Follow Ups:Category: General Interest
From: stephanet (Stephane Tessier)
To: klb (kate bullock)
Date Posted: June 03, 2005 at 00:20:51
Subject: Re: Music technology desperate plea!
Reference: Music technology desperate plea!
Hi Kate,First, let me start by saying that Yes!, there is such a thing as the "sum and difference frequencies" ...
Modulation not only generates a sum but also a difference ; and they CAN serve a practical purpose ...
(all modern telecom (modulation) is based on that !).
Since you mentionned that your fellow lecturer "cannot see HOW a SUM FREQUENCY can exist", I wanted to give
you the "mathematical proof" (which is really a simple trigonometrical equation...!) explainig what's going on ...
I started looking around and into my old university "introductory" telecommunications books, but haven't had the time to
find what I wanted (as simple as possible !) ... and since time (and your session !) marches on, here's the first part of
my reply (!). Mind you, you could also look in basic telecom books to find the explanation of modulation ...
The simplest example being a single tone (sine) being modulated by a carrier (an other sine of higher
frequency) ; the result is the sum and difference around the "center frequency", being the carrier.
By the way, modulation, I think, is in fact in a convolution between the 2 signals, but I have to double
check, so I don't want to mislead you !This enables us to "up-convert" a signal (ie. take an FM signal and broadcast it at 80-110 MHz, for
example) ; you simply filter out what you don't need (ie. the "difference") ...This is also how (with the "difference") you "downconvert" from MHz to "baseband" (ie. around DC or 0 V).
That way, you recuperate the modulated (up-converted) signal.This also helps to understand the Samplig Theory that says that Sampling Frequency must be 2x
the highest frequency component ; because if you don't respect this, the "difference" will bring ("fold")
back some part of the signal on top of your source (called "aliasing") ; so, for example, a 20kHz
signal sampled at 44,1 kHz avoids any aliasing ... (44,1k - 20 k is > than 20 kHz).Analog Devices, a maker of ADCs, DACs, and many other circuits (www.analog.com) has many
tutorials (and good intro papers) on sampling, ADCs, etc.The "difference" also allows some neet "tricks" such as "undersampling", which also acts as
"down converting", if you must follow some important rules ... (which I'll skip here ...) ;-)But my basic question with your quote is "So is sampling a form of modulation ?"
When the author says "...the audio signal modulates the amplitude of the individual samples", I see where
he is going with this, although I would not have thought of it necessarily that way (ie. the individual samples
ARE the amplitude of the audio signal, taken at the sampling period... but if you would not have an audio
signal, the samples would all be of the same amplitude, so in that regard, you could call this modulation !) ...
but then again, regardless, that's why we ALWAYS filter the input signal going to an ADC, just to be sure
no input signal has a frequency component higher than half the sampling frequency (to prevent aliasing).
Hope this answers part of your questions !Stéphane
(M.Eng., by the way ...)