understanding. – Meathead Oct 17 '15 at 16:20

Consider a single sine wave: as already noted it is a single line in the frequency domain.

Now we will add some information. That could be voice, digital data - anything. This information will usually (always in practice) have some bandwidth, but the instantaneous signal will be at some frequency f(x) at some amplitude A(x).

In amplitude modulation (because it is the simplest), we will have, at any instant, a composite signal of f(carrier) +/- f(information). I am not going to derive that here.

As this information signal varies with time, we will get f(carrier) +/- f(information) where the information is a band of signals, when viewed over time.

So if we start with a simple sinusoid (the carrier) and modulate with some complex information signal H(s), we end up with f(carrier) modified by H(s) in the frequency domain.

The simple sinusoid carries no information and this might be key to understanding the issue. The modulated signal contains a known signal - the carrier - (so we can find it in the frequency domain) that is carrying an information signal.

So: the simple sine does not carry any information except where to find it in the frequency domain. We 'piggyback' the information onto it.

The original sinusoid still exists; we have added information to it.

Note: The use of the term information is deliberate, and as further reading for the OP, the definition of information is indistinguishable from that of noise.

All the other answers here are accurate - I am simply trying to answer from a different perspective.

Human speech and music for example, are made up of several sine waves mixed together. In the case of voice, this can be sampled, at a minimum of twice the highest frequency of speech (typical sample rate of 8 kHz for a analog telephone line, see (Nyquist-Shannon sampling theorem). The amount of bits of each sample is usually minimum of 8. These bits represent the amplitude of the signal. This scheme is called pulse code modulation (PCM).

This diagram shows what sampling might look like using 3 bits per channel:

which would not be enough to provide intelligible speech, but shows the idea.

The combination of 8 kHz sampling and 8 bits per sample, means the bandwidth required is 64 kHz.

I have written code that takes 8-bit PCM signals off of a SD card in blocks of 512 bytes at a time, and plays them back using a 125 µs interrupt (corresponding to 8 kHz), to play back voice messages in an embedded system. Running the two tasks (reading the SD card and playing back the samples in the interrupt routine) simultaneously) pretty much maxed out the 8051 I was using.

8 kHz works fine for voice, but is not fast enough for music. CD's use a sampling rate of 44.1 kHz (roughly twice the highest frequency in recorded music of 20 kHz), using 16-bit samples. The rather strange sampling frequency of 44.1 kHz was chosen because it is compatible with both NTSC and PAL video systems.

These digital samples are then used to modulate a sine wave carrier frequency, in one of several ways:

(a) is the digital signal (b) is amplitude modulate (AM) (c) is frequency module (FM) (d) is phase modulation (PM)

It is clear that the end result is no longer a simple sine wave of one frequency.

• Can you please elaborate a little more, especially the last line (I think that holds the core of the answer). Can we please look into the first line of "John D" answer below – Meathead Oct 17 '15 at 15:17
• @Meathead I added additional info to my answer. – tcrosley Oct 18 '15 at 0:40
• Whomever downvoted this, it would be nice to know why. – tcrosley Oct 18 '15 at 18:54