noise power spectral density
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From: Bruno Luong on 31 Mar 2010 17:01 "SARVANI NADIMINTY" <sarvani_nadi(a)yahoo.co.in> wrote in message <hofh8d$no$1(a)fred.mathworks.com>... > How should we calculate noise power spectral density for Additive white gaussian noise when we know only the noise samples? i.e. > Trivial: *White* noise by definition has flat PSD. Bruno
From: Wayne King on 31 Mar 2010 18:44 "SARVANI NADIMINTY" <sarvani_nadi(a)yahoo.co.in> wrote in message <hp0bvo$910$1(a)fred.mathworks.com>... > "Wayne King" <wmkingty(a)gmail.com> wrote in message <hofmj1$q7b$1(a)fred.mathworks.com>... > > "SARVANI NADIMINTY" <sarvani_nadi(a)yahoo.co.in> wrote in message <hofksn$s33$1(a)fred.mathworks.com>... > > > "Wayne King" <wmkingty(a)gmail.com> wrote in message <hofia6$h5j$1(a)fred.mathworks.com>... > > > > "SARVANI NADIMINTY" <sarvani_nadi(a)yahoo.co.in> wrote in message <hofh8d$no$1(a)fred.mathworks.com>... > > > > > How should we calculate noise power spectral density for Additive white gaussian noise when we know only the noise samples? i.e. > > > > > > > > > > i have generated awgn using rand(1,N); where N is some constant. How can i calculate the noise power spectral density without knowing any frequencies and input signal? > > > > > > > > Hi Sarvani, you can estimate the power spectral density as a function of radians/sample. > > > > Note that the frequency axis in the following is from 0 to pi radians/sample > > > > > > > > H=spectrum.periodogram; > > > > x = randn(1000,1); > > > > plot(psd(H,x)); > > > > > > > > Wayne > > > Thank you. Can u pls tell me what is this 'spectrum.periodogram'? > > > > It is a periodogram spectral analysis object. > > > > wayne > Thanks a lot for the reply but i want a specific value for power spectral density to use it in a program. Can you help me to get values Hi, as Bruno wrote you, white noise has a flat power spectral density. A white noise sequence has a theoretical autocorrelation that is equal to the variance of the process at zero lag and zero elsewhere. Therefore, the power spectral density is just equal to the variance at all frequencies (the only nonzero value in the DTFT of the autocorrelation is at zero frequency and that is equal to the variance) H = spectrum.periodogram; x = 4*randn(1000,1); % wgn with a variance of 16 % in dB PSD is flat and equal to 10*log10(16) plot(psd(H,x)); y = randn(1000,1); % wgn with a variance of 1 plot(psd(H,y)); % in dB PSD is flat and equal to 10*log10(1) Note that the periodogram is just an estimate of the theoretical PSD. Wayne
From: SARVANI NADIMINTY on 6 Apr 2010 01:55 "Wayne King" <wmkingty(a)gmail.com> wrote in message <hp0j7k$ot7$1(a)fred.mathworks.com>... > "SARVANI NADIMINTY" <sarvani_nadi(a)yahoo.co.in> wrote in message <hp0bvo$910$1(a)fred.mathworks.com>... > > "Wayne King" <wmkingty(a)gmail.com> wrote in message <hofmj1$q7b$1(a)fred.mathworks.com>... > > > "SARVANI NADIMINTY" <sarvani_nadi(a)yahoo.co.in> wrote in message <hofksn$s33$1(a)fred.mathworks.com>... > > > > "Wayne King" <wmkingty(a)gmail.com> wrote in message <hofia6$h5j$1(a)fred.mathworks.com>... > > > > > "SARVANI NADIMINTY" <sarvani_nadi(a)yahoo.co.in> wrote in message <hofh8d$no$1(a)fred.mathworks.com>... > > > > > > How should we calculate noise power spectral density for Additive white gaussian noise when we know only the noise samples? i.e. > > > > > > > > > > > > i have generated awgn using rand(1,N); where N is some constant. How can i calculate the noise power spectral density without knowing any frequencies and input signal? > > > > > > > > > > Hi Sarvani, you can estimate the power spectral density as a function of radians/sample. > > > > > Note that the frequency axis in the following is from 0 to pi radians/sample > > > > > > > > > > H=spectrum.periodogram; > > > > > x = randn(1000,1); > > > > > plot(psd(H,x)); > > > > > > > > > > Wayne > > > > Thank you. Can u pls tell me what is this 'spectrum.periodogram'? > > > > > > It is a periodogram spectral analysis object. > > > > > > wayne > > Thanks a lot for the reply but i want a specific value for power spectral density to use it in a program. Can you help me to get values > > Hi, as Bruno wrote you, white noise has a flat power spectral density. A white noise sequence has a theoretical autocorrelation that is equal to the variance of the process at zero lag and zero elsewhere. Therefore, the power spectral density is just equal to the variance at all frequencies (the only nonzero value in the DTFT of the autocorrelation is at zero frequency and that is equal to the variance) > > H = spectrum.periodogram; > x = 4*randn(1000,1); % wgn with a variance of 16 > % in dB PSD is flat and equal to 10*log10(16) > plot(psd(H,x)); > y = randn(1000,1); % wgn with a variance of 1 > plot(psd(H,y)); > % in dB PSD is flat and equal to 10*log10(1) > > Note that the periodogram is just an estimate of the theoretical PSD. > > Wayne Thanks a lot . Can we add this noise directly to our signal? does that wgn noise act as additive? or should we do anything else for that noise to add to the transmitted signal?
From: Wayne King on 6 Apr 2010 06:09
"SARVANI NADIMINTY" <sarvani_nadi(a)yahoo.co.in> wrote in message <hpeibs$jal$1(a)fred.mathworks.com>... > "Wayne King" <wmkingty(a)gmail.com> wrote in message <hp0j7k$ot7$1(a)fred.mathworks.com>... > > "SARVANI NADIMINTY" <sarvani_nadi(a)yahoo.co.in> wrote in message <hp0bvo$910$1(a)fred.mathworks.com>... > > > "Wayne King" <wmkingty(a)gmail.com> wrote in message <hofmj1$q7b$1(a)fred.mathworks.com>... > > > > "SARVANI NADIMINTY" <sarvani_nadi(a)yahoo.co.in> wrote in message <hofksn$s33$1(a)fred.mathworks.com>... > > > > > "Wayne King" <wmkingty(a)gmail.com> wrote in message <hofia6$h5j$1(a)fred.mathworks.com>... > > > > > > "SARVANI NADIMINTY" <sarvani_nadi(a)yahoo.co.in> wrote in message <hofh8d$no$1(a)fred.mathworks.com>... > > > > > > > How should we calculate noise power spectral density for Additive white gaussian noise when we know only the noise samples? i.e. > > > > > > > > > > > > > > i have generated awgn using rand(1,N); where N is some constant. How can i calculate the noise power spectral density without knowing any frequencies and input signal? > > > > > > > > > > > > Hi Sarvani, you can estimate the power spectral density as a function of radians/sample. > > > > > > Note that the frequency axis in the following is from 0 to pi radians/sample > > > > > > > > > > > > H=spectrum.periodogram; > > > > > > x = randn(1000,1); > > > > > > plot(psd(H,x)); > > > > > > > > > > > > Wayne > > > > > Thank you. Can u pls tell me what is this 'spectrum.periodogram'? > > > > > > > > It is a periodogram spectral analysis object. > > > > > > > > wayne > > > Thanks a lot for the reply but i want a specific value for power spectral density to use it in a program. Can you help me to get values > > > > Hi, as Bruno wrote you, white noise has a flat power spectral density. A white noise sequence has a theoretical autocorrelation that is equal to the variance of the process at zero lag and zero elsewhere. Therefore, the power spectral density is just equal to the variance at all frequencies (the only nonzero value in the DTFT of the autocorrelation is at zero frequency and that is equal to the variance) > > > > H = spectrum.periodogram; > > x = 4*randn(1000,1); % wgn with a variance of 16 > > % in dB PSD is flat and equal to 10*log10(16) > > plot(psd(H,x)); > > y = randn(1000,1); % wgn with a variance of 1 > > plot(psd(H,y)); > > % in dB PSD is flat and equal to 10*log10(1) > > > > Note that the periodogram is just an estimate of the theoretical PSD. > > > > Wayne > Thanks a lot . Can we add this noise directly to our signal? does that wgn noise act as additive? or should we do anything else for that noise to add to the transmitted signal? Yes, you just add the wgn vector to your signal. You just need to make sure you scale the wgn vector properly to get whatever signal-to-noise ratio you want. Scaling the wgn vector by 0.5, for example 0.5*randn(1000,1) , gives you a wgn vector with standard deviation 0.5, variance 0.25. Wayne Wayne |