Let's say I have some (complex) data in the frequency domain, so essentially I have an array of frequency values and a corresponding array of data. I want to apply a band-pass filter to this data (such as a Butterworth) to zero out the data at high and low frequencies. How can I do this in the frequency domain (without going into the time domain at all)?
I know that there is probably some function to multiply my data by, since multiplication in the frequency domain is equivalent to convolution in the time domain. I know that I can't impose a brick-wall filter of just setting the appropriate data to zero, since that would be equivalent to convolving time-domain data with a sinc function. So what would the appropriate function or procedure be to accomplish band-pass filtering in the frequency domain?