Q:

How can I improve the response time of a low pass filter?

I am busy with a high order low pass filter. How can I improve the response time of a filter? If I use a higher ordered filter, does it improve? Also, if I use an op amp with a faster slew rate, does it improve? 
My application is that amplify and get filter the load cell signal. My load cell signal is changing between 1 Hz to 10 Hz. 
There is three stages in my signal conditioning circuit. First stage Instrumentation Amplifier to amplify the signal(AD8221), second stage is second order low pass filter with OP07C op-amp (Sallen-Key type, corner frequency is 10 Hz), third stage is voltage follower with again OP07C. 
According to my test results, when I compared original signal to output of amplifier (first stage) there was no significant delay between two signals. However when I compared original signal to output of voltage follower there was significant delay. The delay was approximately quarter of a period of original signal. 
So I have thought that I have to improve my filter rise time. Or do I have to change my op-amp with higher slew rate one. According to all your answer, should I use higher cutoff frequecy with same op-amp (OP07C)? 
Most of you mentioned "group delay" of a filter. What does "group delay" depend on? I got it firstly depends on corner frequency of a filter. Is there any effect order of filter to group delay?

A:

You cannot greatly change response time of a low-pass filter by changing its' order. What you have to do is change its cutoff frequency - the higher the cutoff frequency, the faster the response.
Look at it this way. A low-pass filter removes high frequencies, right? And if you want the filter output to change more quickly it must contain more high-frequency components. You know, fast change means high frequency. So the only way to get faster response from the filter is to let more high-frequency signal through, and that means changing the cutoff frequency to a higher one. 

A:

Usually, the higher the order of the filter, the longer the response time so the trick is just filtering sufficiently to get a manageable signal-to-noise ratio. If the interferer is significantly away from the wanted frequencies, different filter types can improve response time of the wanted signal.
If you are looking to keep the time delay between two signals very close and only one of those signals needs to be filtered you can opt to filter both and therefore keep the time delays still acceptably close.

