# Difference b/w freqz and fft

Since both fft ,freqz are used for finding the frequency response of digital filters. the frequency response using freqz function is given below and frequency response using fft function is it seems to be that in case of fft it is mirror image of freqz response. also i want to find value of freq response at pi/8 how can i find it using any of fft or freqz method.

## 1 Answer

First, it is instructive to understand the normalised frequency axis of both the fft and the freqz.

By default, in fft, the frequency axis is normalized by the sampling frequency $f_s$. On the other hand, in freqz, the frequency axis is normalised by $f_s/2$, it seems. Having said that, we note that the radian frequency of $\pi/8$ corresponds to the normalized frequency of $\frac{1}{16}=0.0625$ ($2 \pi \frac{f}{f_s}=\frac{\pi}{8}$) in fft and $\frac{1}{8}=0.125$. In your case, the frequency response at $\pi/8$ seems to be about $-90$ dB.

fft does not provides the mirror image of the freqz. Freqz only shows the half portion of the fft spectrum.