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Low pass filter with minimum group delay

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oyvdahl

oyvdahl

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Hi

I need to design a lowpass filter with as low group delay as possible. The sampling frequency is 70 hz and I need frequencies of approximately 0.5-2Hz to pass the filter with as little attenuation and delay as possible.

Does anyone have any idea what I should be looking at?
 

Hi,

lower bandwidth and/or sharper cutoff -> more group delay.
Why do you need to filter the signal? What is you application?
Regards

Z
 
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    oyvdahl

    oyvdahl

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There are some tricks you can use if you are comparing this signal to another one. Put the other one through an identical filter. The delay difference between them will be the same.
 

Thanks for your replies.
What I am trying to do is to measure the position of a pendulum using a radar and visualize this position on my computer. I want the visualization to look as "real-time" as possible.
But with my current filter, the measured position and the filtered position is about 1/4 - 1/2 pi out of phase.

zorro: Are you saying that if I increase my cut-off frequency, the group-delay becomes smaller?
 

Low order, flat response IIR filters (Bessel, Butterworth) have the smallest group delay for a given cut-off frequency. Obviously, the group delay depends also on the cut-off frequency (tg ~ 1/fc).
 
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    oyvdahl

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FvM said:
Low order, flat response IIR filters (Bessel, Butterworth) have the smallest group delay for a given cut-off frequency. Obviously, the group delay depends also on the cut-off frequency (tg ~ 1/fc).
Click to expand...

Thank you!
 

Hi oyvdahl,

oyvdahl said:
What I am trying to do is to measure the position of a pendulum using a radar and visualize this position on my computer. I want the visualization to look as "real-time" as possible.
Click to expand...
Your signal has essentially just a sinusoidal component of 1 Hz frequency.
In that case, you are interested in phase delay rather than in group delay.
I suggest you to use a second-order passband filter (simple resonator) centered at the pendulum frequency (1 Hz). At the resonant frequency, the phase delay is 0 (input and output are exactly in phase).
Interestingly, tuning the frequency of the resonator (Fo) you can adjust the phase delay: the delay is positive if the signal frequency is higher than Fo, and negative at frequencies below Fo. (Note: that does not mean that the filter "predicts future", because that works in that way only for sinusoids.) The amplitude gain is maximum at Fo.
In that way, it is possible to compensate delays in other parts of the system (sampling, processing, etc.) adjusting Fo of the filter.
The Q of the filter should not be very high. Otherwise, it would be too selective.

zorro: Are you saying that if I increase my cut-off frequency, the group-delay becomes smaller?
Click to expand...
Yes, for a given form of a low-pass filter.

Best regards

Z
 
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    oyvdahl

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zorro said:
Hi oyvdahl,


Your signal has essentially just a sinusoidal component of 1 Hz frequency.
In that case, you are interested in phase delay rather than in group delay.
I suggest you to use a second-order passband filter (simple resonator) centered at the pendulum frequency (1 Hz). At the resonant frequency, the phase delay is 0 (input and output are exactly in phase).
Interestingly, tuning the frequency of the resonator (Fo) you can adjust the phase delay: the delay is positive if the signal frequency is higher than Fo, and negative at frequencies below Fo. (Note: that does not mean that the filter "predicts future", because that works in that way only for sinusoids.) The amplitude gain is maximum at Fo.
In that way, it is possible to compensate delays in other parts of the system (sampling, processing, etc.) adjusting Fo of the filter.
The Q of the filter should not be very high. Otherwise, it would be too selective.


Yes, for a given form of a low-pass filter.

Best regards

Z
Click to expand...

Thank you for a very good answer. It seems like a resonator will solve my problem with the pendulum.

But having that in mind, my next challenge is to track an RC helicopter flying in front of the radar. The helicopter might stand still or it might be moving back and forth, but probably not with a higher frequency than 2 Hz. For this, I was thinking that the group delay was the most important parameter. But maybe I should have a better look at the phase response for different lowpass filters as well.

Best Regards
Oyvind
 

Hi oyvdahl,

I'm here again. Sorry fot this time out of the thread.
In the case you describe now, you are right. You need a lowpass filter with good amplitude and phase or delay response (both of them).
If you don't have undesired signals that need to be filtered off (e.g. noise), you can use a very simple filter with relatively high bandwidth. But if noise is a concern, there is a constraint between eliminate undesired signals and distort the useful one. And there is also a constrint between amplitude response and delay.
Have you noise or "bad" components that must be eliminated?
Regards

Z
 

Hi zorro

I use a tracking algorithm to extract the helicopter position from the raw radar data. Sometimes this algorithm gives me "bad" positions or outliers and sometimes it gives me positions with a small offset. So I would like to filter out most of the outliers and smooth the changes in position offset, so that the visualization looks as smooth as possible.


Regards
Oyvind
 

Hi Oyvind,

the tracking algorithm should filter by itself the positions if it has the right parameters, without need of an extra filter.
The "positions with a small offset" are normal by the smoothing action of the tracker, but not "bad positions or outliers".
Maybe you have a misadjustment or measurement errors?
Regards

Z
 

Well, I have designed the tracking algorithm as well, so there is no smoothing inside of it. Therefore I am designing the smoothing now. The "positions with a small offset" means simply that the tracking algorithm has decided to track a different peak in the same pulse.

There is of course a lot of improvements and adjustments that can be made in the tracker, but I don't think I will ever make a perfect tracker without noise as the raw data is pretty noisy.

Regards
Oyvind
 

Standard tracking algorithms (e.g. alpha-beta filter, Kalman filter) include smoothing.
Sorry, but what does mean that the tracking algorithm has decided to track a different peak in the same pulse? Are there multiple detections fos a single target (false alarms)?
Regards

Z
 

The reflected pulse is not an impulse, so it has several peaks. The algorithm has to decide which peak is the right one to follow.

Regards
Oyvind
 

Can you tell what pulse waveform are you using? Which form of detection and why are there several peaks?
Regards

Z
 

The returned pulse looks like a second order Gaussian pulse with ringing. The detection is based on finding the "best" peak by looking at a certain number of peaks and tracking them over a certain period of time. Then the "best" peak is picked by looking at a few parameters as speed and value.
 

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