Hi,
Transition band is defined as area between pass band and
stop band frequency of the filter. I have filter spectrum in Matlab and
like to calculate slope of transition band.
Y-axis of plot has magnitude (DB) and x-axis has normalized frequency. To
calculate slope, should I use -(y2-y1)/(x2-x1) where (x1, y1) are Cartesian
coordinate points at pass band and (x2, y2) are coordinate points at stop
band.
am I using the right technique to calculate the slope of transition band
??
Hope someone will answer me.
Regards,
Sridhar
This message was sent using the Comp.DSP web interface on
www.DSPRelated.com
Slope of Transition Band
Started by ●April 7, 2005
Reply by ●April 7, 20052005-04-07
"sridhargadda" <sridhargadda@yahoo.com> wrote in message news:8aedncyQ57yvsMjfRVn-sg@giganews.com...> > Hi, > > Transition band is defined as area between pass band and > stop band frequency of the filter. I have filter spectrum in Matlab and > like to calculate slope of transition band. > > Y-axis of plot has magnitude (DB) and x-axis has normalized frequency. To > calculate slope, should I use -(y2-y1)/(x2-x1) where (x1, y1) are > Cartesian > coordinate points at pass band and (x2, y2) are coordinate points at stop > band. > > am I using the right technique to calculate the slope of transition band > ??That's certainly one way. I'm not trying to confuse you - but one can't be sure. Much depends on your objective and context. "Slope" can be defined in a number of ways. In fact, one way to think of "slope" is in graphical terms. If you do that then you can imagine all sorts of x-y axes and plots. - it could be the maximum slope which may occur somewhere in the middle of the transition band or it may occur at the edge of the stop band if there's a zero nearby. - it could be measured as you've done as the transition width divided by the amplitude change (which might be very close to 1.0 depending on how you decide to define amplitude). - it could be measured in absolute amplitude terms or in dB - it could be measured in linear frequency or in log frequency. - the four methods above could be expressed such as %/Hz or dB/octave (linear/linear or log/log) - thus my comment about "graphical". Fred
Reply by ●April 7, 20052005-04-07
Fred Marshall wrote:> "sridhargadda" <sridhargadda@yahoo.com> wrote in message > news:8aedncyQ57yvsMjfRVn-sg@giganews.com... > >>Hi, >> >> Transition band is defined as area between pass band and >>stop band frequency of the filter. I have filter spectrum in Matlab and >>like to calculate slope of transition band. >> >>Y-axis of plot has magnitude (DB) and x-axis has normalized frequency. To >>calculate slope, should I use -(y2-y1)/(x2-x1) where (x1, y1) are >>Cartesian >>coordinate points at pass band and (x2, y2) are coordinate points at stop >>band. >> >>am I using the right technique to calculate the slope of transition band >>?? > > > That's certainly one way. I'm not trying to confuse you - but one can't be > sure. Much depends on your objective and context. > > "Slope" can be defined in a number of ways. In fact, one way to think of > "slope" is in graphical terms. If you do that then you can imagine all > sorts of x-y axes and plots. > - it could be the maximum slope which may occur somewhere in the middle of > the transition band or it may occur at the edge of the stop band if there's > a zero nearby. > - it could be measured as you've done as the transition width divided by the > amplitude change (which might be very close to 1.0 depending on how you > decide to define amplitude). > - it could be measured in absolute amplitude terms or in dB > - it could be measured in linear frequency or in log frequency. > - the four methods above could be expressed such as %/Hz or dB/octave > (linear/linear or log/log) - thus my comment about "graphical". > > FredA measure of slope used in IF filters is skirt selectivity. From Rockwell/Collins mechanical filter description: "Skirt selectivity is specified as shape factor, which is the ratio ratio (bandwidth 60 db below peak) / (bandwidth 6 db below peak)." For analog R-C and L-C filters, (20 dB)*(number of zeros)/decade is the slope. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 8, 20052005-04-08
"Jerry Avins" <jya@ieee.org> wrote in message news:GeWdnVUXeM6kRsjfRVn-2w@rcn.net...> Fred Marshall wrote: >> "sridhargadda" <sridhargadda@yahoo.com> wrote in message >> news:8aedncyQ57yvsMjfRVn-sg@giganews.com... >> >>>Hi, >>> >>> Transition band is defined as area between pass band and >>>stop band frequency of the filter. I have filter spectrum in Matlab and >>>like to calculate slope of transition band. >>> >>>Y-axis of plot has magnitude (DB) and x-axis has normalized frequency. To >>>calculate slope, should I use -(y2-y1)/(x2-x1) where (x1, y1) are >>>Cartesian >>>coordinate points at pass band and (x2, y2) are coordinate points at stop >>>band. >>> >>>am I using the right technique to calculate the slope of transition band >>>?? >> >> >> That's certainly one way. I'm not trying to confuse you - but one can't >> be sure. Much depends on your objective and context. >> >> "Slope" can be defined in a number of ways. In fact, one way to think of >> "slope" is in graphical terms. If you do that then you can imagine all >> sorts of x-y axes and plots. >> - it could be the maximum slope which may occur somewhere in the middle >> of the transition band or it may occur at the edge of the stop band if >> there's a zero nearby. >> - it could be measured as you've done as the transition width divided by >> the amplitude change (which might be very close to 1.0 depending on how >> you decide to define amplitude). >> - it could be measured in absolute amplitude terms or in dB >> - it could be measured in linear frequency or in log frequency. >> - the four methods above could be expressed such as %/Hz or dB/octave >> (linear/linear or log/log) - thus my comment about "graphical". >> >> Fred > > A measure of slope used in IF filters is skirt selectivity. From > Rockwell/Collins mechanical filter description: > > "Skirt selectivity is specified as shape factor, which is the ratio > ratio (bandwidth 60 db below peak) / (bandwidth 6 db below peak)." > > For analog R-C and L-C filters, (20 dB)*(number of zeros)/decade is the > slope. > > JerryYes, I might have mentioned that as well and it's good that you did! Log amplitude and log frequency have a linear slope for such filters after the initial roll off - or is it that it's just asymptotic to a straight line? The latter I think... Handy nonetheless and a very good approximation after what? an octave or so? Fred
Reply by ●April 8, 20052005-04-08
> >Hi, > > Transition band is defined as area between pass band and >stop band frequency of the filter. I have filter spectrum in Matlab and >like to calculate slope of transition band. > > Y-axis of plot has magnitude (DB) and x-axis has normalized frequency.To>calculate slope, should I use -(y2-y1)/(x2-x1) where (x1, y1) areCartesian>coordinate points at pass band and (x2, y2) are coordinate points atstop>band. > > am I using the right technique to calculate the slope of transitionband>?? > > Hope someone will answer me. > >Regards, > >Sridhar > >This message was sent using the Comp.DSP web interface on >www.DSPRelated.comMy filter reponse has an arbitrary shape (FIR Filter). For straight line delta Y/delta X can give slope value. I am confuse how can I calculate the slope for an arbitrary shape filter response in transition band. How should I calculate slope values like dB/octave or db/decade for an arbitrary shape reponse ?? any ideas please ?? With regards, Sridhar This message was sent using the Comp.DSP web interface on www.DSPRelated.com
Reply by ●April 8, 20052005-04-08
Fred Marshall wrote:> ... Log > amplitude and log frequency have a linear slope for such filters after the > initial roll off - or is it that it's just asymptotic to a straight line? > The latter I think... Handy nonetheless and a very good approximation after > what? an octave or so?The beauty of the amplitude portion of a Bode plot is that the entire response curve of many networks can be approximated by straight-lines asymptotes, and that the intersections of the asymptotes are the poles and zeros of the transfer function. With practice, it is possible to read the transfer function from the plot with reasonable accuracy. To draw the plot, I first sketch in the asymptotes, then "round up" the corners. For a single pole or zero, the slope changes by 20 dB/decade. At the corner, the actual response is 3 dB removed from the intersection. An octave away on either side, the actual response is 1 dB away. Three octaves (all right: a decade) away, the departure from the asymptote is zilch. When corner frequencies are closer together than a decade, it is good practice to to sketch each as though the other didn't exist, then (assuming both are of the same order) draw their average. Except for the slight wiggliness that (my) hand drawing makes inevitable, Bode plots drawn this way don't differ from computer-generated curves. Similar rules apply to the phase plots: 90 degrees at a single corner, 26 degrees at an octave, 5.7 degrees at a decade. Superposition applies. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 8, 20052005-04-08
sridhargadda wrote:>>Hi, >> >> Transition band is defined as area between pass band and >>stop band frequency of the filter. I have filter spectrum in Matlab and >>like to calculate slope of transition band. >> >>Y-axis of plot has magnitude (DB) and x-axis has normalized frequency. > > To > >>calculate slope, should I use -(y2-y1)/(x2-x1) where (x1, y1) are > > Cartesian > >>coordinate points at pass band and (x2, y2) are coordinate points at > > stop > >>band. >> >>am I using the right technique to calculate the slope of transition > > band > >>?? >> >> Hope someone will answer me. >> >>Regards, >> >>Sridhar >> >>This message was sent using the Comp.DSP web interface on >>www.DSPRelated.com > > > My filter reponse has an arbitrary shape (FIR Filter). For straight line > delta Y/delta X can give slope value. I am confuse how can I calculate the > slope for an arbitrary shape filter response in transition band. > > How should I calculate slope values like dB/octave or db/decade for an > arbitrary shape reponse ?? > > any ideas please ??A. Divide the transition's change in level by its width. OR B. Draw the transition region. Lay a ruler on the plot for best fit with the curve. The slope of the ruler expressed in the units of the plot is the number you want. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 8, 20052005-04-08
"sridhargadda" <sridhargadda@yahoo.com> wrote in message news:2bOdnaPDkp4q3svfRVn-tA@giganews.com...> > >>Hi, >> >> Transition band is defined as area between pass band and >>stop band frequency of the filter. I have filter spectrum in Matlab and >>like to calculate slope of transition band. >> >> Y-axis of plot has magnitude (DB) and x-axis has normalized frequency. > To >>calculate slope, should I use -(y2-y1)/(x2-x1) where (x1, y1) are > Cartesian >>coordinate points at pass band and (x2, y2) are coordinate points at > stop >>band. >> >> am I using the right technique to calculate the slope of transition > band >>?? >> >> Hope someone will answer me. >> >>Regards, >> >>Sridhar >> >>This message was sent using the Comp.DSP web interface on >>www.DSPRelated.com > > My filter reponse has an arbitrary shape (FIR Filter). For straight line > delta Y/delta X can give slope value. I am confuse how can I calculate the > slope for an arbitrary shape filter response in transition band. > > How should I calculate slope values like dB/octave or db/decade for an > arbitrary shape reponse ?? > > any ideas please ?? > > With regards, > > Sridhar >Sridhar, Well, first, a "slope" defines a "straight line" or at least a straight line segment of arbitrary shortness. So, if all you want is slope then all you need are two points defining a straight line. You can pick the points on a grid of your choice. I think that's what I said before...... Maybe your issue is more fundamental? You need to start with the frequency response of the filter. You need to select two points on that response .... or you might take the first derivative with respect to frequency of an analytical expression of the frequency amplitude response and use its maximum value? or a value in the known transition region or..... Fred
Reply by ●April 8, 20052005-04-08
"Jerry Avins" <jya@ieee.org> wrote in message news:w4mdnQoICf-SHcvfRVn-rA@rcn.net...> Fred Marshall wrote: > > > ... Log > > amplitude and log frequency have a linear slope for such filters after the > > initial roll off - or is it that it's just asymptotic to a straight line? > > The latter I think... Handy nonetheless and a very good approximation after > > what? an octave or so? > > The beauty of the amplitude portion of a Bode plot is that the entire > response curve of many networks can be approximated by straight-lines > asymptotes, and that the intersections of the asymptotes are the poles > and zeros of the transfer function. With practice, it is possible to > read the transfer function from the plot with reasonable accuracy. > > To draw the plot, I first sketch in the asymptotes, then "round up" the > corners. For a single pole or zero, the slope changes by 20 dB/decade. > At the corner, the actual response is 3 dB removed from the > intersection. An octave away on either side, the actual response is 1 dB > away. Three octaves (all right: a decade) away, the departure from the > asymptote is zilch. > > When corner frequencies are closer together than a decade, it is good > practice to to sketch each as though the other didn't exist, then > (assuming both are of the same order) draw their average. Except for the > slight wiggliness that (my) hand drawing makes inevitable, Bode plots > drawn this way don't differ from computer-generated curves. > > Similar rules apply to the phase plots: 90 degrees at a single corner, > 26 degrees at an octave, 5.7 degrees at a decade. Superposition applies.We learned how to draw such Bode plots in one of my early circuits classes (~1991). They even discussed modifying the rounding of the corners based on the Q or damping factor of the complex pole, i.e. use a certain corner shape for Q = 1.0, etc.. It seems a bit quaint now with all the easy-to-use computer-based tools, but still is valuable for quick approximations (and sanity-checking those fancy computer results). -- Jon Harris SPAM blocked e-mail address in use. Replace the ANIMAL with 7 to reply.
Reply by ●April 8, 20052005-04-08
"sridhargadda" <sridhargadda@yahoo.com> wrote in message news:2bOdnaPDkp4q3svfRVn-tA@giganews.com...> > > >Hi, > > > > Transition band is defined as area between pass band and > >stop band frequency of the filter. I have filter spectrum in Matlab and > >like to calculate slope of transition band. > > > > Y-axis of plot has magnitude (DB) and x-axis has normalized frequency. > To > >calculate slope, should I use -(y2-y1)/(x2-x1) where (x1, y1) are > Cartesian > >coordinate points at pass band and (x2, y2) are coordinate points at > stop > >band. > > > > am I using the right technique to calculate the slope of transition > band > >?? > > > > Hope someone will answer me. > > My filter reponse has an arbitrary shape (FIR Filter). For straight line > delta Y/delta X can give slope value. I am confuse how can I calculate the > slope for an arbitrary shape filter response in transition band. > > How should I calculate slope values like dB/octave or db/decade for an > arbitrary shape reponse ??How can you calculate a slope of an arbitrary shaped curve? I suppose you could use the maximum slope, minimum slope, average slope, the slope as a function of frequency, or ??? After you decide that, then the rest should be easy given the definition you already know for slope.
