RE: resolution in the fft

[Schirmacher, Rolf]

> -----Original Message-----
> From: Matthias Brennwald [mailto:address@hidden Behalf Of
> Matthias Brennwald
> Sent: Wednesday, June 10, 2009 7:59 AM
> To: address@hidden
> Subject: Re: resolution in the fft
> 

...

> 
> Dear Markus
> 
> 1. The short answer is: you can't increase the resolution of 
> the fft,  
> because the resolution is given by the number of samples in 
> your signal.
> 2. The somewhat longer answer is: you can increase the resolution of  
> the fft by adding more samples to your signal. You can do 
> this either  
> by using a higher sampling rate (I'd recommend to do this if 
> possible)  

Be careful here! You will get a longer output vector for a longer input
vector, but as long as the time represented in the input vector remains
constant, the frequency resolution will remain constant. The extra output
will represent higher frequencies, i.e. an increase in bandwidth.

> or by padding zeroes at the end of the signal (I'd classify this as  
> cheating, though).

Exactly. The FFT you compute is mathematically correct, of course, but the
time domain signal does no longer represent the physical process you have in
mind ;-)


So, as the physical response is calculated here according to a model, the
best way to increase the frequency resolution is calculate the model
response for a longer time and analyse this longer input vector. This should
also reduce the DC component (which however will always remain as your
signal will be positive >0 for this simple loading / unloading process for
all times, even it is cheasing exponentially ...).

Rolf