Approximate the magnitude response of an analog filter with a digital filter, starting from its gain expression
Did you try to plot this curve in matlab.
I am not sure whether it is any standard high,low or band pass filter.
So, to calculate the impulse response there might be two ways.
1. take the inversefft of the NdB and then do the convolution between your impulse input and the inversefft signal of filter usinc conv(x,y) command.
2. Or convert the impulse input into frequency domain by fft transform in matlab and then just multiply the gain and fft of input impulse and then convert them in time domain.
Can you do it using above method? 
Do you want a matlab code for this method?