Research on Filters: Big Picture Overview

Name: Preston Hoang

Research Questions

• What are the effects of the Park McClellan filter on the amplitude and phase data?

• Are there any other alternative filters that provide more accuracy / efficiency pertaining to the above?– iFilter

• How does the iFilter correspond to data sets that have already been processed?

• How do we characterize the stability of the iFilter?• How do we quantitatively assess signal quality based

on autocorrelation data?

Assessing the Park McClellan Filter

• Experiment #1: Test one sinusoidal signal, change one variable at a time (amplitude or frequency), include a time-gap at the beginning or end– Keep frequency constant (frequency = 0.15Hz), change

amplitude – Keep amplitude constant (amplitude = 0.01), change

frequency• Perform a Hilbert transformation for both the original

and filtered signal, then report the area under the curve and the max amplitude of the original and filtered signal

Assessing the Park McClellan Filter

Conclusion of Experiment #1

• The area under the curve and the average amplitude appear to increase for the filtered signal, independent of amplitude or frequency changes

• The percent errors for both appear to remain around 10 – 15%

Assessing the Park McClellan Filter

• Experiment #2: Introduce three different signals – each with frequencies, amplitudes, and phase data

• 1 Hz - with amplitude 3 and 0 degree phase shift• 2.5 Hz – with amplitude 5.5 and 20 degree phase shift• 4 Hz – with amplitude 8 and 65 degree phase shift

• Combine these signals, run through a band pass filter at a specific frequency, then compare the envelope and phase of the constituent signal after applying the Hilbert transformation

Assessing the Park McClellan Filter

Assessing the Park McClellan Filter

Conclusion of Experiment #2

• The filter can generally extract the amplitudes of the constituent signals within the ballpark range.

• The filter can extract phase data from constituent signals in the middle area, but it is not accurate toward the beginning / end of the signal itself.– Likely: when the filter starts to attenuate /

increase the signal power

Efficiency Standpoint

• ParkMclellan FIR Filter: takes 120 to 240 seconds to run a filter for a specific frequency• Inefficient – as each patient data has multiple breathing frequencies to

be processed• Multiple patients

• What filter is available out there that would improve the efficiency and the accuracy of extracting amplitude and phase data?– iFilter 4 Tom O’Haver, Professor Emeritus of Chemistry and

Biochemistry (U of Maryland)– Used in 75 papers, patents, and theses covering multiple scientific and

engineering fields (e.g. industrial, engineering, military, medical etc.)

Testing the iFilter

• Experiment #3 and 4: Perform the same set of experiments that were done the Park McClellan on the iFilter– Experiment #3 see Experiment #1– Experiment #4 see Experiment #2

Testing the iFilter

Testing the iFilter

Testing the iFilter

Conclusions for Experiment #3 and #4

• Experiment #3: The iFilter appears to reduce the percent error for the area under the curve and the average amplitude to < 1%– Independent of frequency or amplitude changes

• Experiment #4: The filter can extract the amplitudes much more accurately than the Park McClellan FIR filter– Similar to the FIR filter, this one can extract phase data from

constituent signals in the middle area, but it gets less accurate toward the beginning / end of the signal itself.

– Error rates for phase data at the beginning / end is less severe for this filter than the FIR filter

• Takes approximately 2.5 to 5 seconds to band pass a specific frequency for the iFilter

Testing the iFilter

• Experiment #5: All the previous patient’s data has already been processed by the Park McClellan Filter. Are there any differences when the raw data is processed again by the iFilter?

Patient 370 (Phase Difference)

Conclusion of Experiment #5

• Side-by-side comparisons show similar values for both the iFilter and the Park McClellan Filter for all patients (tumor and normal).

• Minor gaps – perhaps we need to find a way to assess signal quality?

Autocorrelation

• Experiment #6: Based on prior experience, one can use filtering and autocorrelation to assess the quality of the signal. Is there a quantitative metric by which we can discern a good or a bad signal from breast cancer patient data sets?

Autocorrelation

Autocorrelation

Conclusion of Experiment #6

• Results from Patient 370 are suggestive that this could be used to assess the quality of signal (see Excel File).

• One of the most reliable indicators of discerning a good and a bad signal is the percent error between the autocorrelation periodicity and the expected periodicity.

• Guaranteed good signal: <10% error, <0.25 std. dev.

iFilter Stability

• Experiment #7: To further validate the data that was processed, what happens if we shift the center of the band pass filter by a certain amount? What happens if we increase or decrease the width of the band pass filter, keeping the center constant?

iFilter Stability

0.1 0.15 0.2 0.25-60

-40

-20

0

20

40

60

80

Breathing frequencies

D-O

-2% shift

-1% shift

Original+1% Shift

+2% Shift

iFilter Stability

0.1 0.15 0.2 0.25-100

-50

0

50

100

150

200

Breathing frequencies

D-O

width = 0.01

width = 0.015

width = 0.025width = 0.035

width = 0.040

Conclusion of Experiment #7

• Most points agree with one another (general trend), regardless of changing the widths or centers

• More erratic if you change the width, especially if you have the value to a low number

• Implications: the patient may not breath at the exact value you may specify