Bandwidth of a time-limited pure sinusoidal signal
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From: cwoptn on 5 Aug 2010 18:02 Hi Folks, I have a very basic question. I am little bit confused about how to know the bandwidth of a time-limited pure sinusoidal signal. I understand bandwidth is defined simply as the difference between highest frequency and lowest frequency, and the bandwidth of a infinitely long pure sinusoid if 0 Hz. But if I have a N sample long 50 Hz sinusoid (sampled at Fs samples per second), how to find bandwith of this signal? Thanks, -- cwoptn
From: dbd on 5 Aug 2010 19:02 On Aug 5, 3:02 pm, "cwoptn" <gopi.allu(a)n_o_s_p_a_m.gmail.com> wrote: > Hi Folks, > > I have a very basic question. I am little bit confused about how to know > the bandwidth of a time-limited pure sinusoidal signal. I understand > bandwidth is defined simply as the difference between highest frequency and > lowest frequency, and the bandwidth of a infinitely long pure sinusoid if 0 > Hz. But if I have a N sample long 50 Hz sinusoid (sampled at Fs samples per > second), how to find bandwith of this signal? > > Thanks, > -- cwoptn The bandwidth of the truncated pure sinusoid is equal to the "effective noise bandwidth" (enbw) of the truncating function, often given in terms of dft bins (Fs/N). For a rectangular truncation function (window), the enbw is 1.0, so 1.0 x Fs / N. For other truncating functions, you can look in the usual windows references like: On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform fred harris, from the IEEE proceedings. available at: http://web.mit.edu/xiphmont/Public/windows.pdf (beware errors in some Blackman and Blackman-Harris window parameters) See section IV, A on page 54. Dale B. Dalrymple
From: Fred Marshall on 5 Aug 2010 19:22 cwoptn wrote: > Hi Folks, > > I have a very basic question. I am little bit confused about how to know > the bandwidth of a time-limited pure sinusoidal signal. I understand > bandwidth is defined simply as the difference between highest frequency and > lowest frequency, and the bandwidth of a infinitely long pure sinusoid if 0 > Hz. But if I have a N sample long 50 Hz sinusoid (sampled at Fs samples per > second), how to find bandwith of this signal? > > Thanks, > -- cwoptn > > A lot depends on what you need the "bandwidth" measure for. A truncated sampled sinusoid will have these characteristics in frequency: - if the number of periods is an integer then there will be a single sample pair in frequency. - if the number of periods isn't an integer then there will be samples with nonzero value throughout frequency that correspond to the Dirichlet of the window (like a periodic sinc function). In that case, the bandwidth is as much as it can possibly be. But, the energy is concentrated at the frequency of the sine above and below fs or zero if you will. - if the window isn't rectangular then you may be able to limit the perceived bandwidth to something less for any particular sinusoid. Fred
From: Steve Pope on 5 Aug 2010 19:23 dbd <dbd(a)ieee.org> wrote: >On Aug 5, 3:02�pm, "cwoptn" <gopi.allu(a)n_o_s_p_a_m.gmail.com> wrote: >> I have a very basic question. I am little bit confused about how to know >> the bandwidth of a time-limited pure sinusoidal signal. I understand >> bandwidth is defined simply as the difference between highest frequency and >> lowest frequency, and the bandwidth of a infinitely long pure sinusoid if 0 >> Hz. But if I have a N sample long 50 Hz sinusoid (sampled at Fs samples per >> second), how to find bandwith of this signal? >The bandwidth of the truncated pure sinusoid is equal to the >"effective noise bandwidth" (enbw) of the truncating function, often >given in terms of dft bins (Fs/N). For a rectangular truncation >function (window), the enbw is 1.0, so 1.0 x Fs / N. >For other truncating functions, you can look in the usual windows >references like: >On the Use of Windows for Harmonic Analysis >with the Discrete Fourier Transform >fred harris, >from the IEEE proceedings. available at: >http://web.mit.edu/xiphmont/Public/windows.pdf >(beware errors in some Blackman and Blackman-Harris window parameters) I find it interesting how often a continuous-time question leads to a discrete-time answer on this newsgroup. S.
From: robert bristow-johnson on 5 Aug 2010 21:56 On Aug 5, 7:23 pm, spop...(a)speedymail.org (Steve Pope) wrote: > dbd <d...(a)ieee.org> wrote: > >On Aug 5, 3:02 pm, "cwoptn" <gopi.allu(a)n_o_s_p_a_m.gmail.com> wrote: > >> I have a very basic question. I am little bit confused about how to know > >> the bandwidth of a time-limited pure sinusoidal signal. I understand > >> bandwidth is defined simply as the difference between highest frequency and > >> lowest frequency, and the bandwidth of a infinitely long pure sinusoid if 0 > >> Hz. But if I have a N sample long 50 Hz sinusoid (sampled at Fs samples per > >> second), how to find bandwith of this signal? > >The bandwidth of the truncated pure sinusoid is equal to the > >"effective noise bandwidth" (enbw) of the truncating function, this i get... > > often given in terms of dft bins (Fs/N). .... that i don't. > I find it interesting how often a continuous-time question > leads to a discrete-time answer on this newsgroup. and, i guess i'm not alone. since a time-limited signal can't also be bandlimited, then the answer depends on how one defines "bandwidth" for something that stretches out to infinity on one or both sides. then for that i think Fred said it well: "A lot depends on what you need the "bandwidth" measure for." r b-j
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