Your data have a maximum sampling interval of 4 and a minimum sampling interval of 2, so you can safely interpolate them with a sampling interval of 2 without compromising your data. (No proof — just personal experience.)
I discourage the use of moving average filters because they offer no specific control over the frequency characteristics of the filter. I always use low-pass filters instead. Note that your signals have broad-band ‘impulse’ noise, so filtering all of it out is not possible.
I would process your signals as:
D = load('Corey Peruffo DataMovingAverage.mat');
t = D.time;
ax = D.ax;
ay = D.ay;
tmsd = [mean(diff(t)) std(diff(t)); max(diff(t)) min(diff(t)); median(diff(t)) mode(diff(t))];
ti = [0:2:max(t)]'; % Interpolating Time Vector
axiayi = interp1(t, [ax ay], ti, 'linear'); % Interpolate Signals
axi = axiayi(:,1);
ayi = axiayi(:,2);
figure(1)
plot(t, [ax ay])
grid
Ts = mean(diff(ti)); % Sampling Interval
Fs = 1/Ts; % Sampling Frequency
Fn = Fs/2; % Nyquist Frequency
L = length(ti);
Fxyi = fft([axi ayi])/L;
Fv = linspace(0, 1, fix(L/2)+1)*Fn; % Frequency Vector
Iv = 1:length(Fv); % Index Vector
figure(2)
semilogy(Fv, abs(Fxyi(Iv,:))*2)
grid
axis([0 0.1 ylim])
Wp = 0.006/Fn; % Passband Frequency (Normalised)
Ws = 0.012/Fn; % Stopband Frequency (Normalised)
Rp = 1; % Passband Ripple (dB)
Rs = 25; % Stopband Ripple (dB)
[n,Wn] = buttord(Wp, Ws, Rp, Rs); % Optimal Filter Order
[b,a] = butter(n,Wn,'low'); % Filter Transfer Finction Coefficients
[sos,g] = tf2sos(b,a); % Convert To Second-Order-Section For Stability
figure(3)
freqz(sos) % Filter Bode Plot
filt_xyi = filtfilt(sos, g, [axi, ayi]); % Filter Signal
figure(4)
plot(ti, filt_xyi)
grid
The numerator values of ‘Wp’ and ‘Ws’ are in Hz (or the inverse of whatever time interval your ‘time’ variable is). Experiment with those to get the result you want in the filtered signal. They might be too low to recover all the frequencies you want. I put ‘Ws’ at twice ‘Wp’. Putting them too close together will result in an unstable filter and no useful output. For a low-pass filter, ‘Ws’ must be greater than ‘Wp’.
