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Entry  Wed Jul 16 22:17:40 2014, Akhil, Summary, Electronics, Bode Plots and complete Characterization of Frequency Counter Phase_Data.zipBode100MHz.png
    Reply  Wed Jul 16 23:02:16 2014, Koji, Summary, Electronics, Bode Plots and complete Characterization of Frequency Counter 
       Reply  Fri Jul 18 19:32:50 2014, Akhil, Summary, Electronics, Filters used inside the Frequency Counter TheoreticalGainPlot.pngTFexpected.png
          Reply  Mon Jul 21 12:16:27 2014, Akhil, Summary, Electronics, Filters used inside the Frequency Counter FC_TF_Characterization.png
Message ID: 10239     Entry time: Fri Jul 18 19:32:50 2014     In reply to: 10223     Reply to this: 10246
Author: Akhil 
Type: Summary 
Category: Electronics 
Subject: Filters used inside the Frequency Counter 

 

 Thanks Koji , for your  hint for the brain teasing puzzle. I was looking into Filters that are usually used in devices like counters, DSO and other scopes. I found that , to improve the quality of the measurement one of the best approach  is averaging. I looked deeper into averaging and found out this:

There are two general use-cases for averaging . The first, successive sample averaging, takes a single acquisition and averages between its samples. The second, successive capture averaging, combines the corresponding  samples of multiple captures to create a single capture. Successive sample averaging is also called boxcar filtering or moving average filtering. In an implementation of this type of averaging each output sample represents the average value of M consecutive input samples. This type of averaging removes noise (one of the reasons the noise level was not bad: http://nodus.ligo.caltech.edu:8080/40m/10151) by decreasing the device's bandwidth(could be one of the reasons why the FC operates in 4 different frequency ranges). It applies an LPF function with a 3dB point approximated by  0.433 * s / M, where M is the number of samples to be averaged, and s is the sample rate in samples per second. 

Now I tried verifying the 3 dB points in the gain plots I generated :

For 1 s Sampling time : the 3 dB point for such a Boxcar filter should be at 0.433* 1/M. If we assume that it averages for 2 samples, M=2 which gives the 3dB point at 0.288 Hz but occurs somewhere between 0.3 and 0.4 Hz.  (http://nodus.ligo.caltech.edu:8080/40m/140619_120548/GainVsFreq.png)

For 0.1s Sampling time: the 3dB point should be at 2.17 Hz and in reality is 2.5 Hz(http://nodus.ligo.caltech.edu:8080/40m/140701_211904/gain.png).

Also, This type of filter will have very sharp nulls at frequencies corresponding to signals whose periods are integer sub-multiples of M/s. As seen my previous plots (http://nodus.ligo.caltech.edu:8080/40m/10118 , http://nodus.ligo.caltech.edu:8080/40m/10070) there are sharp nulls at frequencies

0.4 Hz for 1S sampling time and

at 1.5 Hz,3 Hz for 0.1 S sampling time as correctly predicted.

The moving average filter is  L-sample moving average FIR, with the frequency response as:   H(ω) = (1/L) (1 − e− jω L)/(1 − e− jω)..

There is an overall delay of (M - 1)/2 samples from such a length-M causal FIR filter. 

The expected bode plots for such a filter with L= 5 is attached(attachment 2).

Attachment 1: TheoreticalGainPlot.png  18 kB  | Hide | Hide all
TheoreticalGainPlot.png
Attachment 2: TFexpected.png  17 kB  Uploaded Mon Jul 21 12:42:54 2014  | Hide | Hide all
TFexpected.png
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