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<blockquote data-quote="Peter Morris" data-source="post: 147691" data-attributes="member: 652"><p>Re: FIR filters</p><p></p><p></p><p></p><p><span style="font-size: 12px"><span style="color: #000000"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'">Yes there will be pre and post ringing and it will be equal and opposite in the pass bands. There are ways of designing the filters to minimize this to below the point of audibility, but with everything there are some compromises.</span></span></span></span></span></span></p><p><span style="font-size: 12px"><span style="color: #000000"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"></span></span></span></span></span></span></p><p><span style="font-size: 12px"><span style="color: #000000"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'">A couple of Tims links touch on this issue. Here is another link that may be of interest.</span></span></span></span></span></span></p><p><span style="font-size: 12px"><span style="color: #000000"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"></span></span></span></span></span></span></p><p><span style="font-size: 12px"><span style="color: #000000"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"><span style="font-family: 'Calibri'"></span></span></span></span></span></span><a href="http://www.resonessencelabs.com/digital-filters/" target="_blank">http://www.resonessencelabs.com/digital-filters/</a></p><p><em>"The second phenomenon present in linear phase FIR filters is sometimes called “pre-ringing”. It is a tendency of the filter to output a small signal of increasing amplitude just prior to the main “step” of the signal, and then after that step has passed, ring a little at the new output level. The ringing after the step has passed is common in analog filters as well, and is due to the high Q that some filters exhibit.</em></p><p><em></em></p><p><em>Indeed this is the origin of the word “ringing”: having struck a bell with a hammer we expect it to ring a little thereafter. Pre-ringing of the symmetric FIR filter seems bizarre: it is as though the bell knows when you are going to strike it, and makes a little ringing sound before it is hit. This is very counter intuitive, and a great concern to many audiophiles, who therefore seek a filter that has no pre-ringing.</em></p><p><em></em></p><p><em>This however, cannot be achieved to perfection with linear phase filters, hence any filter designed to suppress pre-ringing completely, is dispersive. So called “Minimum Phase” filters (sometimes called “Minimum Delay” filters) are those filters that are designed to show virtually no pre-ringing (and consequently they tend to have low group delay because the maximum values in the impulse response are near the beginning of the filter). They do not have linear phase, and they consequently have dispersion.</em></p><p><em></em></p><p><em>A compromise is possible: a filter can be designed as linear phase, and hence having a symmetrical impulse response, but the coefficient list can be ‘shaped’ by what is called a ‘window’ function. This window function suppresses pre-ringing to a certain degree, but the more it suppresses pre-ringing, the more it compromises the action of the filter. That is, the more the filter fails to block the signals it is trying to stop. Such filters that apply window functions to filter coefficients in order to reduce pre-ringing are sometimes called Apodizing filters. The word means “to remove the foot”.</em></p><p><em></em></p><p><em>All the various trade-offs discussed here, but particularly Apodizing filters, show us a fundamental relationship: as a filter is designed to be optimum in the time domain, it cannot be optimum in the frequency domain. The two are related in a very fundamental way, it is the same relationship that governs the whole world of physics: Heisenberg’s Uncertainty principle that says if you know the particles position exactly, you cannot know its momentum, or vice-versa, is because mathematically one (the position for example) is the Fourier transform of the other (momentum for example) and as the “width” in position becomes better defined, the “width” in the momentum domain, being the Fourier transform, becomes less well defined."</em></p></blockquote><p></p>
[QUOTE="Peter Morris, post: 147691, member: 652"] Re: FIR filters [SIZE=3][COLOR=#000000][FONT=Calibri][FONT=Calibri][FONT=Calibri][FONT=Calibri]Yes there will be pre and post ringing and it will be equal and opposite in the pass bands. There are ways of designing the filters to minimize this to below the point of audibility, but with everything there are some compromises. A couple of Tims links touch on this issue. Here is another link that may be of interest. [/FONT][/FONT][/FONT][/FONT][/COLOR][/SIZE][URL]http://www.resonessencelabs.com/digital-filters/[/URL] [I]"The second phenomenon present in linear phase FIR filters is sometimes called “pre-ringing”. It is a tendency of the filter to output a small signal of increasing amplitude just prior to the main “step” of the signal, and then after that step has passed, ring a little at the new output level. The ringing after the step has passed is common in analog filters as well, and is due to the high Q that some filters exhibit. Indeed this is the origin of the word “ringing”: having struck a bell with a hammer we expect it to ring a little thereafter. Pre-ringing of the symmetric FIR filter seems bizarre: it is as though the bell knows when you are going to strike it, and makes a little ringing sound before it is hit. This is very counter intuitive, and a great concern to many audiophiles, who therefore seek a filter that has no pre-ringing. This however, cannot be achieved to perfection with linear phase filters, hence any filter designed to suppress pre-ringing completely, is dispersive. So called “Minimum Phase” filters (sometimes called “Minimum Delay” filters) are those filters that are designed to show virtually no pre-ringing (and consequently they tend to have low group delay because the maximum values in the impulse response are near the beginning of the filter). They do not have linear phase, and they consequently have dispersion. A compromise is possible: a filter can be designed as linear phase, and hence having a symmetrical impulse response, but the coefficient list can be ‘shaped’ by what is called a ‘window’ function. This window function suppresses pre-ringing to a certain degree, but the more it suppresses pre-ringing, the more it compromises the action of the filter. That is, the more the filter fails to block the signals it is trying to stop. Such filters that apply window functions to filter coefficients in order to reduce pre-ringing are sometimes called Apodizing filters. The word means “to remove the foot”. All the various trade-offs discussed here, but particularly Apodizing filters, show us a fundamental relationship: as a filter is designed to be optimum in the time domain, it cannot be optimum in the frequency domain. The two are related in a very fundamental way, it is the same relationship that governs the whole world of physics: Heisenberg’s Uncertainty principle that says if you know the particles position exactly, you cannot know its momentum, or vice-versa, is because mathematically one (the position for example) is the Fourier transform of the other (momentum for example) and as the “width” in position becomes better defined, the “width” in the momentum domain, being the Fourier transform, becomes less well defined."[/I] [/QUOTE]
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