Filtering with MATLAB's ifftshift
in [DSP]
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From: Greg Heath on 15 May 2010 09:24 The MATLAB fft is defined over the nonnegative time interval t = dt*(0:N-1); t = 0:dt:T-dt; t = linspace(0,T-dt,N); where dt = 1/Fs and T = N*dt is the temporal period (corresponding discrete time period is N) induced by ifft(fft(x)) When xb is defined over the "centered" bipolar time interval tb = t - dt*ceil((N-1)/2); = dt*[-ceil((N-1)/2) : floor((N-1)/2))]; the location of the negative time components can be periodically shifted N units into the proper positive time interval location by using ifftshift x = ifftshift(xb); and recovered by using the inverse fftshift xb = fftshift(x); X = fft(x) yields a transform with a spectral period Fs (discrete frequency period N) that is defined over the nonnegative frequency interval f = df*(0:N-1); f = 0:df:Fs-df; f = linspace(0,Fs-df,N); where df = 1/T = Fs/N Xb, the "centered" bipolar frequency transform defined over the spectral interval fb = f - df*ceil((N-1)/2) = df*[-ceil((N-1)/2) : floor((N-1)/2))]; is obtained by using fftshift Xb = fftshift(X) and X is recovered using ifftshift X = ifftshift(Xb) If a time signal xb is defined over the centered bipolar time interval and is filtered using a transform, Hb, that is defined over the centered bipolar frequency interval, the resulting output, yb can be obtained in 7 steps: xb => x => X => Xb => Yb = Hb.*Xb => Y => y => yb which, of course are typically combined by the experienced user. Note that ifftshift is identical to fftshift when N is even Hope this helps. Greg
From: Greg Heath on 15 May 2010 14:23 On May 15, 1:45 pm, "Dave Robinson" <dave.robin...(a)somewhere.biz> wrote: > Greg Heath <he...(a)alumni.brown.edu> wrote in message <e48ebf08-396a-42de-8fe5-bedf08c96...(a)p17g2000vbe.googlegroups.com>... > > The MATLAB fft is defined over the nonnegative > > time interval > > t = dt*(0:N-1); > > t = 0:dt:T-dt; > > t = linspace(0,T-dt,N); > > where > > dt = 1/Fs > > and > > T = N*dt > > is the temporal period (corresponding discrete > > time period is N) induced by ifft(fft(x)) > > > When xb is defined over the "centered" bipolar time > > interval > > tb = t - dt*ceil((N-1)/2); > > = dt*[-ceil((N-1)/2) : floor((N-1)/2))]; > > the location of the negative time components can be > > periodically shifted N units into the proper positive > > time interval location by using ifftshift > > x = ifftshift(xb); > > and recovered by using the inverse fftshift > > xb = fftshift(x); > > > X = fft(x) yields a transform with a spectral > > period Fs (discrete frequency period N) that is > > defined over the nonnegative frequency interval > > f = df*(0:N-1); > > f = 0:df:Fs-df; > > f = linspace(0,Fs-df,N); > > where > > df = 1/T = Fs/N > > > Xb, the "centered" bipolar frequency transform > > defined over the spectral interval > > fb = f - df*ceil((N-1)/2) > > = df*[-ceil((N-1)/2) : floor((N-1)/2))]; > > is obtained by using fftshift > > Xb = fftshift(X) > > and X is recovered using ifftshift > > X = ifftshift(Xb) > > > If a time signal xb is defined over the > > centered bipolar time interval and is > > filtered using a transform, Hb, that is defined > > over the centered bipolar frequency interval, > > the resulting output, yb can be obtained in 7 > > steps: > > xb => x => X => Xb => Yb = Hb.*Xb => Y > > => y => yb > > which, of course are typically combined by the > > experienced user. > > > Note that ifftshift is identical to fftshift > > when N is even > > > Hope this helps. > > > Greg > > Ok Greg, now we know what the answer is, what was the question? ;-) The question is posed in Newsgroups: comp.soft-sys.matlab From: "Nicolas " <nico_spect...(a)hotmail.com> Date: Sat, 15 May 2010 00:36:04 +0000 (UTC) Local: Fri, May 14 2010 8:36 pm Subject: FFT-filter-IFFT problem http://groups.google.com/group/comp.soft-sys.matlab/msg/5ea90824ec15e2f5?hl=en My reply to him was to refer to this thread. Since many other posters have had problems with MATLAB concerning a. negative times and frequencies using fft/ifft b. zero matrix indices c. ifftshift vs fftshift I felt that this was the best way to respond. Hope this helps. Greg
From: dbd on 15 May 2010 20:23 On May 15, 11:23 am, Greg Heath <he...(a)alumni.brown.edu> wrote: > On May 15, 1:45 pm, "Dave Robinson" <dave.robin...(a)somewhere.biz> > wrote: > ... > > > Ok Greg, now we know what the answer is, what was the question? ;-) > ----------------------------------------------------------------------------------------------------------------------------------- Many thanks to Dave for having the good sense to not cross-post his question to comp.dsp ----------------------------------------------------------------------------------------------------------------------------------- > The question is posed in > > Newsgroups: comp.soft-sys.matlab > From: "Nicolas " <nico_spect...(a)hotmail.com> > Date: Sat, 15 May 2010 00:36:04 +0000 (UTC) > Local: Fri, May 14 2010 8:36 pm > Subject: FFT-filter-IFFT problem > > http://groups.google.com/group/comp.soft-sys.matlab/msg/5ea90824ec15e... > > My reply to him was to refer to this thread. > > Since many other posters have had problems with MATLAB > concerning > > a. negative times and frequencies using fft/ifft > b. zero matrix indices > c. ifftshift vs fftshift > > I felt that this was the best way to respond. > > Hope this helps. > > Greg Your other thread is not in comp.dsp. Why did you crosspost this here? The OP of your other thread had a question that did not use or require the use of a Matlab syntax containing "shift" So why spout FUD? Here? Your "Filtering with MATLAB's ifftshift" does not address the implementation requirements specific to filtering with fft-ifft even if you do choose to use a "shift" syntax so it is still off topic here, so why crosspost it here? How can this possibly be helpful here? Dale B. Dalrymple
From: Greg Heath on 15 May 2010 22:02 On May 15, 8:23 pm, dbd <d...(a)ieee.org> wrote: > On May 15, 11:23 am, Greg Heath <he...(a)alumni.brown.edu> wrote:> On May 15, 1:45 pm, "Dave Robinson" <dave.robin...(a)somewhere.biz> > > wrote: > > ... > > > > Ok Greg, now we know what the answer is, what was the question? ;-) > > ----------------------------------------------------------------------------- > Many thanks to Dave for having the good sense to not cross- > post his question to comp.dsp > --------------------------------------------------------------------------- > > The question is posed in > > > Newsgroups: comp.soft-sys.matlab > > From: "Nicolas " <nico_spect...(a)hotmail.com> > > Date: Sat, 15 May 2010 00:36:04 +0000 (UTC) > > Local: Fri, May 14 2010 8:36 pm > > Subject: FFT-filter-IFFT problem > > >http://groups.google.com/group/comp.soft-sys.matlab/msg/5ea90824ec15e... > > > My reply to him was to refer to this thread. > > > Since many other posters have had problems with MATLAB > > concerning > > > a. negative times and frequencies using fft/ifft > > b. zero matrix indices > > c. ifftshift vs fftshift > > > I felt that this was the best way to respond. > > > Hope this helps. > > > Greg > > Your other thread is not in comp.dsp. Why did you crosspost >this here? 1. It was not "my" thread. 2. I found it difficult to answer OPs question directly because of the can-of-worms syndrome. 3. My solution was to address how the problem could be done without getting into his specific code. 4. As I began writing, images of previous posts in comp.dsp as well as comp.soft-sys.matlab came to mind regarding MATLAB fft/ifft problems with fftshift/ifftshift and negative times/frequencies 5. Therefore, I posted to both groups and referred the OP to the new thread. > The OP of your other thread had a question that did not use > or require the use of a Matlab syntax containing "shift" Incorrect. The correct use of fftshift and ifftshift to deal with negative times and frequencies is the most essential component in solving his problem. > So why spout FUD? Here? There has been confusion in this group w.r.t. the use of MATLABs ifftshift and fftshift w.r.t. dealing with negative times and negative frequencies. I was hoping the post would help clarify matters. > Your "Filtering with MATLAB's ifftshift" does not address the > implementation requirements specific to filtering with fft-ifft even > if you do choose to use a "shift" syntax I have no idea what that means. > so it is still off topic here, so why crosspost it here? > > How can this possibly be helpful here? I assumed that comp.dsp is read by users of MATLAB that could use the info. You haven't convinced me otherwise. Greg
From: Jerry Avins on 15 May 2010 23:13 On 5/15/2010 10:02 PM, Greg Heath wrote: > On May 15, 8:23 pm, dbd<d...(a)ieee.org> wrote: >> On May 15, 11:23 am, Greg Heath<he...(a)alumni.brown.edu> wrote:> On May 15, 1:45 pm, "Dave Robinson"<dave.robin...(a)somewhere.biz> >>> wrote: >>> ... >> >>>> Ok Greg, now we know what the answer is, what was the question? ;-) >> >> ---------------------------------------------------------------------------�-- >> Many thanks to Dave for having the good sense to not cross- >> post his question to comp.dsp >> ---------------------------------------------------------------------------� >>> The question is posed in >> >>> Newsgroups: comp.soft-sys.matlab >>> From: "Nicolas "<nico_spect...(a)hotmail.com> >>> Date: Sat, 15 May 2010 00:36:04 +0000 (UTC) >>> Local: Fri, May 14 2010 8:36 pm >>> Subject: FFT-filter-IFFT problem >> >>> http://groups.google.com/group/comp.soft-sys.matlab/msg/5ea90824ec15e... >> >>> My reply to him was to refer to this thread. >> >>> Since many other posters have had problems with MATLAB >>> concerning >> >>> a. negative times and frequencies using fft/ifft >>> b. zero matrix indices >>> c. ifftshift vs fftshift >> >>> I felt that this was the best way to respond. >> >>> Hope this helps. >> >>> Greg >> >> Your other thread is not in comp.dsp. Why did you crosspost>this here? > > 1. It was not "my" thread. > 2. I found it difficult to answer OPs question directly because of the > can-of-worms syndrome. > 3. My solution was to address how the problem could > be done without getting into his specific code. > 4. As I began writing, images of previous posts in > comp.dsp as well as comp.soft-sys.matlab came to mind > regarding MATLAB fft/ifft problems with fftshift/ifftshift and > negative times/frequencies > 5. Therefore, I posted to both groups and referred the > OP to the new thread. > >> The OP of your other thread had a question that did not use >> or require the use of a Matlab syntax containing "shift" > > Incorrect. The correct use of fftshift and ifftshift > to deal with negative times and frequencies is > the most essential component in solving his problem. > >> So why spout FUD? Here? > > There has been confusion in this group w.r.t. the > use of MATLABs ifftshift and fftshift w.r.t. dealing > with negative times and negative frequencies. > > I was hoping the post would help clarify matters. > >> Your "Filtering with MATLAB's ifftshift" does not address the >> implementation requirements specific to filtering with fft-ifft even >> if you do choose to use a "shift" syntax > > I have no idea what that means. > >> so it is still off topic here, so why crosspost it here? >> >> How can this possibly be helpful here? > > I assumed that comp.dsp is read by users of > MATLAB that could use the info. > > You haven't convinced me otherwise. Thanks for the post. It's on topic if Matlab is. Jerry -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." --Barbara Smuts, U. Mich. �����������������������������������������������������������������������
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