A filter with 8000 coefficients is likely an FIR filter. For a simple bandpass or bandstop application, an IIR elliptical filter is much more efficient.
If you have R2018a or later, use either the bandpass or bandstop functions, depending on what you want to do. They will design an efficient IIR filter that you can use with filtfilt if you need to use those filters on other signals. If you do not have an earlier release than R2018a, it is still straightforward to design an elliptical filter that will do what you want.
A functioning bandpass elliptical filter prototype for your application is:
Fs = 1000; % Sampling Frequency
Fn = Fs/2; % Nyquist Frequency
Wp = [0.5 35]/Fn; % Passband Normalised
Ws = [0.25 40]/Fn; % Stopband Normalised
Rp = 1; % Passband Ripple (Irrelevant in Butterworth)
Rs = 50; % Stopband Attenuation
[n,Wp] = ellipord(Wp,Ws,Rp,Rs); % Order Calculation
[z,p,k] = ellip(n,Rp,Rs,Wp); % Zero-Pole-Gain
[sos,g] = zp2sos(z,p,k); % Second-Order Section For Stability
figure
freqz(sos, 2^16, Fs) % Filter Bode Plot
The only thing you may need to change is the sampling frequency (‘Fs’) to match the sampling frequency of your signal. Use filtfilt to filter your signal with this filter.
