Hi all, I have the following question that I would really like some help figuring out what I need. <<< start question >>> I have the following signal: xa(t) = xa1(t) + xa2(t) + xa3(t) where: xa1(t) = cos(2*pi*1.5kHz*t) + 2cos(2*pi*2.5kHz*t) xa2(t) = cos(2*pi*0.5kHz*t + pi/3) + 0.5cos(2*pi*3.5kHz*t) xa3(t) = pi^2/3 - 4*cos(2*pi*1kHz*t) + cos(2*pi*2kHz*t) - 4/9*cos(2*pi*3kHz*t) + cos(2*pi*4kHz*t)/4 I need to filter out xa3(t) first then I need to separate xa1(t) and xa2(t). The filters used must not introduce any phase distortion in the passband. <<< end of question >>> Based on the last statement, I know I should use FIR filters so I can meet the "no distortion in the passband" requirement. My first guess is to design a notching filter to filter out xa3(t) but a notching filter is IIR. I know that once I filter out xa3, I can use a BandPassFilter to get xa1 and a StopBandFilter to get xa2. Can anyone shed a little light on this? How can I filter out xa3(t) from this signal without introducing any distortion in the passband? Thanks in advance!
Design filters for the following signal???
Started by ●May 31, 2009
Reply by ●May 31, 20092009-05-31
On May 31, 1:34�pm, "v333k" <v3...@yahoo.com> wrote:> Hi all, > I have the following question that I would really like some help figuring > out what I need. > > <<< start question >>> > > I have the following signal: > xa(t) = xa1(t) + xa2(t) + xa3(t) > > where: > xa1(t) = cos(2*pi*1.5kHz*t) + 2cos(2*pi*2.5kHz*t) > xa2(t) = cos(2*pi*0.5kHz*t + pi/3) + 0.5cos(2*pi*3.5kHz*t) > xa3(t) = pi^2/3 - 4*cos(2*pi*1kHz*t) + cos(2*pi*2kHz*t) - > 4/9*cos(2*pi*3kHz*t) + cos(2*pi*4kHz*t)/4 > > I need to filter out xa3(t) first then I need to separate xa1(t) and > xa2(t). The filters used must not introduce any phase distortion in the > passband. > > <<< end of question >>> > > Based on the last statement, I know I should use FIR filters so I can meet > the "no distortion in the passband" requirement. > > My first guess is to design a notching filter to filter out xa3(t) but a > notching filter is IIR. > > I know that once I filter out xa3, I can use a BandPassFilter to get xa1 > and a StopBandFilter to get xa2. > > Can anyone shed a little light on this? How can I filter out xa3(t) from > this signal without introducing any distortion in the passband? > > Thanks in advance!so this is homework , correct? hint: are the wanted and unwanted signal signals on different frequencies? Mark
Reply by ●May 31, 20092009-05-31
>On May 31, 1:34=A0pm, "v333k" <v3...@yahoo.com> wrote: >> Hi all, >> I have the following question that I would really like some helpfiguring>> out what I need. >> >> <<< start question >>> >> >> I have the following signal: >> xa(t) =3D xa1(t) + xa2(t) + xa3(t) >> >> where: >> xa1(t) =3D cos(2*pi*1.5kHz*t) + 2cos(2*pi*2.5kHz*t) >> xa2(t) =3D cos(2*pi*0.5kHz*t + pi/3) + 0.5cos(2*pi*3.5kHz*t) >> xa3(t) =3D pi^2/3 - 4*cos(2*pi*1kHz*t) + cos(2*pi*2kHz*t) - >> 4/9*cos(2*pi*3kHz*t) + cos(2*pi*4kHz*t)/4 >> >> I need to filter out xa3(t) first then I need to separate xa1(t) and >> xa2(t). The filters used must not introduce any phase distortion inthe>> passband. >> >> <<< end of question >>> >> >> Based on the last statement, I know I should use FIR filters so I canmee=>t >> the "no distortion in the passband" requirement. >> >> My first guess is to design a notching filter to filter out xa3(t) buta>> notching filter is IIR. >> >> I know that once I filter out xa3, I can use a BandPassFilter to getxa1>> and a StopBandFilter to get xa2. >> >> Can anyone shed a little light on this? How can I filter out xa3(t)from>> this signal without introducing any distortion in the passband? >> >> Thanks in advance! > >so this is homework , correct? > >hint: are the wanted and unwanted signal signals on different >frequencies? > >Mark > > >Hi Mark, Thanks! Well, I don't know if you will believe me or not, but I took DSP during undergrad in 2004, and I struggled a bit through it. Now, I am reviewing my notes (trying to remember what I've learned and try to learn some more since my job started requiring me to work on DSP related stuff). So, no - it is not for homework, but yes, it is a question in my homework from my DSP course. Although, your method is quite fine for me. I am not looking for an answer that I can "copy-and-paste". To look into your hint: the signals contains the following frequency components: xa3 - DC, 1kHz, 2kHz, 3kHz, and 4kHz. (unwanted) xa2 - 0.5kHz, and 2.5kHz (wanted) xa1 - 1.5kHz and 2.5kHz (wanted) What do you mean with different frequencies? is it if they contain different frequency components? If so, then my answer is yes, they are on different frequencies, but if I use a notching filter to get rid of xa3, wouldn't that cause distortion and delay in the resulting output? I will be using the resulting output to obtain xa1 and xa2. thanks!
Reply by ●May 31, 20092009-05-31
v333k wrote: ...> Hi Mark, > Thanks! Well, I don't know if you will believe me or not, but I took DSP > during undergrad in 2004, and I struggled a bit through it. Now, I am > reviewing my notes (trying to remember what I've learned and try to learn > some more since my job started requiring me to work on DSP related stuff). > So, no - it is not for homework, but yes, it is a question in my homework > from my DSP course. Although, your method is quite fine for me. I am not > looking for an answer that I can "copy-and-paste". > > To look into your hint: > the signals contains the following frequency components: > xa3 - DC, 1kHz, 2kHz, 3kHz, and 4kHz. (unwanted) > xa2 - 0.5kHz, and 2.5kHz (wanted) > xa1 - 1.5kHz and 2.5kHz (wanted) > > What do you mean with different frequencies? is it if they contain > different frequency components? If so, then my answer is yes, they are on > different frequencies, but if I use a notching filter to get rid of xa3, > wouldn't that cause distortion and delay in the resulting output? I will be > using the resulting output to obtain xa1 and xa2.Bandstop and bandpass filters needn't be FIR. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 31, 20092009-05-31
>v333k wrote: > > ... > >> Hi Mark, >> Thanks! Well, I don't know if you will believe me or not, but I tookDSP>> during undergrad in 2004, and I struggled a bit through it. Now, I am >> reviewing my notes (trying to remember what I've learned and try tolearn>> some more since my job started requiring me to work on DSP relatedstuff).>> So, no - it is not for homework, but yes, it is a question in myhomework>> from my DSP course. Although, your method is quite fine for me. I amnot>> looking for an answer that I can "copy-and-paste". >> >> To look into your hint: >> the signals contains the following frequency components: >> xa3 - DC, 1kHz, 2kHz, 3kHz, and 4kHz. (unwanted) >> xa2 - 0.5kHz, and 2.5kHz (wanted) >> xa1 - 1.5kHz and 2.5kHz (wanted) >> >> What do you mean with different frequencies? is it if they contain >> different frequency components? If so, then my answer is yes, they areon>> different frequencies, but if I use a notching filter to get rid ofxa3,>> wouldn't that cause distortion and delay in the resulting output? Iwill be>> using the resulting output to obtain xa1 and xa2. > >Bandstop and bandpass filters needn't be FIR. > >Jerry >-- >Engineering is the art of making what you want from things you can get. >����������������������������������������������������������������������� >Hi Jerry - my understanding is FIR filters do no introduce distortion in the pass band while IIR filters do. vartan
Reply by ●May 31, 20092009-05-31
v333k wrote: ...> Hi Jerry - my understanding is FIR filters do no introduce distortion in > the pass band while IIR filters do.If you mean phase distortion, that's correct, and you wrote it earlier. So make all your filters symmetric FIRs. Jerry -- Engineering is the art of making what you want from things you can get.
Reply by ●June 1, 20092009-06-01
On May 31, 4:47�pm, Jerry Avins <j...@ieee.org> wrote:> v333k wrote: > > � �... > > > Hi Jerry - my understanding is FIR filters do no introduce distortion in > > the pass band while IIR filters do. > > If you mean phase distortion, that's correct, and you wrote it earlier. > So make all your filters symmetric FIRs. > > Jerry > -- > Engineering is the art of making what you want from things you can get.All he needs is a simple multiband design done with a Parks McClellan algorithm. Clay
Reply by ●June 1, 20092009-06-01
clay@claysturner.com wrote: > On May 31, 4:47 pm, Jerry Avins <j...@ieee.org> wrote: >> v333k wrote: >> >> ... >> >>> Hi Jerry - my understanding is FIR filters do no introduce distortion in >>> the pass band while IIR filters do. >> If you mean phase distortion, that's correct, and you wrote it earlier. >> So make all your filters symmetric FIRs. >> >> Jerry >> -- >> Engineering is the art of making what you want from things you can get. > > > All he needs is a simple multiband design done with a Parks McClellan > algorithm. Yes, but first the unwarranted assumptions need to be cleared away. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●June 3, 20092009-06-03
>clay@claysturner.com wrote: > > On May 31, 4:47 pm, Jerry Avins <j...@ieee.org> wrote: > >> v333k wrote: > >> > >> ... > >> > >>> Hi Jerry - my understanding is FIR filters do no introduce >distortion in > >>> the pass band while IIR filters do. > >> If you mean phase distortion, that's correct, and you wrote itearlier.> >> So make all your filters symmetric FIRs. > >> > >> Jerry > >> -- > >> Engineering is the art of making what you want from things you canget.> > > > > > All he needs is a simple multiband design done with a Parks McClellan > > algorithm. > >Yes, but first the unwarranted assumptions need to be cleared away. > >Jerry >-- >Engineering is the art of making what you want from things you can get. >����������������������������������������������������������������������� >Hi Clay/Jerry, I guess to reiterate my confusion (in simpler form), if I need to assure no distortion in the passband, and I need a notching filter, will this not work? Is there a problem with this question to begin with? thanks again Vartan
Reply by ●June 3, 20092009-06-03
v333k wrote:>> clay@claysturner.com wrote: >>> On May 31, 4:47 pm, Jerry Avins <j...@ieee.org> wrote: >>>> v333k wrote: >>>> >>>> ... >>>> >>>>> Hi Jerry - my understanding is FIR filters do no introduce >> distortion in >>>>> the pass band while IIR filters do. >>>> If you mean phase distortion, that's correct, and you wrote it > earlier. >>>> So make all your filters symmetric FIRs. >>>> >>>> Jerry >>>> -- >>>> Engineering is the art of making what you want from things you can > get. >>> >>> All he needs is a simple multiband design done with a Parks McClellan >>> algorithm. >> Yes, but first the unwarranted assumptions need to be cleared away. >> >> Jerry >> -- >> Engineering is the art of making what you want from things you can get. >> > > Hi Clay/Jerry, > I guess to reiterate my confusion (in simpler form), if I need to assure > no distortion in the passband, and I need a notching filter, will this not > work? Is there a problem with this question to begin with?I'm confused. You "need to assure no distortion in the passband" -- I assume you mean phase distortion -- and you want to use notching (i.e. band reject) filters. You now know that symmetric FIRs can do the job. What is your question? Jerry -- Engineering is the art of making what you want from things you can get.
