Filter Selection for Noisy Signal

Hello,

I am filtering a noisy signal that has a carrier frequency of 800 Hz, but was sampled at a very high frequency, ~250 kHz. I generated the following code, and it filters the signal, but produces a start-up transient (which doesn't filter the beginning of the data). It may just be a feature of the first order filter that I am using (which has a tau). Are there any other filters available that could accomplish my goal (filtering all of the data w/o a transient)? I attached 3 pictures: the first is the entire signal (zoomed out); the second is of the start up transient, and the third is of a portion of the signal that shows I am filtering it (at least in the time domain).

        Fc = 800;      % filter corner (Hz)

  Wc = 2*pi*Fc;      % filter corner (rad/sec)

  tau = 1/Wc;    % filter time constant (sec)

  %  First order lag

        %                1

  %   G(s) =  _____________

  %            tau*s  + 1

  num = [1];

  den = [tau   1];

  printsys(num,den);    % analog filter 
    
  %  Data sampled at 249,600 Hz

  Ts = 4.0064e-06    
    
  % Convert analog filter to digital
    
  [b,a] = c2dm(num,den,Ts);

  printsys(b,a,'z');

  den = [a(1) a(2)];

        num =  [b(1) b(2)];

        test = filter(num,den,data);

  figure; plot(data); hold on; plot(test, 'r')

Answer 1

[Star Strider]

If you have the Signal Processing Toolbox, use the filtfilt (link) function instead of filter.

[C. Robinson]

I tried filtfilt and still received an undesirable start up transient. I'm wondering if a higher order filter would address this issue along with the use of filtfilt.

[Star Strider]

Higher-order filters are usually better. Also, with filtfilt, you can use second-order-section representation, usually more stable. Use the tf2sos function to do that transformation.

[C. Robinson]

When I tried filtfilt before, my input wasn't of type double, and that was the reason for me not getting a desirable response. I attached two plots; the one entitled Filtered Signal 3 displays filter vs. filtfilt, and the one entitled Filtered Signal 4 displays the filtfilt response on top of the noisy signal (no unwanted transient). I was able to do it with a first order filter. Thanks for your help! I really appreciate it.

[Star Strider]

As always, my pleasure!