Filtering In Frequency Domain v Time Domain

[Bret Cahill]

A low pass time domain filter has a roll off. A low pass Fourier
transform frequency filter can eliminate all the frequencies above a
cutoff frequency 100% without attenuating any of the lower frequencies
at all.

If the goal is to determine a phase angle between two signals, is
there any advantage in low pass filtering in the time domain before
frequency filtering in the frequency domain?


Bret Cahill

 

[John Larkin]

On Sat, 5 Mar 2011 09:49:41 -0800 (PST), Bret Cahill
<BretCahill@peoplepc.com> wrote:

A low pass time domain filter has a roll off. A low pass Fourier
transform frequency filter can eliminate all the frequencies above a
cutoff frequency 100% without attenuating any of the lower frequencies
at all.

If the goal is to determine a phase angle between two signals, is
there any advantage in low pass filtering in the time domain before
frequency filtering in the frequency domain?


Bret Cahill

A filter is a filter. Which domain (and there are more than two) you
prefer to evaluate it in is your choice.

John

 

[Fred Marshall]

On 3/5/2011 9:49 AM, Bret Cahill wrote:

A low pass time domain filter has a roll off. A low pass Fourier
transform frequency filter can eliminate all the frequencies above a
cutoff frequency 100% without attenuating any of the lower frequencies
at all.

If the goal is to determine a phase angle between two signals, is
there any advantage in low pass filtering in the time domain before
frequency filtering in the frequency domain?


Bret Cahill

Bret,

Well...........
From an operational point of view, of course "filter can eliminate all
the frequencies above a cutoff frequency 100%" by multiplying (perhaps
actually replacing) with zeros.

But, you have to ask yourself what this does in the time domain.

Any flat-zero segment in one domain will create an "infinite" sequence
in the transform. This is what happens when we zero-pad a time sequence
in order to have higher frequency resolution or to implement circular
convolution. This doesn't mean, necessarily, that doing something like
this is "bad". You just have to know a bit about what you're doing.

One of my favorite applications of doing just that is this:
- The objective is temporal interpolation of a sequence - which is
basically an increase of the sample rate with some filtering involved.
- One simple way is to intersperse a bunch of regular, zero-valued
samples in time and then pass the new padded sequence through a lowpass
filter in order to get nonzero values where those added zeros were place.
- Another way is to rather "assume" the new sample rate and plot the new
frequency content. This will look like the original spectrum but
repeated as many times as the interpolation factor "I". THEN, we
lowpass filter (by multiplying in frequency) to remove all of the energy
bumps at fsOLD, 2fsOLD .... up to but not including the fsNEW.
That suggests the same process you describe.

The real trick here is to not create any "sharp edges" when multiplying
by a contiguous sequence of zeros. If you do, there will be stuff
spread out in time just the transform dual of spectral spreading when we
use a rectangular window in time.

So, one approach in this interpolation case is to do this.
- Assume we know little or nothing of the signal spectrum because, after
all, we're building an interpolation "system". So, if we just multiply
by a sequence of zeros, we have no idea what anomalies we're creating.
- Do the interpolation in stages. In fact, the first stage would be to
repeat the spectral sequence to only 2fsOLD and then lowpass filter the
data with an actual LPF - so that the spectral energy is fairly well
limited to 1/4 the fsNEW1 or 1/2 fsOLD.
Only now can you know that the spectral data at fsNEW/4 to 3fsNEW/4 will
be "nearly zero".
- Now you can pad the spectral sequence with zeros symmetrically about
fs/2 - effectively increasing the value of fs or N ... whichever way you
like to think of it. This padding operation is exactly like what we do
in the time domain when we want higher N but have limited data - for
whatever reason. NOTE: This padding is exactly the same as looking at
the repeated spectrum up to I*fsOLD and then multiplying that sequence
with zeros from fsOLD/2 to fsNEW-fsOLD/2.

In effect, the edges of the zero sequence will fall on frequencies where
there is little energy (due to the prefiltering). And so, there will be
assuredly little temporal spreading caused by doing this.

So this is an example of doing what you want but taking the precaution
of pre-filtering before multplying by a sequence of zeros. It's the same
sort of thing as doing windowing in time to reduce the effects of
rectangular windowing - done in advance of zero padding in time. But,
in this case our "window" in frequency has the shape of an actual
lowpass filter - which is a "rectangular window with smoothed edges and
long (nonzero) stopband tails"

So, that's a long-winded caveat. Now on to your question:

First of all, "time domain" filtering and "frequency domain filtering"
are two different animals. You can't do temporal IIR filtering in
frequency unless it's a special case made to look like a FIR. So that's
a limitation of sorts. And, you are forcing yourself to do block or
finite sequence oriented processing. If your objective is to deal with
streaming data then maybe time domain processing is better - or you will
have to deal with how to combine the blocks.

The advantage of frequency domain filtering is that it can save a LOT of
compute time if the (FIR) filter has any appreciable length.

As long as you pay attention to the sequence lengths and what that means
in your system then I see no reason to do time domain filtering *before*
frequency domain filtering. Also remember that frequency domain
filtering is equivalent to circular convolution in time and the temporal
sequences have to account for that (be zero padded) to avoid overlap in
time.

Fred

 

[Fred Marshall]

On 3/5/2011 11:22 AM, Fred Marshall wrote:

This padding is exactly the same as looking at the repeated spectrum up
to I*fsOLD and then multiplying that sequence with zeros from fsOLD/2 to
fsNEW-fsOLD/2.

Or, one might chose to have the zeros run from fsOLD to fsNEW-fsOLD so
that the stopband of the lowpass filter are included, rather than
forcing those values to zero as well.

One might also imagine that avoiding sharp edges caused by multiplying
by a sequence of zeros would be helped if the value and perhaps the
first derivative of the original lowpassed sequence were to be zero at
the edges of the "split point" .. the fs/2 point at this stage. So, if
the requirements are particularly stiff then that might be a
consideration. Again, similar to tapered time domain windowing ideas.

Fred

 

[Bret Cahill]

This padding is exactly the same as looking at the repeated spectrum up
to I*fsOLD and then multiplying that sequence with zeros from fsOLD/2 to
fsNEW-fsOLD/2.

Or, one might chose to have the zeros run from fsOLD to fsNEW-fsOLD so
that the stopband of the lowpass filter are included, rather than
forcing those values to zero as well.

One might also imagine that avoiding sharp edges caused by multiplying
by a sequence of zeros would be helped if the value and perhaps the
first derivative of the original lowpassed sequence were to be zero at
the edges of the "split point" .. the fs/2 point at this stage.  So, if
the requirements are particularly stiff then that might be a
consideration.  Again, similar to tapered time domain windowing ideas.

What is interesting is how much time you can spend playing around with
these transforms.

Does a 10 degree lag phase angle in the reference introduce amplitude
errors in match filtering?

You can find out on Excel.


Bret Cahill

 

[Bret Cahill]

This padding is exactly the same as looking at the repeated spectrum up
to I*fsOLD and then multiplying that sequence with zeros from fsOLD/2 to
fsNEW-fsOLD/2.

Or, one might chose to have the zeros run from fsOLD to fsNEW-fsOLD so
that the stopband of the lowpass filter are included, rather than
forcing those values to zero as well.

One might also imagine that avoiding sharp edges caused by multiplying
by a sequence of zeros would be helped if the value and perhaps the
first derivative of the original lowpassed sequence were to be zero at
the edges of the "split point" .. the fs/2 point at this stage.  So, if
the requirements are particularly stiff then that might be a
consideration.  Again, similar to tapered time domain windowing ideas..

What is interesting is how much time you can spend playing around with
these transforms.

Does a 10 degree lag phase angle in the reference introduce amplitude
errors in match filtering?

You can find out on Excel.

Unlike phase sensitive filtering where the phase must be known to get
the amplitude the phase of the reference must be irrelevant with match
filtering.

I'll check it out to make sure.


Bret Cahill

 

[Fred Marshall]

On 3/5/2011 9:49 AM, Bret Cahill wrote:

If the goal is to determine a phase angle between two signals,

Bret,

What are you trying to do?

If there are 2 sinusoids, at different frequencies, then there is no
"phase angle" between them - although there may be a delay between them.

If there are 2 sinusoids at the same frequency then, in the context of a
single DFT, they will add and appear to be one sinusoid. But, maybe the
system is different.

If they happen at different times then there are other system
considerations - as in "where is the time reference?"

Fred

 

[Fred Marshall]

On 3/6/2011 3:37 PM, Bret Cahill wrote:

Bret,

What are you trying to do?
Match filter with an out of phase reference.

Bret,

Well, I don't know what it means to have an "out of phase reference" in
the context of a matched filter.

The classical matched filter uses a time-reversed complex conjugate of
the known signal to convolve with what is received in order to detect
the presence of the waveform. There is no temporal reference (thus no
phase reference) because it's going to be a convolution - that is, the
two signals are multiplied together and integrated for *all* reasonable
time shifts - thus for all reasonable phases. That's one of the
fundamental underpinnings of the thing - to get phase alignment at one
of the shifts.

Of course, temporal convolution *is* a filtering operation.

If you want to do this in the frequency domain then you would take the
Discrete Fourier Transform of the temporal filter (the time reversed
complex conjugate of the desired signal to detect) suitably zero-padded
to match the required sequence length.

Then, grabbing likely overlapping sequences of suitable length coming
out of the "receiver", you would DFT them and multiply with the saved
FFT of the filter.

Then, you might keep multiple results and search over some history for
peaks in time and frequency - a 2-D search.

Fred

 

[Bret Cahill]

If the goal is to determine a phase angle between two signals,

Bret,

What are you trying to do?

Match filter with an out of phase reference. For awhile I thought it
wouldn't matter and in fact the absolute value in the frequency domain
is the same for two signals that are identical except for a phase
angle..

But after trying it out on Excel it seems the phase angle must still
be calculated from the real and imaginary components, the difference
in the angles between the signals.

The noise will probably require some kind of average of the phase
angles.

An iterative technique may be necessary. First you get an estimate of
the phase angle from the noisy signal and reference then you phase
adjust the reference then you match filter then you recheck to see if
the phase angle is converging.

If there are 2 sinusoids, at different frequencies, then there is no
"phase angle" between them - although there may be a delay between them.

Assume just one fundamental frequency.

If there are 2 sinusoids at the same frequency then, in the context of a
single DFT, they will add and appear to be one sinusoid.  But, maybe the
system is different.

If they happen at different times then there are other system
considerations - as in "where is the time reference?"

The SNR may be as high as 20 so hopefully one cycle will be enough.
In that case only 90% of the noise needs to be eliminated.


Bret Cahill

 

[Jamie]

Fred Marshall wrote:

On 3/6/2011 3:37 PM, Bret Cahill wrote:

Bret,

What are you trying to do?

Match filter with an out of phase reference.


Bret,

Well, I don't know what it means to have an "out of phase reference" in
the context of a matched filter.

The classical matched filter uses a time-reversed complex conjugate of
the known signal to convolve with what is received in order to detect
the presence of the waveform. There is no temporal reference (thus no
phase reference) because it's going to be a convolution - that is, the
two signals are multiplied together and integrated for *all* reasonable
time shifts - thus for all reasonable phases. That's one of the
fundamental underpinnings of the thing - to get phase alignment at one
of the shifts.

Of course, temporal convolution *is* a filtering operation.

If you want to do this in the frequency domain then you would take the
Discrete Fourier Transform of the temporal filter (the time reversed
complex conjugate of the desired signal to detect) suitably zero-padded
to match the required sequence length.

Then, grabbing likely overlapping sequences of suitable length coming
out of the "receiver", you would DFT them and multiply with the saved
FFT of the filter.

Then, you might keep multiple results and search over some history for
peaks in time and frequency - a 2-D search.

Fred



Finally, Some one knows what they're talking about!

Good show mate!

Jamie

 

[Bret Cahill]

 What are you trying to do?
Match filter with an out of phase reference.

Bret,

Well, I don't know what it means to have an "out of phase reference" in
the context of a matched filter.

The classical matched filter uses a time-reversed complex conjugate of
the known signal to convolve with what is received in order to detect
the presence of the waveform.  There is no temporal reference (thus no
phase reference) because it's going to be a convolution - that is, the
two signals are multiplied together and integrated for *all* reasonable
time shifts - thus for all reasonable phases.  That's one of the
fundamental underpinnings of the thing - to get phase alignment at one
of the shifts.

So the filter gives the phase angle or at least the time between the
reference and the return of the now noisy signal?

This would make sense for radar.

Of course, temporal convolution *is* a filtering operation.

If you want to do this in the frequency domain then you would take the
Discrete Fourier Transform of the temporal filter (the time reversed
complex conjugate of the desired signal to detect) suitably zero-padded
to match the required sequence length.

So if the noisy signal was top down in time on Excel then the
reference should be bottom up?

Then take the transforms of both and then take the dot product?

Then, grabbing likely overlapping sequences of suitable length coming
out of the "receiver", you would DFT them and multiply with the saved
FFT of the filter.

Then, you might keep multiple results and search over some history for
peaks in time and frequency - a 2-D search.

What about the inverse transform?


Bret Cahill

 

[Bret Cahill]

 What are you trying to do?
Match filter with an out of phase reference.

Bret,

Well, I don't know what it means to have an "out of phase reference" in
the context of a matched filter.

The classical matched filter uses a time-reversed complex conjugate of
the known signal to convolve with what is received in order to detect
the presence of the waveform.  There is no temporal reference (thus no
phase reference) because it's going to be a convolution - that is, the
two signals are multiplied together and integrated for *all* reasonable
time shifts - thus for all reasonable phases.  That's one of the
fundamental underpinnings of the thing - to get phase alignment at one
of the shifts.

So the filter gives the phase angle or at least the time between the
reference and the return of the now noisy signal?

This would make sense for radar.

Of course, temporal convolution *is* a filtering operation.
If you want to do this in the frequency domain then you would take the
Discrete Fourier Transform of the temporal filter (the time reversed
complex conjugate of the desired signal to detect) suitably zero-padded
to match the required sequence length.

So if the noisy signal was top down in time on Excel then the
reference should be bottom up?

All that does is reverse the sign of one of the inverse transform
signals. The amplitude drops non linearly in the signal that is a
little out of phase.

Then take the transforms of both and then take the dot product?

Then, grabbing likely overlapping sequences of suitable length coming
out of the "receiver", you would DFT them and multiply with the saved
FFT of the filter.
Then, you might keep multiple results and search over some history for
peaks in time and frequency - a 2-D search.

That would be easy in Excel.

What about the inverse transform?

Bret Cahill

 

[Fred Marshall]

On 3/6/2011 6:33 PM, Bret Cahill wrote:

What are you trying to do?
Match filter with an out of phase reference.

Bret,

Well, I don't know what it means to have an "out of phase reference" in
the context of a matched filter.

The classical matched filter uses a time-reversed complex conjugate of
the known signal to convolve with what is received in order to detect
the presence of the waveform. There is no temporal reference (thus no
phase reference) because it's going to be a convolution - that is, the
two signals are multiplied together and integrated for *all* reasonable
time shifts - thus for all reasonable phases. That's one of the
fundamental underpinnings of the thing - to get phase alignment at one
of the shifts.

So the filter gives the phase angle or at least the time between the
reference and the return of the now noisy signal?

This would make sense for radar.

Of course, temporal convolution *is* a filtering operation.
If you want to do this in the frequency domain then you would take the
Discrete Fourier Transform of the temporal filter (the time reversed
complex conjugate of the desired signal to detect) suitably zero-padded
to match the required sequence length.

So if the noisy signal was top down in time on Excel then the
reference should be bottom up?

All that does is reverse the sign of one of the inverse transform
signals. The amplitude drops non linearly in the signal that is a
little out of phase.

Then take the transforms of both and then take the dot product?

Then, grabbing likely overlapping sequences of suitable length coming
out of the "receiver", you would DFT them and multiply with the saved
FFT of the filter.
Then, you might keep multiple results and search over some history for
peaks in time and frequency - a 2-D search.

That would be easy in Excel.

What about the inverse transform?


Bret Cahill

I don't know what Excel has to do with it...... Lots of things can be
done with Excel - indeed sometimes to good advantage.

You can surely compute the inverse transform to get a temporal view of
the result... You may want to do multiple sequences overlapped to get
the best results to look at.

I don't think it best to consider the reference as having a time
reference - other than it begins and ends. The time reference is likely
best determined by when you snagged the received signal sequence - the
absolute time of the signal sequence. Then, the output of the matched
filter would be referenced to that time frame.

Fred

 

[HardySpicer]

On Mar 6, 6:49 am, Bret Cahill <BretCah...@peoplepc.com> wrote:

A low pass time domain filter has a roll off.  A low pass Fourier
transform frequency filter can eliminate all the frequencies above a
cutoff frequency 100% without attenuating any of the lower frequencies
at all.

If the goal is to determine a phase angle between two signals, is
there any advantage in low pass filtering in the time domain before
frequency filtering in the frequency domain?

Bret Cahill

Not true since each frequency bin is finite = N/fs. You cannot have a
brick wall filter even in teh freq domain.
You can however make an approximation by using the uncausal part of a
filter and introducing a time-delay.


Hardy

 

[Rune Allnor]

On Mar 5, 6:49 pm, Bret Cahill <BretCah...@peoplepc.com> wrote:

A low pass time domain filter has a roll off.  A low pass Fourier
transform frequency filter can eliminate all the frequencies above a
cutoff frequency 100% without attenuating any of the lower frequencies
at all.

Wrong. At least under the usual assumptions about context.

The time domain (TD) filter can work on a signal of arbitrary
length, so it should be analyzed in Frequency Domain using
the (infinite length) Discrete Time Fourier Transform (DTFT).
The DTFT produces a continuous spectrum.

If you *choose* to use the DFT and do the filtering in Frequency
Domain (FD), you also *choose* to

- Work with a finite amount of data
- Work with a finite number of spectral samples

So you are comparing apples and oranges.

If you work through the maths, you will find that the 'true'
spectrum of the finite number of samples in fcat is
continuous, and that it ripples between the normalized
frequencies w_k = 2*pi*kn/N.

You will find the analysis in any half decent textbook on DSP.
Look for the term 'spectral sampling'.

Rune

 

[Bret Cahill]

A low pass time domain filter has a roll off.  A low pass Fourier
transform frequency filter can eliminate all the frequencies above a
cutoff frequency 100% without attenuating any of the lower frequencies
at all.

Wrong. At least under the usual assumptions about context.

The time domain (TD) filter can work on a signal of arbitrary
length, so it should be analyzed in Frequency Domain using
the (infinite length) Discrete Time Fourier Transform (DTFT).
The DTFT produces a continuous spectrum.

If you *choose* to use the DFT and do the filtering in Frequency
Domain (FD), you also *choose* to

- Work with a finite amount of data
- Work with a finite number of spectral samples

It's over a finite period of time, a time period that might be known
in advance, so the number of samples and data points are finite.

If that's the case and if FFTs are possible then it may be a waste of
time to pre filter in the time domain.


Bret Cahill

So you are comparing apples and oranges.

If you work through the maths, you will find that the 'true'
spectrum of the finite number of samples in fcat is
continuous, and that it ripples between the normalized
frequencies w_k = 2*pi*kn/N.

You will find the analysis in any half decent textbook on DSP.
Look for the term 'spectral sampling'.

 

[Bret Cahill]

What are you trying to do?
Match filter with an out of phase reference.

Bret,

Well, I don't know what it means to have an "out of phase reference" in
the context of a matched filter.

The classical matched filter uses a time-reversed complex conjugate of
the known signal to convolve with what is received in order to detect
the presence of the waveform. There is no temporal reference (thus no
phase reference) because it's going to be a convolution - that is, the
two signals are multiplied together and integrated for *all* reasonable
time shifts - thus for all reasonable phases. That's one of the
fundamental underpinnings of the thing - to get phase alignment at one
of the shifts.

So the filter gives the phase angle or at least the time between the
reference and the return of the now noisy signal?

This would make sense for radar.

Of course, temporal convolution *is* a filtering operation.
If you want to do this in the frequency domain then you would take the
Discrete Fourier Transform of the temporal filter (the time reversed
complex conjugate of the desired signal to detect) suitably zero-padded
to match the required sequence length.

So if the noisy signal was top down in time on Excel then the
reference should be bottom up?

All that does is reverse the sign of one of the inverse transform
signals. The amplitude drops non linearly in the signal that is a
little out of phase.

Then take the transforms of both and then take the dot product?

Then, grabbing likely overlapping sequences of suitable length coming
out of the "receiver", you would DFT them and multiply with the saved
FFT of the filter.
Then, you might keep multiple results and search over some history for
peaks in time and frequency - a 2-D search.

That would be easy in Excel.

What about the inverse transform?

I don't know what Excel has to do with it...... Lots of things can be
done with Excel - indeed sometimes to good advantage.

I was using it to get an idea of what kind reduction of noise is
possible with reference filtering in the time domain [phase sensitive
rectification (PSR)] v reference filtering in the frequency domain.

A PSR simulator on Excel cycles different noise -- use the RAND() for
different "noise" phase angles and frequencies -- at several hertz so
it's easy to imagine what a histogram would look like in just a minute
or so. What I found was dozens or hundreds of cycles might be
necessary to get the noise down to an acceptable level -- not fast
enough.

Even worse, PSR + an unknown phase angle could create bigger errors in
the magnitude than leaving the unfiltered signal alone.

Frequency domain filtering should solve both problems. A match filter
can determine the time period between the reference and the signal,
what I've been calling a phase angle.

Once that is known and corrected another FFT based reference filter
can reduce the noise in one or two cycles.

Excel's FFT is too unwieldy to quickly try dozens of different noise
levels but from the few I've tried it seems to reduce noise much
faster than PSR.

The CORREL function may be the fast way to go. It isn't giving the
same results as the FFT reference filter, however.

You can surely compute the inverse transform to get a temporal view of
the result... You may want to do multiple sequences overlapped to get
the best results to look at.

I may have done that. The IMABS of the inverse transform maxes out
when the reference and the signal are in the same time period.

That's how I may wind up determing "phase angle."

I don't think it best to consider the reference as having a time
reference - other than it begins and ends. The time reference is likely
best determined by when you snagged the received signal sequence - the
absolute time of the signal sequence. Then, the output of the matched
filter would be referenced to that time frame.

Isn't that how radar works? They keep taking FFTs and dot products
until the correlation spikes?

That seems like it would be nearly impossible without computers.


Bret Cahill

 

[Jason]

On Mar 6, 6:37 pm, Bret Cahill <BretCah...@peoplepc.com> wrote:

If the goal is to determine a phase angle between two signals,

Bret,

What are you trying to do?

Match filter with an out of phase reference.  For awhile I thought it
wouldn't matter and in fact the absolute value in the frequency domain
is the same for two signals that are identical except for a phase
angle..

But after trying it out on Excel it seems the phase angle must still
be calculated from the real and imaginary components, the difference
in the angles between the signals.

The noise will probably require some kind of average of the phase
angles.

An iterative technique may be necessary.  First you get an estimate of
the phase angle from the noisy signal and reference then you phase
adjust the reference then you match filter then you recheck to see if
the phase angle is converging.

If you're seeing the magnitude of the matched filter output change
based on a constant phase shift between the signal you're processing
and the reference, then you're doing something wrong. Convolution is a
linear operation. A constant phase shift on the template signal is
equivalent to multiplying the reference by exp(j*theta), a constant.
Therefore, if;

y[n] = conv(x[n], r[n])

Then:

exp(j*theta) * y[n] = conv(x[n], exp(j*theta) * r[n])

The magnitudes of y[n] and exp(j*theta) * y[n] are equal for all n (a
phase shift does not affect the magnitude of a complex number). So, if
you're observing that this is not the case, something is wrong with
your simulation.

Note that you will see attenuation if there is a *frequency* offset
between the signal and the reference; this is a well-known phenomenon
for communication receivers that use "long" correlators, such as
direct-sequence spread-spectrum systems. If the frequency offset
between the transmitter and receiver is a significant fraction of the
inverse of the reference's length in time, then you will start to
observe attenuation in the matched filter's output. This problem is
often addressed by using a bank of parallel correlators, spaced in
frequency, such that the signal of interest will be near the center of
one of the filters in the bank.

Jason

 

[Fred Marshall]

On 3/7/2011 5:05 AM, Bret Cahill wrote:
Fred said:

I don't know what Excel has to do with it...... Lots of things can be
done with Excel - indeed sometimes to good advantage.

I was using it to get an idea of what kind reduction of noise is
possible with reference filtering in the time domain [phase sensitive
rectification (PSR)] v reference filtering in the frequency domain.

How in the world did PSR get into this thread? I thought we were
talking about matched filters and whether there were any differences
between time domain implementation and frequency domain implementation.

OK, I found a description:
http://techdoc.kvindesland.no/radio/ymse1/20061216153544735.pdf

Geez. This looks a lot like a phase-locked loop (PLL) receiver of the
sort that's used, for example, in deep space communications. In those
applications, the data bandwidth is very low so that the receiver
bandwidth can be very low (thus improving SNR at the output).

Matched filters are most often used in pulse systems like radar and
sonar; although they tend to work better in radar. There's a ton of
literature on the subject.

PLL receivers tend to work on continuous signals. There is generally a
"lock" period to get the phase right and the receiver can also "lose lock".

The difference seems rather stark to me. One is for short, known
signals (known modulation if you will) and the other is for long, known
frequency, signals of unknown modulation. That may not be the best
description but it's close enough for now.

So, it appears you're pondering a *system design* question in addition
to your original question about matched filtering.


Fred

 

[Bret Cahill]

I don't know what Excel has to do with it......  Lots of things can be
 done with Excel - indeed sometimes to good advantage.

I was using it to get an idea of what kind reduction of noise is
possible with reference filtering in the time domain [phase sensitive
rectification (PSR)] v reference filtering in the frequency domain.

How in the world did PSR get into this thread?  

It was a stepping stone to using Excel for match filtering.

I thought we were
talking about matched filters and whether there were any differences
between time domain implementation and frequency domain implementation.

It's no longer of interest so feel free to ignore it.

OK, I found a description:http://techdoc.kvindesland.no/radio/ymse1/20061216153544735.pdf

Geez.  This looks a lot like a phase-locked loop (PLL) receiver of the
sort that's used, for example, in deep space communications.

The time multiplication step is the heart of PSR and lock in.

 In those
applications, the data bandwidth is very low so that the receiver
bandwidth can be very low (thus improving SNR at the output).

Matched filters are most often used in pulse systems like radar and
sonar; although they tend to work better in radar.  There's a ton of
literature on the subject.

PLL receivers tend to work on continuous signals.  There is generally a
"lock" period to get the phase right and the receiver can also "lose lock".

The phase may not always be known in which case it won't work for
precision amplitude measurements. It may very well be worse than the
noise.

The difference seems rather stark to me.  

It would be surprising if the two types of reference or "adaptive"
filtering weren't compared before now.

One is for short, known
signals (known modulation if you will) and the other is for long, known
frequency, signals of unknown modulation.  That may not be the best
description but it's close enough for now.

A lot more cycles [time] should be necessary with PSR to get the same
reduction of noise as FFT reference filtering.

With a FFT you know everything possible about the signal and with
reference filtering in the frequency domain, all that information is
utilized. That may be why they call the match filter the "optimal"
filter. It may be the absolute best you can do.

With PSR you only know or need to know the phase angle. Many lock in
systems simply multiply with a square wave. All the information in
the wave form is tossed with PSR.

So, it appears you're pondering a *system design* question in addition
to your original question about matched filtering.

The PSR is only of interest now if it was possible to somehow glean a
phase angle, maybe by comparing the reference * signal with the
reference * reference or the signal * signal. If that's not possible
then the phase angle will have to be determined by some kind of
convolution / match filtering.

Once phi is determined than the reference can be corrected in either
domain.


Bret Cahill