performing ifft of frequency response

I have measured the frequency response of two filters separately. For each, I have the frequency at which the response was measured and the real and imaginary parts of that signal.

1. I would like to perform the ifft to get their individual impulse responses.
2. Then I would like to convolve these responses to get their combined impulse response.
3. Then I would like to do a fft to get the frequency response of them combined.
4. Then I would like to plot the magnitude and phase of this response with frequency on the x axis and magnitude or phase on the y-axis. I really just need to figure out how to convert the sample number of the impulse response to frequency.

How do I do this? I'm looking online and I am having trouble putting all the pieces together.

Can someone lend a hand please?

[Star Strider]

Context: http://www.mathworks.com/matlabcentral/answers/285860-how-do-you-multiply-two-transfer-functions-numerically

Answer 1

[Windell]

Thanks Star. You're probing helped me tons! I just realized that I can use the convolution theorem to help me. Given two frequency responses, I can get their combined frequency response by performing a point-by-point multiplication in the frequency domain. Sweet!

[Star Strider]

My pleasure!

That’s frequency-domain convolution. I would do convolution in the time domain by using the conv function on the numerator and denominator polynomials. Then use those polynomials as the transfer function for your system.

I would then use the minreal function in the Control System Toolbox. That would eliminate pole-zero cancellations and simplify your convolved model. That would make your model more stable and your simulations more efficient.

It’s taking me a while to understand what you’re doing.