# group delay of an fir filter

suppose we have an fir filter: t=[-50:50]; x=[sinc(.1*t).*cos(2*pi*.15*t),sinc(.1*t),sinc(.1*t).*cos(2*pi*.3*t)]; using matlab command grpdelay(x,1),we observe the groupd dalay of the system. then we have y=conv(x,x),again using the matlab command grpdelay(y,1) what changes in group delay would you expect to see in convolved signal. how convolving a signal by itself would effect the group delay of the output signal in compare to x signal. any help much appriciated

• Is this homework? – Phonon Feb 23 '14 at 10:27

## 2 Answers

x is the filter? conv(x,x) is then identical to cascading two of these filters. The group delay is equivalent to the delay of the signal through the filter. The rest of the reasoning is left as a rather trivial exercise.

• Thanks,but it didn't really answer my question.I want to know if cascading or convolving a signal or a filter by it self would effect it is group delay. – user7999 Feb 23 '14 at 23:55
• Well, it did in fact. Note that the group delay of a particular frequency is equal to the delay of a signal of the frequency through the filter. Hence, passing through two filters would double the delay, which then is the effect of convolving two filters. – Oscar Feb 24 '14 at 6:05

This is related to FIR filters and the linearity (flat) of the Group delay that they possess. That article helped me to understand the fundamental concepts of group delay:http://www.scribd.com/doc/41169598/Group-Delay And Richard G. Lyons Understanding Digital Signal Processing 1996 book has a very nice explanation for FIR filtering where you will understand,how the pulses are used and how you would possibly proceed with the above problem. Anyway if you put the expression you shared above in MATLAB you will be able to draw some conclusions about the group delay behavior of that design.