# convolution and groupdelay

I have been given a sinusoidal signal x in time domain,asked to investigate the frequncy responce of the signal using matlab and observing the result,and using grpdelay(x,1) command in matlab to observe the group delay of the signal .and taking y=conv(x,x);which define the convolution of x signal by itself and then asked to use the grpdelay(y,1). My question here is what change should I exspect to see in group delay figure of conv(x,x)? or better to say how convolving of the signal by itself would effect the group delay of the signal. Thanks