Why there are amplitude distortion for a single frequency signal passing through filter?

Hi,

I did the simulation again with the following specifications using �sptool� of Matlab:
1) Fs=25MHz, 
2) fstop1=2.0MHz, 
3) fpasss1=2.5MHz, 
4) fpass2=3.5MHz, 
5) fstop2=4.0MHz. 
6) Astop1=80dB, Apass=1dB, Astop2=80dB.
7) IIR Butterworth filter. 

�sptool� filter design tool gives me a filter of the following specs:
- Structure: Direct form II, 2nd-order section
- Order: 32
- Sections: 16
- Stable: Yes

Then I imported a sequence of 3MHz pure tone signal from Matlab�s workspace onto �sptool�, and applied the designed 32-order filter onto the pure tone signal. I observed that there is ringing at the beginning of the filtered signal and it eventually dies down. As I want to learn how this transient ringing effect will have on narrow band filter, I reduce the passband of the filter further to the followings:
1) Fs=25MHz, 
2) fstop1=2.99MHz, 
3) fpasss1=2.999MHz, 
4) fpass2=3.001MHz, 
5) fstop2=3.01MHz. 
6) Astop1=80dB, Apass=1dB, Astop2=80dB.
7) IIR Butterworth filter. 


�sptool� filter design tool then gives me a filter of the following specs:
- Structure: Direct form II, 2nd-order section
- Order: 10
- Sections: 5
- Stable: Yes

Again, I applied this filter onto the 3MHz pure tone signal, and this time I observed that there is much strong ringing effect at the beginning of the filtered signal and it lasted much longer time (probably 1.5ms) with higher amplitude fluctuations (20% at highest amplitude).

May I know what the cause of this transient ringing effect is?
And how can it be removed for this narrow bandpass filter?

Thank you.

On Wed, 06 Feb 2013 18:12:26 -0800, yweesoon wrote:

> Hi,
> 
> I did the simulation again with the following specifications using
> ‘sptool’ of Matlab: 1) Fs=25MHz,
> 2) fstop1=2.0MHz,
> 3) fpasss1=2.5MHz,
> 4) fpass2=3.5MHz,
> 5) fstop2=4.0MHz.
> 6) Astop1=80dB, Apass=1dB, Astop2=80dB. 7) IIR Butterworth filter.
> 
> ‘sptool’ filter design tool gives me a filter of the following specs: -
> Structure: Direct form II, 2nd-order section - Order: 32
> - Sections: 16
> - Stable: Yes
> 
> Then I imported a sequence of 3MHz pure tone signal from Matlab’s
> workspace onto ‘sptool’, and applied the designed 32-order filter onto
> the pure tone signal. I observed that there is ringing at the beginning
> of the filtered signal and it eventually dies down. As I want to learn
> how this transient ringing effect will have on narrow band filter, I
> reduce the passband of the filter further to the followings: 1)
> Fs=25MHz,
> 2) fstop1=2.99MHz,
> 3) fpasss1=2.999MHz,
> 4) fpass2=3.001MHz,
> 5) fstop2=3.01MHz.
> 6) Astop1=80dB, Apass=1dB, Astop2=80dB. 7) IIR Butterworth filter.
> 
> 
> ‘sptool’ filter design tool then gives me a filter of the following
> specs: - Structure: Direct form II, 2nd-order section - Order: 10
> - Sections: 5
> - Stable: Yes
> 
> Again, I applied this filter onto the 3MHz pure tone signal, and this
> time I observed that there is much strong ringing effect at the
> beginning of the filtered signal and it lasted much longer time
> (probably 1.5ms) with higher amplitude fluctuations (20% at highest
> amplitude).
> 
> May I know what the cause of this transient ringing effect is? And how
> can it be removed for this narrow bandpass filter?

The cause of the ringing is that the filter bandwidth is narrow.  And 
while there may be details that you can change that will help things, the 
only way that you can significantly reduce it is to open up the filter.

Basically, the reason that this effect happens is because your tone 
starts and stops.  A sinusoid that lasts forever exists at one pure 
frequency.  But a sinusoid that is zero up to some time, then starts up, 
has a spectrum that extends to infinity.  When you run that sinusoid 
through a narrow filter, you see the transient.

A filter could probably be designed to at least have an output that 
smoothly rose to its maximum amplitude, without ringing.  But you'd need 
more sections, and the filter couldn't have as flat a bandpass response.

-- 
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com