hi all, i'm having trouble to get transfer function for these sub-band frequency.

Delta = 0 - 4 Hz 
theta = 4 - 8 Hz
Alpha =8 - 13 Hz
Beta = 13 - 31 Hz
Gamma= 31 - 51 Hz
High Gamma= 51 - 120 Hz

sampling frquency=1000 Hz
eeg channel from 1-19 channel

Answer 1

[Star Strider]

EEG filters are extremely difficult to design because of the frequency definitions. They are best filtered with active filters in hardware.

These look reasonable, and are the best I can design:

frq_pb = [2.1  4;  4  8;  8  13;  13  31;  31  51;  51  120];           % Passband Matrix
frq_sb = [frq_pb(:,1)-2  frq_pb(:,2)+2];                                % Stopband Matrix
Fs = 1000;                                                              % Sampling Frequency (Hz)
Fn = Fs/2;                                                              % Nyquist Frequency (Hz)
Rp = 30;                                                                % Passband Ripple (dB)
Rs = 10;                                                                % Stopband Ripple (dB)
for k1 = 1:size(frq_pb,1)
    [n,Ws] = cheb2ord(frq_pb(k1,:)/Fn, frq_sb(k1,:)/Fn, Rp, Rs);        % Chebyshev Type II Filter Order
    n = max(k1+1, real(n));
    [b,a] = cheby2(n, Rs, Ws);                                          % Transfer Function Polynomial Coefficients
    [SOS{k1}, G{k1}] = tf2sos(b,a);                                     % Second-Order-Section For Stability
end

for k1 = 1:size(frq_pb,1)                                               % Plot Filter Passbands
    figure(k1)
    freqz(SOS{k1}, 4096, Fs)
    set(subplot(2,1,1), 'XLim',[0  150])                                % Set X-Axis Limits To Improve Visibility
    set(subplot(2,1,2), 'XLim',[0  150])
end

Experiment with them to get the result you want. You can also experiment with using designfilt to see if it can produce a better design. I use a Chebyshev Type II FIR filter here, but other designs and IIR filters may also be appropriate.

[alaisya]

why when i try run this coding it say empty transfer function?

[Star Strider]

I have no idea. It ran for me without error, and produced appropriate Bode plots for all the filters, or I’d not have posted it. (I am running R2016b.)

[alaisya]

i'm using matlab r2008a.. is it suitable to used

[Star Strider]

The functions should be available to you. There are probably version differences in the functions between R2008a and R2016b. Beyond that, I have no idea what the problem could be.

I am attaching the filter coefficient cell arrays here. It contains the ‘SOS’ and ‘G’ values calculated from the code I posted, so they are already documented. You can load them directly into your workspace. (See the documentation on the load function for details.)

Remember to use the filtfilt function with them to filter your signals.