Ideal Low Pass Filter: Why Can't It Be Real?

[boredaxel]

Hey guys, I have some problem understanding why an ideal low pass filter cannot be implemented in reality. I do not understand the reason given in wiki " because the sinc function's support region extends to all past and future times. The filter would therefore need to have infinite delay, or knowledge of the infinite future and past, in order to perform the convolution"

Can someone enlighten me? Thanks in advance

 

[f95toli]

Hey guys, I have some problem understanding why an ideal low pass filter cannot be implemented in reality. I do not understand the reason given in wiki " because the sinc function's support region extends to all past and future times. The filter would therefore need to have infinite delay, or knowledge of the infinite future and past, in order to perform the convolution"

Can someone enlighten me? Thanks in advance

It basically means that in order to implement a perfect filter you would need to know what the signal will look like BEFORE it arrives. This is obviously not possible with a real-time filter.
Also, even if you were filtering a known signal (say something saved on your harddrive) the signal/filter would have to be inifinitly long in order to implement a perfect filter.

Btw, it might be worth looking up the difference between a IIR and FIR filter (and why the later always need to use a memory/buffer of some sort).

 

[boredaxel]

Can I clarify that the reason such a filter cannot be constructed is because sinc function extends to infinity and not because the impulse response is non zero for negative time? Is it possible to construct a filter which is non zero for negative time?

Thanks in advance

 

[Mike_In_Plano]

Pretty much. The more taps you pay for, the sharper the edge :-)

 

[The Electrician]

Volume 18 of the Rad Lab series:

http://web.mit.edu/klund/www/weblatex/node7.html

http://www.ioffer.com/i/155136380

contains an appendix A which discusses the Paley-Wiener criterion.

The thing which makes an ideal low pass filter non-causal is the infinite attenuation over a finite band of frequencies.

For example, an elliptic low-pass filter which has a finite number of zeros in the stop band is causal because the infinite attenuation only occurs at a finite number of discrete frequencies, not a band of frequencies.

 

[Bob S]

A fundamental problem with simple low-pass (base) and high-pass (treble) filters used in audio systems is that for every dB of attenuation, there is a corresponding 6.6 degrees of phase retardation (1 radian per neper (8.686 dB)). For serious audiophiles, this is a significant distortion.

Bob S

 

[ask_LXXXVI]

An ideal low pass filter can never be constructed. Because -as you read from wiki-the impulse response extends to both positive and negative infinities.

We can at best try to approximate our practical real life filter as far as possible to the ideal low pass filter.