impulse response cascaded with time reversed of itself Consider a filter with real-valued impulse response $h[n]$. The filter is cascaded with another filter whose impulse response is $h'[n] = h[-n]$, i.e. whose impulse response is the time-reversed version of $h[n]$.

$h[n]$ cascaded with $h[-n]$

i think we have to perform convolution

if so what is phase of new cascaded impulse response
HINT: See what happens in the frequency domain. Convolution corresponds to multiplication. You just have to figure out the Fourier transform of $h[-n]$, expressed in terms of the Fourier transform of $h[n]$. Multiplying the two functions results in the Fourier transform of the convolution of $h[n]$ with $h[-n]$. The result has a special property which makes it very easy to determine its phase.