DFT VS DTFT

Started by praveen July 21, 2003
Hello,

I wanted to know the difference between discrete fourier transform and
discrete time fourier transform.


waiting for reply
praveen
"praveen" <praveenkumar1979@rediffmail.com> wrote in message
news:ff8a3afb.0307210538.423b953@posting.google.com...
> Hello, > > I wanted to know the difference between discrete fourier transform and > discrete time fourier transform.
You can consider four versions of the 1-dimensional Fourier Transform: Time Frequency Continuous Continuous Discrete Continuous Continuous Discrete Discrete Discrete DTFT generally means the Discrete/Continous version. If you Google on DTFT, you will find the Discrete/Continuous version. The time series is infinite discrete and the frequency function is continuous, periodic. So, a discrete sum is used in the transform to go from time to frequency and a continous integral over one period is used in the transform to go from frequency to time. Fred
praveen <praveenkumar1979@rediffmail.com> wrote:
> Hello, > > I wanted to know the difference between discrete fourier transform and > discrete time fourier transform. > > > waiting for reply > praveen
The DTFT is aperiodic-discrete and the DFT is periodic-discrete. Tom --
Tom <T.Otermans_REMOVE_THIS_@home.nl> wrote in message
news:<slrnbho1p5.aeh.T.Otermans_REMOVE_THIS@noritake.basement>...
> praveen <praveenkumar1979@rediffmail.com> wrote: > > Hello, > > > > I wanted to know the difference between discrete fourier transform and > > discrete time fourier transform. > > > > > > waiting for reply > > praveen > > The DTFT is aperiodic-discrete and the DFT is periodic-discrete. > > > Tom > > --
Can DFT be viewed as sampled version of DTFT and hence it is periodic? I am not sure about this but intuitively it is easier to think so. -Nithin
"Tom" <T.Otermans_REMOVE_THIS_@home.nl> wrote in message
news:slrnbho1p5.aeh.T.Otermans_REMOVE_THIS@noritake.basement...
> praveen <praveenkumar1979@rediffmail.com> wrote: > > Hello, > > > > I wanted to know the difference between discrete fourier transform and > > discrete time fourier transform. > > > > > > waiting for reply > > praveen > > The DTFT is aperiodic-discrete and the DFT is periodic-discrete.
Tom, How can that be for the DTFT case? That is, if I understand what domains you're referring to.... I would have said: discrete <-> continous periodic for DTFT where <-> denotes transform pair. and discrete periodic <-> discrete periodic for DFT. Fred
Fred Marshall wrote:
> "Tom" <T.Otermans_REMOVE_THIS_@home.nl> wrote in message > news:slrnbho1p5.aeh.T.Otermans_REMOVE_THIS@noritake.basement... > >>praveen <praveenkumar1979@rediffmail.com> wrote: >> >>>Hello, >>> >>>I wanted to know the difference between discrete fourier transform and >>>discrete time fourier transform. >>> >>> >>>waiting for reply >>>praveen >> >>The DTFT is aperiodic-discrete and the DFT is periodic-discrete. > > > Tom, > > How can that be for the DTFT case? That is, if I understand what domains > you're referring to.... > I would have said: discrete <-> continous periodic for DTFT > where <-> denotes transform pair. > and > discrete periodic <-> discrete periodic for DFT. > > Fred > >
Fred, The Z transform is continuous for any finite length sequence. There are formulas relating the DFT and the Z transform in Oppenheim. The chirp Z transform is a valid DFT, isn't it? Stan
"Stan Pawlukiewicz" <stanp@nospam_mitre.org> wrote in message
news:bfjrv8$4rm$1@newslocal.mitre.org...
> Fred Marshall wrote: > > "Tom" <T.Otermans_REMOVE_THIS_@home.nl> wrote in message > > news:slrnbho1p5.aeh.T.Otermans_REMOVE_THIS@noritake.basement... > > > >>praveen <praveenkumar1979@rediffmail.com> wrote: > >> > >>>Hello, > >>> > >>>I wanted to know the difference between discrete fourier transform
and
> >>>discrete time fourier transform. > >>> > >>> > >>>waiting for reply > >>>praveen > >> > >>The DTFT is aperiodic-discrete and the DFT is periodic-discrete. > > > > > > Tom, > > > > How can that be for the DTFT case? That is, if I understand what
domains
> > you're referring to.... > > I would have said: discrete <-> continous periodic for DTFT > > where <-> denotes transform pair. > > and > > discrete periodic <-> discrete periodic for DFT. > > > > Fred > > > > > Fred, > The Z transform is continuous for any finite length sequence. > There are formulas relating the DFT and the Z transform in Oppenheim. > The chirp Z transform is a valid DFT, isn't it?
Stan, You probably know better than I. It appears so from a quick look. Not something I've dealt with directly. Fred
All I know about CTFT, DTFT, and DFT

Given a continous signal x[t}
and take the fourier transfrom we got CTFT X(jw).
Notice: X(jw) is a continuous spectrum.

Given a discrete sequence f[n] 
and take the fourier transform we got DTFT F(e^jw).
Notice: X(e^jw) is also a continuous spectrum.

If we take the discrete samples of the continous spectrum DTFT X(e^jw), 
we got the discrete spectrum DFT X[k].

that is my 2 cents

good luck
Shouldn't one of the headings be "Amplitude" ?


> You can consider four versions of the 1-dimensional Fourier Transform: > > Time Frequency > > Continuous Continuous
<Snip>
In article <3f211e89$0$49116$e4fe514c@news.xs4all.nl>,
"hans" <nospam@microsoft.com> wrote:

>Subject: Re: DFT VS DTFT >From: "hans" <nospam@microsoft.com> >Date: Fri, 25 Jul 2003 14:11:52 +0200 >Newsgroups: comp.dsp > >Shouldn't one of the headings be "Amplitude" ?
No. Time can be either continuous or discrete and either unbounded or periodic. There are four cases. Frequency can be either continuous or discrete and either unbounded or periodic. There are four cases. The pairing of the cases is quite simple. Unbounded time goes with continuous frequencies and periodic time goes with discrete frequencies. Continuous time goes with unbounded frequencies and discrete time goes with periodic frequencies. Notice that if the time and requency labels are exchanged nothing is changed. Time Frequency Name Continuous Unbounded Unbounded Continuous Fourier Integral Continuous Periodic Unbounded Discrete Fourier Series Discrete Unbounded Periodic Continuous Fourier Sequences Discrete Periodic Periodic Discrete Discrete Fourier The names are by no means standardized. Fourier Integral is real line for time to real line for frequency Fourier Series is circle for time to integers for frequency Fourier Sequences is integers for time to circle for frequency Discrete Fourier is mod integers for time to mod integers for frequency Fourier Integral has no sampling. Fourier Series and Fourier Sequences have sampling of either time or frequency but not both. You have to say which to separate these two which are often confused as their names are not well separated. Discrete Fourier has sampling of both time and frequency. In each case time forms a group and the operation is the Fourier Transform approriate to that group. So rather than say that one Fourier Transform is an approximation to another one should say that the group that it is defined over approximates the other group. So the integers approximate the real line or the mod integers with a large modulus approximate the integers.
> >> You can consider four versions of the 1-dimensional Fourier Transform: >> >> Time Frequency >> >> Continuous Continuous > ><Snip> > >
nitin_hsn@yahoo.com (Nithin) wrote in message
news:<96e5ea15.0307211613.fe84778@posting.google.com>...
> Tom <T.Otermans_REMOVE_THIS_@home.nl> wrote in message
news:<slrnbho1p5.aeh.T.Otermans_REMOVE_THIS@noritake.basement>...
> > praveen <praveenkumar1979@rediffmail.com> wrote: > > > Hello, > > > > > > I wanted to know the difference between discrete fourier transform
and
> > > discrete time fourier transform. > > > > > > > > > waiting for reply > > > praveen > > > > The DTFT is aperiodic-discrete and the DFT is periodic-discrete. > > > > > > Tom > > > > -- > > Can DFT be viewed as sampled version of DTFT and hence it is periodic? > I am not sure about this but intuitively it is easier to think so.
both the DFT and the DTFT are periodic with identical period (if scaling is matched appropriately). one legitimate version of defining the DFT is that it is the sampled DTFT of the zero-extended x[n] of finite-length. another way of looking at the DFT is that it is the periodic Fourier Series coefs of the discrete x[n] that is periodically extended. sometimes we fight about this topic on comp.dsp. r b-j
"hans" <nospam@microsoft.com> wrote in message
news:3f211e89$0$49116$e4fe514c@news.xs4all.nl...
> Shouldn't one of the headings be "Amplitude" ? > > > > You can consider four versions of the 1-dimensional Fourier Transform: > > > > Time Frequency > > > > Continuous Continuous >
hans, Hmmmm. I don't think so as far as this table is concerned. I'm talking about the functions. If you allow them to be complex functions then this should be enough shouldn't it? Amplitude is pretty clearly implied. The only distinction I was making her was about continuous vs. discrete. Didn't even mention periodic. Don't we say: "continuous function" instead of "a function whose amplitude is continuously defined from -in to +inf"? Isn't the former description clear enough? Maybe I've missed your point though.... Fred
In article <3f211e89$0$49116$e4fe514c@news.xs4all.nl>,
"hans" <nospam@microsoft.com> wrote:

>Subject: Re: DFT VS DTFT >From: "hans" <nospam@microsoft.com> >Date: Fri, 25 Jul 2003 14:11:52 +0200 >Newsgroups: comp.dsp > >Shouldn't one of the headings be "Amplitude" ?
No. Time can be either continuous or discrete and either unbounded or periodic. There are four cases. Frequency can be either continuous or discrete and either unbounded or periodic. There are four cases. The pairing of the cases is quite simple. Unbounded time goes with continuous frequencies and periodic time goes with discrete frequencies. Continuous time goes with unbounded frequencies and discrete time goes with periodic frequencies. Notice that if the time and requency labels are exchanged nothing is changed. Time Frequency Name Continuous Unbounded Unbounded Continuous Fourier Integral Continuous Periodic Unbounded Discrete Fourier Series Discrete Unbounded Periodic Continuous Fourier Sequences Discrete Periodic Periodic Discrete Discrete Fourier The names are by no means standardized. Fourier Integral is real line for time to real line for frequency Fourier Series is circle for time to integers for frequency Fourier Sequences is integers for time to circle for frequency Discrete Fourier is mod integers for time to mod integers for frequency Fourier Integral has no sampling. Fourier Series and Fourier Sequences have sampling of either time or frequency but not both. You have to say which to separate these two which are often confused as their names are not well separated. Discrete Fourier has sampling of both time and frequency. In each case time forms a group and the operation is the Fourier Transform approriate to that group. So rather than say that one Fourier Transform is an approximation to another one should say that the group that it is defined over approximates the other group. So the integers approximate the real line or the mod integers with a large modulus approximate the integers.
> >> You can consider four versions of the 1-dimensional Fourier Transform: >> >> Time Frequency >> >> Continuous Continuous > ><Snip> > >
Shouldn't one of the headings be "Amplitude" ?


> You can consider four versions of the 1-dimensional Fourier Transform: > > Time Frequency > > Continuous Continuous
<Snip>
All I know about CTFT, DTFT, and DFT

Given a continous signal x[t}
and take the fourier transfrom we got CTFT X(jw).
Notice: X(jw) is a continuous spectrum.

Given a discrete sequence f[n] 
and take the fourier transform we got DTFT F(e^jw).
Notice: X(e^jw) is also a continuous spectrum.

If we take the discrete samples of the continous spectrum DTFT X(e^jw), 
we got the discrete spectrum DFT X[k].

that is my 2 cents

good luck
"Stan Pawlukiewicz" <stanp@nospam_mitre.org> wrote in message
news:bfjrv8$4rm$1@newslocal.mitre.org...
> Fred Marshall wrote: > > "Tom" <T.Otermans_REMOVE_THIS_@home.nl> wrote in message > > news:slrnbho1p5.aeh.T.Otermans_REMOVE_THIS@noritake.basement... > > > >>praveen <praveenkumar1979@rediffmail.com> wrote: > >> > >>>Hello, > >>> > >>>I wanted to know the difference between discrete fourier transform
and
> >>>discrete time fourier transform. > >>> > >>> > >>>waiting for reply > >>>praveen > >> > >>The DTFT is aperiodic-discrete and the DFT is periodic-discrete. > > > > > > Tom, > > > > How can that be for the DTFT case? That is, if I understand what
domains
> > you're referring to.... > > I would have said: discrete <-> continous periodic for DTFT > > where <-> denotes transform pair. > > and > > discrete periodic <-> discrete periodic for DFT. > > > > Fred > > > > > Fred, > The Z transform is continuous for any finite length sequence. > There are formulas relating the DFT and the Z transform in Oppenheim. > The chirp Z transform is a valid DFT, isn't it?
Stan, You probably know better than I. It appears so from a quick look. Not something I've dealt with directly. Fred
Fred Marshall wrote:
> "Tom" <T.Otermans_REMOVE_THIS_@home.nl> wrote in message > news:slrnbho1p5.aeh.T.Otermans_REMOVE_THIS@noritake.basement... > >>praveen <praveenkumar1979@rediffmail.com> wrote: >> >>>Hello, >>> >>>I wanted to know the difference between discrete fourier transform and >>>discrete time fourier transform. >>> >>> >>>waiting for reply >>>praveen >> >>The DTFT is aperiodic-discrete and the DFT is periodic-discrete. > > > Tom, > > How can that be for the DTFT case? That is, if I understand what domains > you're referring to.... > I would have said: discrete <-> continous periodic for DTFT > where <-> denotes transform pair. > and > discrete periodic <-> discrete periodic for DFT. > > Fred > >
Fred, The Z transform is continuous for any finite length sequence. There are formulas relating the DFT and the Z transform in Oppenheim. The chirp Z transform is a valid DFT, isn't it? Stan
"Tom" <T.Otermans_REMOVE_THIS_@home.nl> wrote in message
news:slrnbho1p5.aeh.T.Otermans_REMOVE_THIS@noritake.basement...
> praveen <praveenkumar1979@rediffmail.com> wrote: > > Hello, > > > > I wanted to know the difference between discrete fourier transform and > > discrete time fourier transform. > > > > > > waiting for reply > > praveen > > The DTFT is aperiodic-discrete and the DFT is periodic-discrete.
Tom, How can that be for the DTFT case? That is, if I understand what domains you're referring to.... I would have said: discrete <-> continous periodic for DTFT where <-> denotes transform pair. and discrete periodic <-> discrete periodic for DFT. Fred
Tom <T.Otermans_REMOVE_THIS_@home.nl> wrote in message
news:<slrnbho1p5.aeh.T.Otermans_REMOVE_THIS@noritake.basement>...
> praveen <praveenkumar1979@rediffmail.com> wrote: > > Hello, > > > > I wanted to know the difference between discrete fourier transform and > > discrete time fourier transform. > > > > > > waiting for reply > > praveen > > The DTFT is aperiodic-discrete and the DFT is periodic-discrete. > > > Tom > > --
Can DFT be viewed as sampled version of DTFT and hence it is periodic? I am not sure about this but intuitively it is easier to think so. -Nithin
praveen <praveenkumar1979@rediffmail.com> wrote:
> Hello, > > I wanted to know the difference between discrete fourier transform and > discrete time fourier transform. > > > waiting for reply > praveen
The DTFT is aperiodic-discrete and the DFT is periodic-discrete. Tom --