Frequency domain filtering (rectangular window question)

rhnlogic@yahoo.com wrote:
> Jerry Avins wrote:
> 
>>rhnlogic@yahoo.com wrote:
>>
>>>Is there any rule-of-thumb on what the phase response needs to look
>>>like near any artificially sharp transition in a frequency domain
>>>filter in order to reduce ripple (caused by the sharp transition)
>>>in the continuous frequency response, if that's at all possible?
>>
>>We both know that linear-phase filters can be made arbitrarily sharp,
>>so I don't understand what you're asking for.
> 
> 
> I was refering not to arbitrarily sharp filters, but to artificially
> sharp filters, such as the one the OP was using which quantizes
> the magnitude response to either 1.0 or zero (obvious not a flat
> filter).  My question was about whether allowing degrees of freedom
> in the phase response would help anything (assuming more than 1 bin
> of 1.0 coefficients, or course).  e.g. would his box filter get
> any "better" if he removed all linear phase restrictions?

Those filters aren't arbitrarily sharp. They can't be sharper than the 
bin spacing, even in one's dreams. A plot of the continuous frequency 
response shows poor attenuation between the zeroed-out bins and between 
the unity-gain bins near the transition. Using a longer FFT to put the 
bins closer together raises the frequency of the Gibbs oscillations, 
just as adding more frequency terms to a synthesized square wave does, 
but it doesn't affect the amplitudes.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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