Using Estimated Frequency responce function ,to find output vector

So,I got this vector of sampled input data in Matlab,which is vector of approx 1x25000 length. I have frequency responce function attained by different estimators (H1,H2,Arx). Anyway,my FRF is also a vector of 1x129 length.

Those two are different sized vectors.How should I find the output data using input data and this obtained FRF vector?

One way is to transform input vector (which is sampled data) with FFT ,and then just multiply input vector with FRF,element by element = X(i)*Y(u) .But those two vectors would be different sizes,how should I make them both same size? What is the correct approach in this case?I remember learning something about zero padding,how is it done?

Second way is transform FRF (IFFT) into time domain vector,and then convolve those two vectors.But again,those two will be different sized vectors,how should I do it?

Thanks in advance!

Answer 1

[Dishant Arora]

I don't see any reason why you can't perform the second task. There's no such constraint that vectors should be of equal length for convolution.

y = conv(ifft(frf) , inputSignal)

Answer 2

[Jake]

Hmm,thanks,that was very helpfull. Now ,different problem: I have to compare original output with the one I got now ,with this method (compare by coherence function). But original output and this new output have different length,how can I make them the same length?

[Dishant Arora]

Pad zeros to your input signal.