John Monro wrote:> Rick Lyons wrote: > (snip) > > > > "The DFT's second and third bins centers > > (2*Fs/N and 3*Fs/N respectively) are separated > > by 100 Hz." > > > > > Rick, > > Shouldn't that be "... (Fs/N and 2*Fs/N respectively)..."? > > Regards, > JohnMore nomeclature ambiguity. Is the DC term of a DFT/FFT more commonly refered to as the first bin or the zero-th bin? -- rhn A.T nicholson d.0.t C-o-M
proper terminology for one bin of an fft/dft?
Started by ●March 13, 2006
Reply by ●March 20, 20062006-03-20
Reply by ●March 20, 20062006-03-20
John Monro wrote:> Rick Lyons wrote: > (snip) > > > > "The DFT's second and third bins centers > > (2*Fs/N and 3*Fs/N respectively) are separated > > by 100 Hz." > > > > > Rick, > > Shouldn't that be "... (Fs/N and 2*Fs/N respectively)..."? > > Regards, > JohnMore nomeclature ambiguity. Is the DC term of a DFT/FFT more commonly refered to as the first bin or the zero-th bin? -- rhn A.T nicholson d.0.t C-o-M
Reply by ●March 20, 20062006-03-20
John Monro wrote:> Rick Lyons wrote: > (snip) > > > > "The DFT's second and third bins centers > > (2*Fs/N and 3*Fs/N respectively) are separated > > by 100 Hz." > > > > > Rick, > > Shouldn't that be "... (Fs/N and 2*Fs/N respectively)..."? > > Regards, > JohnMore nomeclature ambiguity. Is the DC term of a DFT/FFT more commonly refered to as the first bin or the zero-th bin? -- rhn A.T nicholson d.0.t C-o-M
Reply by ●March 20, 20062006-03-20
John Monro wrote:> Rick Lyons wrote: > (snip) > > > > "The DFT's second and third bins centers > > (2*Fs/N and 3*Fs/N respectively) are separated > > by 100 Hz." > > > > > Rick, > > Shouldn't that be "... (Fs/N and 2*Fs/N respectively)..."? > > Regards, > JohnMore nomeclature ambiguity. Is the DC term of a DFT/FFT more commonly refered to as the first bin or the zero-th bin? -- rhn A.T nicholson d.0.t C-o-M
Reply by ●March 20, 20062006-03-20
John Monro wrote:> Rick Lyons wrote: > (snip) > > > > "The DFT's second and third bins centers > > (2*Fs/N and 3*Fs/N respectively) are separated > > by 100 Hz." > > > > > Rick, > > Shouldn't that be "... (Fs/N and 2*Fs/N respectively)..."? > > Regards, > JohnMore nomeclature ambiguity. Is the DC term of a DFT/FFT more commonly refered to as the first bin or the zero-th bin? -- rhn A.T nicholson d.0.t C-o-M
Reply by ●March 20, 20062006-03-20
Ron N. wrote:> John Monro wrote: > >>Rick Lyons wrote: >>(snip) >> >>> "The DFT's second and third bins centers >>> (2*Fs/N and 3*Fs/N respectively) are separated >>> by 100 Hz." >>> >> >> >>Rick, >> >>Shouldn't that be "... (Fs/N and 2*Fs/N respectively)..."? >> >>Regards, >>John > > > More nomeclature ambiguity. Is the DC term of a DFT/FFT more > commonly refered to as the first bin or the zero-th bin? > >Ron, The term 'zero-th' is ugly, harder to say, and little used. The term 'first' is universally understood, and it would be a pity to mess around with the concept. If you still feel there could be some ambiguity in areas of technology such as DSP where it is convenient to start numbering from zero, you can simply avoid 'first,' 'second' etc. and refer to 'bin 0,' 'bin 1' and so on. To answer your question, I would say that the DC term is commonly said to be either 'in the first bin,' or 'in bin zero.' I don't think anyone finds the use of 'first' ambiguous but it would soon become ambiguous if the term 'zero-th' became popular. I will stop now, as I had a similar discussion with Jerry, and I don't want to appear to be trolling, or to be pushing a particular hobby horse. Regards, John
Reply by ●March 20, 20062006-03-20
in article 1142906425.123342.171790@u72g2000cwu.googlegroups.com, Ron N. at rhnlogic@yahoo.com wrote on 03/20/2006 21:00:> John Monro wrote: >> Rick Lyons wrote: >> (snip) >>> >>> "The DFT's second and third bins centers >>> (2*Fs/N and 3*Fs/N respectively) are separated >>> by 100 Hz." >>> >> >> >> Rick, >> >> Shouldn't that be "... (Fs/N and 2*Fs/N respectively)..."? > > More nomeclature ambiguity. Is the DC term of a DFT/FFT more > commonly refered to as the first bin or the zero-th bin?it depends on if you're a MATLAB or Fortran user (and happy with it) or not. i heartily disagree with John Monro on this, but we are all free to believe what we will about the same. it is not the time of Galileo. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●March 21, 20062006-03-21
Mark Borgerding wrote:> Bob Cain wrote: > >> Consider the transform of an FIR. There is a smooth frequency domain >> function describing it. > > Perhaps there is continuous function that describes any given sequence > of length N, but there is also a sum-of-sinusoids function that > describes it. As soon as you perform a DFT of a length N, the latter is > what you get. Any continuous behavior is gone.Not true. It's similar to the time domain sampling process. In that case the continuous function of time isn't gone, it's implied and fully specified by the samples and can be disclosed by convolution with the sinc that originally band limited it. What occurs in the frequency domain is the same in principle. The FIR has an output for any frequency it's given and any DFT sufficiently long to contain it tells us what that output will be for the specific "bin" frequencies. As we make the DFT longer, more and more of the intermediate values are disclosed but those at the original bin frequencies, if they also appear in the longer DFT, will be the same (within an overall scaling factor.) Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein
Reply by ●March 21, 20062006-03-21
Bob Cain wrote:> > Mark Borgerding wrote: > >>Bob Cain wrote: >> >> >>>Consider the transform of an FIR. There is a smooth frequency domain >>>function describing it. >> >>Perhaps there is continuous function that describes any given sequence >>of length N, but there is also a sum-of-sinusoids function that >>describes it. As soon as you perform a DFT of a length N, the latter is >>what you get. Any continuous behavior is gone. > > > Not true. It's similar to the time domain sampling process. In that > case the continuous function of time isn't gone, it's implied and fully > specified by the samples and can be disclosed by convolution with the > sinc that originally band limited it.But in time-domain sampling, the continuous behavior *is* gone. Any frequency components above fs/2 are aliased into those compatible with the sampling rate. Of course, an analog anti-aliasing filter usually controls this.> What occurs in the frequency domain is the same in principle. The FIR > has an output for any frequency it's given and any DFT sufficiently long > to contain it tells us what that output will be for the specific "bin" > frequencies. As we make the DFT longer, more and more of the > intermediate values are disclosed but those at the original bin > frequencies, if they also appear in the longer DFT, will be the same > (within an overall scaling factor.) > > > BobThe DFT does not "sample" a continuous spectrum. Not unless you extend your analogy to include a sin(x)/x filter that is applied to the frequency domain before sampling. This would duplicate the effects of the time-windowing inherent in any DFT. too much If the DFT *did* sample the continuous spectrum, then the DFT of a time sequence with a single sinusoid would be all zeros except in the lucky case where the time window happened to concide exactly with a integer number of the sinusoidal periods. Consider this from another perspective: If a time domain sequence with a single pulse is sampled, such that pulse duration << sampling period (In other words, not band-limited) There are two possibilities for how the sampling will turn out, depending on phase: 1) There is one non-zero sample. 2) All samples are zero Energy is aliased in both case. In the first case, the aliasing is constructive, in the second case, the aliased spectra destroy each other. If time-domain sampling acted as you suggest (i.e. convolved with a sinc) then the pulse would be sampled as a sinc wave, implying that the anti-aliasing were somehow implicit in the sampling process. -- Mark
Reply by ●March 21, 20062006-03-21
