# Using DFT Circular convolution property

I am trying to make proper use of the circular convolution property of DFT. I was taught that the DFT of x[n]*CircularConv*y[n], would be equal the product of the individual DFT's X[k],Y[k].

On the problem im trying to solve, the signal x[n] is convolved (Circular convolution) with the discrete impulse response y[n] to produce the output signal z[n]. (x[n]*y[n]=z[n]) Having the signals z[n],y[n]+their DFT's, and using the property mentioned above, can I conclude that X[k]=Z[k]/Y[k] immediately? are there any limitations? or am I doing it totally wrong?

• When you are using DFTs to find the response of an actual system, you need to be sure that the result of $$\text{"take DFTs, multiply pointwise, take inverse DFT"}$$ which gives the circular or periodic convolution of $x[n]$ and $y[n]$ actually computes the linear or aperiodic convolution of $x[n]$ and $y[n]$ that the system will give you. For example, if the system is an IIR filter, your DFT method might not work. – Dilip Sarwate Jun 21 '13 at 12:54

Yes, that conclusion would be valid. However, as you suspected, there are some limitations. Consider the case where the system's frequency response $Y[k]$ contains one or more zeros. In that case, corresponding frequency bin in your estimate of the input signal $X[k]$ would diverge to infinity (because of the division by zero).