Matlab FFT Reconstruction from Physiologic Frequency-Varying Signal

DSP Experts,

I am analyzing a physiologic signal that has a varying fundamental
frequency. To create a more accurate reconstruction from the FFT, I wish to
include the bins immediately and symmetrically on either side of the
fundamental bins. I refer to this as the "distribution method."

I am confident I have been able to do a reconstruction using the
fundamental bins (a standard reconstruction). I also performed a
reconstruction for the distribution method. The mean squared error
(comparing both reconstructions to data in the time domain) for the
distribution method is lower than for the standard indicating the
distribution method is potentially more accurate. However, the distribution
reconstruction features an increase in difference between the maximums and
minimums of each subsequent cycle.

I have vigorously checked my Matlab code for potential errors in selecting
components and performing operations; however, I have not been able to
identify any. Hence, I am writing to request assistance in determining if
this widening effect is an undesirable characteristic of the distribution
method or whether there truly is an error in my code. I recognize that an
FFT reconstruction should feature the exact same waveform for every cycle.


I do not have a strong background in digital processing or signal analysis;
however, I am eagerly learning on the fly.

Thanks for any help you might be able to provide.

-BMEngineer

P.S. Plots and segments of my Matlab code are available to email as
necessary.

	 

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On Mon, 30 Mar 2015 16:53:34 -0500, "BMEngineer" <104668@dsprelated>
wrote:

>DSP Experts,
>
>I am analyzing a physiologic signal that has a varying fundamental
>frequency. To create a more accurate reconstruction from the FFT, I wish to
>include the bins immediately and symmetrically on either side of the
>fundamental bins. I refer to this as the "distribution method."
>
>I am confident I have been able to do a reconstruction using the
>fundamental bins (a standard reconstruction). I also performed a
>reconstruction for the distribution method. The mean squared error
>(comparing both reconstructions to data in the time domain) for the
>distribution method is lower than for the standard indicating the
>distribution method is potentially more accurate. However, the distribution
>reconstruction features an increase in difference between the maximums and
>minimums of each subsequent cycle.
>
>I have vigorously checked my Matlab code for potential errors in selecting
>components and performing operations; however, I have not been able to
>identify any. Hence, I am writing to request assistance in determining if
>this widening effect is an undesirable characteristic of the distribution
>method or whether there truly is an error in my code. I recognize that an
>FFT reconstruction should feature the exact same waveform for every cycle.
>
>
>I do not have a strong background in digital processing or signal analysis;
>however, I am eagerly learning on the fly.
>
>Thanks for any help you might be able to provide.
>
>-BMEngineer
>
>P.S. Plots and segments of my Matlab code are available to email as
>necessary.

Any FFT bins other than those that you are using for the
reconstruction that have non-zero magnitude would otherwise influence
the reconstructed signal.   Harmonics, especially, even with
relatively low magnitudes, can have a significant influence on the
amplitude of an output sine wave. 

When the fundamental is not centered on a bin it's DFT magnitude will
naturally be lower than it would be if centered.   The same is true
for harmonics, so even if harmonic energy is not readily apparent in
the DFT output there could easily be energy there that will affect the
amplitude of your resconstructed signal.

The bottom line is that you're using only a small part of the DFT
information to reconstruct your output signal, so the loss of the rest
of the information is reasonably expected to have an affect on your
signal.

Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

---
This email has been checked for viruses by Avast antivirus software.
http://www.avast.com

>On Mon, 30 Mar 2015 16:53:34 -0500, "BMEngineer" <104668@dsprelated>
>wrote:
>
>>DSP Experts,
>>
>>I am analyzing a physiologic signal that has a varying fundamental
>>frequency. To create a more accurate reconstruction from the FFT, I wish
to
>>include the bins immediately and symmetrically on either side of the
>>fundamental bins. I refer to this as the "distribution method."
>>
>>I am confident I have been able to do a reconstruction using the
>>fundamental bins (a standard reconstruction). I also performed a
>>reconstruction for the distribution method. The mean squared error
>>(comparing both reconstructions to data in the time domain) for the
>>distribution method is lower than for the standard indicating the
>>distribution method is potentially more accurate. However, the
distribution
>>reconstruction features an increase in difference between the maximums
and
>>minimums of each subsequent cycle.
>>
>>I have vigorously checked my Matlab code for potential errors in
selecting
>>components and performing operations; however, I have not been able to
>>identify any. Hence, I am writing to request assistance in determining
if
>>this widening effect is an undesirable characteristic of the
distribution
>>method or whether there truly is an error in my code. I recognize that
an
>>FFT reconstruction should feature the exact same waveform for every
cycle.
>>
>>
>>I do not have a strong background in digital processing or signal
analysis;
>>however, I am eagerly learning on the fly.
>>
>>Thanks for any help you might be able to provide.
>>
>>-BMEngineer
>>
>>P.S. Plots and segments of my Matlab code are available to email as
>>necessary.
>
>Any FFT bins other than those that you are using for the
>reconstruction that have non-zero magnitude would otherwise influence
>the reconstructed signal.   Harmonics, especially, even with
>relatively low magnitudes, can have a significant influence on the
>amplitude of an output sine wave. 
>
>When the fundamental is not centered on a bin it's DFT magnitude will
>naturally be lower than it would be if centered.   The same is true
>for harmonics, so even if harmonic energy is not readily apparent in
>the DFT output there could easily be energy there that will affect the
>amplitude of your resconstructed signal.
>
>The bottom line is that you're using only a small part of the DFT
>information to reconstruct your output signal, so the loss of the rest
>of the information is reasonably expected to have an affect on your
>signal.
>
>Eric Jacobsen
>Anchor Hill Communications
>http://www.anchorhill.com
>
>---
>This email has been checked for viruses by Avast antivirus software.
>http://www.avast.com

I understand the technicalities of your comments. They get at what I am
trying to accomplish with the distribution method of reconstruction, which
is to recover the spectral energy immediately adjacent to the harmonics,
which is due to variability in the fundamental frequency. (The sampling
frequency is sufficiently high such that aliasing is not an issue.)
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>Any FFT bins other than those that you are using for the
>reconstruction that have non-zero magnitude would otherwise influence
>the reconstructed signal.   Harmonics, especially, even with
>relatively low magnitudes, can have a significant influence on the
>amplitude of an output sine wave. 
>
>When the fundamental is not centered on a bin it's DFT magnitude will
>naturally be lower than it would be if centered.   The same is true
>for harmonics, so even if harmonic energy is not readily apparent in
>the DFT output there could easily be energy there that will affect the
>amplitude of your resconstructed signal.
>
>The bottom line is that you're using only a small part of the DFT
>information to reconstruct your output signal, so the loss of the rest
>of the information is reasonably expected to have an affect on your
>signal.
>
>Eric Jacobsen
>Anchor Hill Communications
>http://www.anchorhill.com
>
>---
>This email has been checked for viruses by Avast antivirus software.
>http://www.avast.com


A further analysis of my distribution method reconstruction reveals that
the generated waveform has lower frequency sine waves contributing to the
undesirable distortions.
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The issue has been resolved.
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