Like Matt L. pointed out, alpha and beta is unclear as is 'type 1'.
You can use the command fdatool to interactively design filters in MATLAB, although you may need the DSP system toolbox installed.
From there, you can apply the filter using the filter() function.
As an example, if you design the filter using FDAtool, and the filter is an FIR, you can use filter(Hd.numerator,1,X,Fs) if Hd is your filter object, X is the input sequence, and Fs is your sampling rate. This is not the only way to do this, but just the way I would go about it.
X could be generated as a sin(2*pinf*t) where t = 1/fs and n is an index in a for loop or shortened to 1:ns for the number ns you wish to have your input sequence have as a length.