# Sub : Help on FSK demodulation

Started by January 2, 2004
```Hello

I am using binay FSK.  The symbol duration is 'T'. Let the two
signal frequencies be f1 and f2.
Ideally, we need to select f1 and f2, such that  (f1-f2)= k/T;
{k=1,2..}.
Both my frequencies are less that 2kHz.
'T' is in the order of 20 micro secs.

My question:
1.In a practical scenario, do we have to choose f1 and f2, that
precisely satisfies the above equation? If not, what is the tolerance
that can could be feasible?

2. In the above equation ,if 'k' increases, is the performance
guaranteed to improve?

3. In literature, we come across two types of noncoherent
FSKdemodulators
(b)Receiver with bandpass filters and envelop detectors.
Is there any obligations in choosing any one of the two demodulators?
{Note my frequencies are < 2kHz}

4. Is the information given insufficient?

Partha
```
```"Parthasarathy" <parth175@yahoo.co.in> wrote in message
> Hello
>
>       I am using binay FSK.  The symbol duration is 'T'. Let the two
> signal frequencies be f1 and f2.
> Ideally, we need to select f1 and f2, such that  (f1-f2)= k/T;
> {k=1,2..}.
> Both my frequencies are less that 2kHz.
> 'T' is in the order of 20 micro secs.
>
> My question:
> 1.In a practical scenario, do we have to choose f1 and f2, that
> precisely satisfies the above equation? If not, what is the tolerance
> that can could be feasible?
>
> 2. In the above equation ,if 'k' increases, is the performance
> guaranteed to improve?
>
> 3. In literature, we come across two types of noncoherent
> FSKdemodulators
>       (b)Receiver with bandpass filters and envelop detectors.
> Is there any obligations in choosing any one of the two demodulators?
> {Note my frequencies are < 2kHz}
>
> 4. Is the information given insufficient?
>

Partha,

Looks like homework.  So, what are your thoughts?
What is your understanding of the relation of k to f1 and f2?  Where does
the assertion:
"ideally, we need to select f1 and f2, such that  (f1-f2)= k/T; {k=1,2..}."
come from and why?
Where are you having trouble? etc.

Fred

```
```> Partha,
>
> Looks like homework.  So, what are your thoughts?
> What is your understanding of the relation of k to f1 and f2?  Where does
> the assertion:
> "ideally, we need to select f1 and f2, such that  (f1-f2)= k/T; {k=1,2..}."
> come from and why?

Fred,
(forgive me, if I am wrong)
I am surprised,to learn that the assertion is obscure.
One can prove this using the orthogonality constraint viz..
Integral(0 to T)[cos(2*pi*f1*t+phi)*cos(2*pi*f2*t)] dt =0.
A detailed proof of the assertion can be found in "Digital
Communications" by Bernard Sklar.

> Where are you having trouble? etc.
>

In one of the projects, where we are using FSK, is not working as
predicted by us. So I wanted to find out, whether, there was still
something elusive as far as the intricacies of FSK demodulation is
concerned.

Answers to all the above questions are indispensable. Do u need

Partha
```
```parth175@yahoo.co.in (Parthasarathy) wrote in message news:<7f126353.0401042104.30cd9a39@posting.google.com>...
> > Partha,
> >
> > Looks like homework.  So, what are your thoughts?
> > What is your understanding of the relation of k to f1 and f2?  Where does
> > the assertion:
> > "ideally, we need to select f1 and f2, such that  (f1-f2)= k/T; {k=1,2..}."
> > come from and why?
>

With k = 1 this is known as Sunde's FSK.  f1-f2 doesn't have to be
perfect for incoherent demodulation.  For low-speed, cheap, yet decent
performance it's hard to beat incoherent demodulation using, say, an
NJM2211 FSK demod chip.

Coherent demodulation yields only mariginally better BER performance.
Increasing the difference (k) usually improves performance because the
filter overlap decreases.

CC
```
```"Parthasarathy" <parth175@yahoo.co.in> wrote in message
> In one of the projects, where we are using FSK, is not working as
> predicted by us. So I wanted to find out, whether, there was still
> something elusive as far as the intricacies of FSK demodulation is
> concerned.

With T = 20 microseconds and f1 and f2 being 2 kHz or less, you
are rather far from the ideal (f1 - f2) = k/T with k being an integer.
So it is not clear why you are expecting FSK to work as predicted
by the theory of orthogonal signaling.  And, in answer to a question

Ideally the performance of the FSK system does not depend on the
actual value of k as long as it is an integer.  However, if (f1 - f2)T is
a large number, then it does not matter as much if (f1 - f2)T is not
exactly an integer.  The difference in performance between a system
with (f1 - f2)T = 10 and a system with (f1 - f2)T = 10.1 is quite small;
the difference in performance between a system with (f1 - f2)T = 1
and a system with (f1 - f2)T = 1.1 (or (f1-f2)T = 0.04 as in your case)
is more substantial.

```
```"Dilip V. Sarwate" <sarwate@YouEyeYouSee.edu> wrote in message
news:btcdh8\$rnd\$1@news.ks.uiuc.edu...
>
> "Parthasarathy" <parth175@yahoo.co.in> wrote in message
> > In one of the projects, where we are using FSK, is not working as
> > predicted by us. So I wanted to find out, whether, there was still
> > something elusive as far as the intricacies of FSK demodulation is
> > concerned.
>
> With T = 20 microseconds and f1 and f2 being 2 kHz or less, you
> are rather far from the ideal (f1 - f2) = k/T with k being an integer.
> So it is not clear why you are expecting FSK to work as predicted
> by the theory of orthogonal signaling.  And, in answer to a question
>
> Ideally the performance of the FSK system does not depend on the
> actual value of k as long as it is an integer.  However, if (f1 - f2)T is
> a large number, then it does not matter as much if (f1 - f2)T is not
> exactly an integer.  The difference in performance between a system
> with (f1 - f2)T = 10 and a system with (f1 - f2)T = 10.1 is quite small;
> the difference in performance between a system with (f1 - f2)T = 1
> and a system with (f1 - f2)T = 1.1 (or (f1-f2)T = 0.04 as in your case)
> is more substantial.

I can't see why k should be an integer.  I accept that it allows for much
easier maths in most situations, but don't see why it should be 2 as opposed
to 2.5  surely if you have the available clean bandwidth then as large a k
as possible would be preferred? to allow for less dependance on frequency
stability, ie a small frequency jitter in either the transmitter or the
receiver would equal a very small change in the received signal, ie very
much far below the change from the comparatively huge change in frequency
with a larger k.

Can anyone enlighten me? I'm not fully conversant with communication systems
yet :s

```
```>
> With T = 20 microseconds and f1 and f2 being 2 kHz or less, you
> are rather far from the ideal (f1 - f2) = k/T with k being an integer.
> So it is not clear why you are expecting FSK to work as predicted
> by the theory of orthogonal signaling.  And, in answer to a question

Sorry, my 'T' is around 20 millisecond.

> Ideally the performance of the FSK system does not depend on the
> actual value of k as long as it is an integer.  However, if (f1 - f2)T is
> a large number, then it does not matter as much if (f1 - f2)T is not
> exactly an integer.  The difference in performance between a system
> with (f1 - f2)T = 10 and a system with (f1 - f2)T = 10.1 is quite small;
> the difference in performance between a system with (f1 - f2)T = 1
> and a system with (f1 - f2)T = 1.1 (or (f1-f2)T = 0.04 as in your case)
> is more substantial.

3. In literature, we come across two types of noncoherent
FSKdemodulators
(b)Receiver with bandpass filters and envelop detectors.
Is there any obligations in choosing any one of the two demodulators?
{Note my frequencies are < 2kHz}

Partha
```
```"Bevan Weiss" <kaizen__@NOSPAMhotmail.com> wrote in message news:<AHmKb.2936\$9k7.68990@news.xtra.co.nz>...

> I can't see why k should be an integer.  I accept that it allows for much
> easier maths in most situations, but don't see why it should be 2 as opposed
> to 2.5

If k is not an integer, the resulting waveform is not smooth. To see why,
take the bit pattern 010101, with f1 for 0 and f2 for 1. If k is not an
integer the waveform is not smooth, there are abrupt changes. This results
in lot more power residing in the higher frequency ranges (if u take a
fourier transform of the waveform). If this signal were to pass thru
any comm channel, the distortion wud be much higher.

ganesh
```
```> > I can't see why k should be an integer.  I accept that it allows for
much
> > easier maths in most situations, but don't see why it should be 2 as
opposed
> > to 2.5
>
>    If k is not an integer, the resulting waveform is not smooth. To see
why,
> take the bit pattern 010101, with f1 for 0 and f2 for 1. If k is not an
> integer the waveform is not smooth, there are abrupt changes. This results
> in lot more power residing in the higher frequency ranges (if u take a
> fourier transform of the waveform). If this signal were to pass thru
> any comm channel, the distortion wud be much higher.

I thought that k was only to do with the frequency deviation, and that
whether or not the change was smooth was based more on the method used for
modulation and whether it was phase coherant or otherwise.
ie using a Direct Digital Synthesiser (DDS) with phase accumulator as the
frequency modulator would produce a phase coherant FSK signal, no abrupt
amplitude changes would be present, however an abrupt frequency change would
obviously be present at the point the frequency word of the DDS is loaded.

In the above example it doesn't matter what the new frequency word is loaded
to, there will still be no abrupt amplitude change, the amplitude will
simply change at the newly loaded frequency.

```
```ganesh wrote:

> "Bevan Weiss" <kaizen__@NOSPAMhotmail.com> wrote in message news:<AHmKb.2936\$9k7.68990@news.xtra.co.nz>...
>
>
>>I can't see why k should be an integer.  I accept that it allows for much
>>easier maths in most situations, but don't see why it should be 2 as opposed
>>to 2.5
>
>
>    If k is not an integer, the resulting waveform is not smooth. To see why,
> take the bit pattern 010101, with f1 for 0 and f2 for 1. If k is not an
> integer the waveform is not smooth, there are abrupt changes. This results
> in lot more power residing in the higher frequency ranges (if u take a
> fourier transform of the waveform). If this signal were to pass thru
> any comm channel, the distortion wud be much higher.
>
> ganesh

Surely there aren't two oscillators running continuously, with the one
to be transmitted selected by the bit to be transmitted. A simple way to
describe a better way is to ask you to imagine that both frequencies are
created by dividing a common clock, and that the bit (1 or 0) selects
the divide ratio. Then whether k is an integer or not, the waveform is
continuous and its derivative is not.

Jerry
--
Engineering is the art of making what you want from things you can get.
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```