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

In summary: However, the closer we get the more distortion we will experience. This is because for every dB of attenuation there is a corresponding 6.6 degrees of phase retardation.
  • #1
boredaxel
19
0
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
 
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  • #2
boredaxel said:
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).
 
  • #3
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
 
  • #4
Pretty much. The more taps you pay for, the sharper the edge :-)
 
  • #5
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.
 
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  • #6
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
 
  • #7
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.
 

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

1. What is an ideal low pass filter?

An ideal low pass filter is an electronic circuit that allows low frequency signals to pass through while blocking high frequency signals. It is used to remove unwanted noise or distortions from a signal.

2. Why can't an ideal low pass filter be real?

An ideal low pass filter is a theoretical concept and cannot be achieved in real life due to various limitations such as resistance, capacitance, and inductance in electronic components. These components have inherent properties that create limitations on the performance of the filter.

3. What are the main characteristics of an ideal low pass filter?

The main characteristics of an ideal low pass filter include a perfectly flat frequency response, no phase shift, no attenuation of low frequencies, and infinite attenuation of high frequencies.

4. How is an ideal low pass filter different from a real low pass filter?

An ideal low pass filter has perfect performance with no limitations, while a real low pass filter has practical limitations due to the characteristics of electronic components. This results in a non-flat frequency response, phase shift, and attenuation of low frequencies in a real low pass filter.

5. Can an ideal low pass filter be approximated in real life?

Yes, an ideal low pass filter can be approximated in real life by using various techniques such as using higher quality components, cascading multiple filters, and implementing digital filters. However, a perfectly ideal low pass filter cannot be achieved.

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