In graphical convolution either the system impulse response h(n) or the input x(n) is folded/flipped and then slid across the other to determine the system response y(n). Why is this so? I have reasoned this as being necessary to align the "present" input to the "present" output of the system response to get the correct system time output. Is this reasoning valid? None of the several signals and systems texts I have consulted simply enumerate the mechanical steps without any further clarification. Can someone please help me with this vexation. Thanks
CONVOLUTION
Started by ●May 1, 2009
Reply by ●May 1, 20092009-05-01
On 1 Mai, 15:02, "AHSHAH" <azharsha...@yahoo.com> wrote:> In graphical convolution either the system impulse response h(n) or the > input x(n) is folded/flipped and then slid across the other to determine > the system response y(n). Why is this so? I have reasoned this as being > necessary to align the "present" input to the "present" output of the > system response to get the correct system time output. Is this reasoning > valid? None of the several signals and systems texts I have consulted > simply enumerate the mechanical steps without any further clarification.The best explanation offered so far on comp.dsp is this one: http://groups.google.no/group/comp.dsp/msg/f99bcd270cc776d8?hl=no& The convolution sum formula is derived from the most basic propertes of an LTI system. If you do that, the flipping is one way of interpreting the resulting formula. Rune
Reply by ●May 1, 20092009-05-01
Rune Allnor wrote:> On 1 Mai, 15:02, "AHSHAH" <azharsha...@yahoo.com> wrote: >> In graphical convolution either the system impulse response h(n) or >> the input x(n) is folded/flipped and then slid across the other to >> determine the system response y(n). Why is this so? I have reasoned >> this as being necessary to align the "present" input to the >> "present" output of the system response to get the correct system >> time output. Is this reasoning valid? None of the several signals >> and systems texts I have consulted simply enumerate the mechanical >> steps without any further clarification. >Here's my take on it: Start with the impulse response y(t) or the unit sample response y(n) of the system. We usually plot these with time or index increasing to the right. So, the initial part starts on the left. Now consider a signal. We usually plot signals the same way. But, when we pass a signal through a system it is the "first part" of the signal that kicks off the "first part" of the system response. The point of the convolution is to calculate the output of the system for a particular signal. Of course this requires using the system response in the calculation. So, putting it all together, we need to operate on the first part of the signal with the first part of the system response and next the "second part" of the signal on the first part of the system response while operating on the "second part" of the system response with the first part of the signal and so on. If this is clear then the reason for flipping should be clear enough. You have to butt the beginnings together to start the calculation. The system doesn't really have a "present" except when there are initial conditions. Generally the system is considered to be at rest when the input is applied. Thus whatever state the system takes is due to the signal - so the system's present state is completely dependent on the present state of the input and *its* history - the system characteristics affect what the system state becomes but only due to the input. It might also help to consider superposition which works very nicely in linear time-invariant systems: - first I put in this little signal piece. - then I put in another little signal piece. - etc. the system responds first to one and then the other while still responding to the first ... and so on. The responses to the two are superimposed. The graphical method helps to envision how this works I do believe. Fred
Reply by ●May 2, 20092009-05-02
Rune Allnor <allnor@tele.ntnu.no> writes:> On 1 Mai, 15:02, "AHSHAH" <azharsha...@yahoo.com> wrote: >> In graphical convolution either the system impulse response h(n) or the >> input x(n) is folded/flipped and then slid across the other to determine >> the system response y(n). Why is this so? I have reasoned this as being >> necessary to align the "present" input to the "present" output of the >> system response to get the correct system time output. Is this reasoning >> valid? None of the several signals and systems texts I have consulted >> simply enumerate the mechanical steps without any further clarification. > > The best explanation offered so far on comp.dsp is this one: > > http://groups.google.no/group/comp.dsp/msg/f99bcd270cc776d8?hl=no&I agree, Rune, that this is the best, and simplest, illustration of convolution I know, and it answers the OP's question nicely. I'll bet Dilip is one of the best college propfessors at any school today, judging from this and the many other helpful and intelligent answers he has provided here in the past. -- % Randy Yates % "So now it's getting late, %% Fuquay-Varina, NC % and those who hesitate %%% 919-577-9882 % got no one..." %%%% <yates@ieee.org> % 'Waterfall', *Face The Music*, ELO http://www.digitalsignallabs.com
Reply by ●May 2, 20092009-05-02
On May 2, 2:23�pm, Randy Yates <ya...@ieee.org> wrote:> Rune Allnor <all...@tele.ntnu.no> writes: > > On 1 Mai, 15:02, "AHSHAH" <azharsha...@yahoo.com> wrote: > >> In graphical convolution either the system impulse response h(n) or the > >> input x(n) is folded/flipped and then slid across the other to determine > >> the system response y(n). Why is this so? I have reasoned this as being > >> necessary to align the "present" input to the "present" output of the > >> system response to get the correct system time output. Is this reasoning > >> valid? None of the several signals and systems texts I have consulted > >> simply enumerate the mechanical steps without any further clarification. > > > The best explanation offered so far on comp.dsp is this one: > > >http://groups.google.no/group/comp.dsp/msg/f99bcd270cc776d8?hl=no& > > I agree, Rune, that this is the best, and simplest, illustration of > convolution I know, and it answers the OP's question nicely. > > I'll bet Dilip is one of the best college propfessors at any > school today, judging from this and the many other helpful > and intelligent answers he has provided here in the past. > -- > % �Randy Yates � � � � � � � � �% "So now it's getting late, > %% Fuquay-Varina, NC � � � � � �% � �and those who hesitate > %%% 919-577-9882 � � � � � � � �% � �got no one..." > %%%% <ya...@ieee.org> � � � � � % 'Waterfall', *Face The Music*, ELOhttp://www.digitalsignallabs.comI concur. He is one of those who makes comp.dsp worthwhile. John
Reply by ●May 2, 20092009-05-02
John wrote:> On May 2, 2:23 pm, Randy Yates <ya...@ieee.org> wrote: >> Rune Allnor <all...@tele.ntnu.no> writes: >>> On 1 Mai, 15:02, "AHSHAH" <azharsha...@yahoo.com> wrote: >>>> In graphical convolution either the system impulse response h(n) or the >>>> input x(n) is folded/flipped and then slid across the other to determine >>>> the system response y(n). Why is this so? I have reasoned this as being >>>> necessary to align the "present" input to the "present" output of the >>>> system response to get the correct system time output. Is this reasoning >>>> valid? None of the several signals and systems texts I have consulted >>>> simply enumerate the mechanical steps without any further clarification. >>> The best explanation offered so far on comp.dsp is this one: >>> http://groups.google.no/group/comp.dsp/msg/f99bcd270cc776d8?hl=no& >> I agree, Rune, that this is the best, and simplest, illustration of >> convolution I know, and it answers the OP's question nicely. >> >> I'll bet Dilip is one of the best college propfessors at any >> school today, judging from this and the many other helpful >> and intelligent answers he has provided here in the past. >> -- >> % Randy Yates % "So now it's getting late, >> %% Fuquay-Varina, NC % and those who hesitate >> %%% 919-577-9882 % got no one..." >> %%%% <ya...@ieee.org> % 'Waterfall', *Face The Music*, ELOhttp://www.digitalsignallabs.com > > I concur. He is one of those who makes comp.dsp worthwhile.One of my minor regrets is that I didn't know he was at Princeton until he wasn't any more. I would like to have met him in person. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 5, 20092009-05-05
>On 1 Mai, 15:02, "AHSHAH" <azharsha...@yahoo.com> wrote: >> In graphical convolution either the system impulse response h(n) orthe>> input x(n) is folded/flipped and then slid across the other todetermine>> the system response y(n). Why is this so? I have reasoned this asbeing>> necessary to align the "present" input to the "present" output of the >> system response to get the correct system time output. Is thisreasoning>> valid? None of the several signals and systems texts I have consulted >> simply enumerate the mechanical steps without any furtherclarification.> >The best explanation offered so far on comp.dsp is this one: > >http://groups.google.no/group/comp.dsp/msg/f99bcd270cc776d8?hl=no& > >The convolution sum formula is derived from the most basic >propertes of an LTI system. If you do that, the flipping >is one way of interpreting the resulting formula. > >Rune >Hi Rune, The convolution example illustrated at the web site suggested by you has helped in clearing the confusion. Thanks a lot for your help. Regards Azhar
