Confusing Spectrogram of a chirp signal
in [DSP]
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From: jumpfunky on 6 May 2010 08:43 Hi, I'm used follwing MatLab-Code to visualize a spectogram of a linear chirp signal: n=(1:1:512); for ind=1:512; fac = 0.2*ind; S3(ind)=sin(fac*pi*ind/512); end u = specgram(S3,512,512,64,63); figure, imagesc(abs(u)); So, i think there must be frequencies between 0.1 and 51.2, but the spectrogram shows me frequencies between 0 and ~100. That's a bit confusing! I would be grateful if there any ideas how this can be explained. Thank you.
From: Rune Allnor on 6 May 2010 08:46 On 6 Mai, 14:43, "jumpfunky" <jumpfunky(a)n_o_s_p_a_m.web.de> wrote: > Hi, > > I'm used follwing MatLab-Code to visualize a spectogram of a linear chirp > signal: > > n=(1:1:512); > for ind=1:512; > fac = 0.2*ind; > S3(ind)=sin(fac*pi*ind/512); > end > u = specgram(S3,512,512,64,63); > figure, imagesc(abs(u)); > > So, i think there must be frequencies between 0.1 and 51.2, but the > spectrogram shows me frequencies between 0 and ~100. > > That's a bit confusing! > I would be grateful if there any ideas how this can be explained. You could start by explaining why you expect the numbers you state. And proceed by writing a code snippet that does not rely on the signal processing toolbox (or matlab at all, for that matter). Rune
From: jumpfunky on 6 May 2010 09:26 >You could start by explaining why you expect the numbers you state. >And proceed by writing a code snippet that does not rely on the >signal processing toolbox (or matlab at all, for that matter). Okay, the Signal (linear chirp) is defined as: s[n] = sin(0,2*n*pi*n/512) 1 <= n <= 512 and n is element of natural numbers. As 2D-Plot: http://img689.imageshack.us/img689/6402/71183907.jpg For n = 1 the frequency of sine is 0.1 Hz. For n = 512 the frequency is 51,2Hz. Since the frequency of the chirp-Signal grows linear, the sine contains only frequencys between 0.1Hz and 51,2Hz. And now the Spectrogram calculated by matlab: http://img689.imageshack.us/img689/6067/s3sm.jpg As you can see, matlab says: There are frequencies above 50Hz! The Spectrogram is calculated by means of a windowed (hann) FFT. The windows used 64 samples per section and the sections overlapps each other with 63 samples.
From: Jerry Avins on 6 May 2010 09:44 On 5/6/2010 9:26 AM, jumpfunky wrote: ... > For n = 1 the frequency of sine is 0.1 Hz. For n = 512 the frequency is > 51,2Hz. Since the frequency of the chirp-Signal grows linear, the sine > contains only frequencys between 0.1Hz and 51,2Hz. That's an understandable error that has been made before. It is tantamount to the claim that a frequency modulated signal fits into a channel as wide as its peak deviation. "Taint so. It has to be wider. ... Jerry -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." --Barbara Smuts, U. Mich. �����������������������������������������������������������������������
From: Mark on 6 May 2010 10:41
On May 6, 9:26 am, "jumpfunky" <jumpfunky(a)n_o_s_p_a_m.web.de> wrote: > >You could start by explaining why you expect the numbers you state. > >And proceed by writing a code snippet that does not rely on the > >signal processing toolbox (or matlab at all, for that matter). > > Okay, the Signal (linear chirp) is defined as: > s[n] = sin(0,2*n*pi*n/512) 1 <= n <= 512 and n is element of natural > numbers. > As 2D-Plot:http://img689.imageshack.us/img689/6402/71183907.jpg > > For n = 1 the frequency of sine is 0.1 Hz. For n = 512 the frequency is > 51,2Hz. Since the frequency of the chirp-Signal grows linear, the sine > contains only frequencys between 0.1Hz and 51,2Hz. > > And now the Spectrogram calculated by matlab:http://img689.imageshack.us/img689/6067/s3sm.jpg > > As you can see, matlab says: There are frequencies above 50Hz! The > Spectrogram is calculated by means of a windowed (hann) FFT. The windows > used 64 samples per section and the sections overlapps each other with 63 > samples. are the frequencies you see that you don't expect to see, EXACTLY 2x the ones you do expcet to see? also how about the low end, do you see a 2x error there too... Mark? |