I need to analyze the magnitude spectra of some data sets. Every data vector will have 128 or fewer complex samples. I window all the data using a Chebyshev window with a certain level of relative sidelobe attenuation. Normally, I zero pad the windowed data and take a 128-pt FFT. Now I'm experimenting with longer FFTs (256 and 512) in an attempt to get a higher resolution look at the spectrum. I'm wondering about the benefits of taking a longer FFT versus merely interpolating between the bins of a shorter FFT. For example, might the difference between the results of each method be significant enough to warrant using the longer FFT (even if it's computationally expensive)? Also, if I were to interpolate, what are some good methods for doing it? Linear? I'm sure the answer is "It depends on what you're doing." I'm new to this and am hoping you guys can get me to thinking about what the tradeoffs are and what questions I need to be asking myself in order to decide what to do. Thanks.

# longer FFT v. shorter FFT with interpolation

Started by ●May 9, 2007

Posted by ●May 10, 2007

On 10 May, 01:44, Gilead <Gilead.Tisch...@gmail.com> wrote:> I need to analyze the magnitude spectra of some data sets. Every data > vector will have 128 or fewer complex samples. I window all the data > using a Chebyshev window with a certain level of relative sidelobe > attenuation. Normally, I zero pad the windowed data and take a 128-pt > FFT. Now I'm experimenting with longer FFTs (256 and 512) in an > attempt to get a higher resolution look at the spectrum.Be very careful about how you use the terms. "Resolution" can mean one of two things: - Be able to separate two sines close together - Be able to pin-point the frequency of one sine By zero-padding you can (some times, depending on noise and a couple of other factors) be able to estimate the frequency of your sinusoidal better than with the raw data. You will, however, not be a ble to separate two sinusoidals in the zero-padded spectrum if they were not separable in the original spectrum.> I'm > wondering about the benefits of taking a longer FFT versus merely > interpolating between the bins of a shorter FFT. For example, might > the difference between the results of each method be significant > enough to warrant using the longer FFT (even if it's computationally > expensive)? Also, if I were to interpolate, what are some good > methods for doing it? Linear?Zero padding the data prior to computing the DFT *is* to interpolate the spectrum. Rune

Posted by ●May 13, 2007

On 10 May 2007 09:26:15 -0700, Rune Allnor <allnor@tele.ntnu.no> wrote:>On 10 May, 01:44, Gilead <Gilead.Tisch...@gmail.com> wrote: >> I need to analyze the magnitude spectra of some data sets. Every data >> vector will have 128 or fewer complex samples. I window all the data >> using a Chebyshev window with a certain level of relative sidelobe >> attenuation. Normally, I zero pad the windowed data and take a 128-pt >> FFT. Now I'm experimenting with longer FFTs (256 and 512) in an >> attempt to get a higher resolution look at the spectrum. > >Be very careful about how you use the terms. "Resolution" can mean >one of two things: > >- Be able to separate two sines close together >- Be able to pin-point the frequency of one sine > >By zero-padding you can (some times, depending on noise and >a couple of other factors) be able to estimate the frequency >of your sinusoidal better than with the raw data. You will, >however, not be a ble to separate two sinusoidals in the >zero-padded spectrum if they were not separable in the >original spectrum. > >> I'm >> wondering about the benefits of taking a longer FFT versus merely >> interpolating between the bins of a shorter FFT. For example, might >> the difference between the results of each method be significant >> enough to warrant using the longer FFT (even if it's computationally >> expensive)? Also, if I were to interpolate, what are some good >> methods for doing it? Linear? > >Zero padding the data prior to computing the DFT *is* to interpolate >the spectrum. > >RuneHi Rune, those were good answers. [-Rick-]