Here’s a tool that plots frequency response from filter coefficients.
The coefficients fields are tolerant of input format. Most characters that don’t look like numbers are treated as separators. So, you can enter coefficients separated by spaces or commas, or on different lines, separated by returns. That makes it easier to copy and paste coefficients from online filter calculators. They also ignore numbers that are followed by “=” or “ =”, so that “a0 = 0.1234” is seen as “0.1234”. Click the chart to accept coefficient changes, or change one of the controls.
Important: This tool does not assume that the filter coefficients are normalized to y0. So, in most cases you’ll need to insert a “1” as the first pole coefficient, the b0 term.
If there are no pole coefficients, it’s an FIR filter—all zeros.
Again, the convention of this website is that coefficients corresponding to zeros (left side of a direct form I) are the a coefficients, and poles the b coefficients. It’s usually easy to see because most IIR filter calculators normalize the output. So, if you are missing a0, it probably means that a and b are swapped with respect to this site’s convention—just paste them in the opposite coefficients fields (and remember to use a 1 for the missing coefficient). Also, negative signs at the summation for the feedback terms (b) are not rolled into the coefficients.