Spectrum analysis characterizes the frequency content of signals. Power spectral estimation methods obtain an approximate estimate of the power spectral density of random processes. Non-parametric power spectral estimation does not assume any data generation process or model, and involves dividing a signal into segments and averaging the periodograms of each segment to reduce variance. Common non-parametric methods include Bartlett's method, Welch's method, and Blackman-Tukey method.

1. February 10, 2012 Presented by Diwaker Pant

2. The signal processing methods which characterises the frequency content of signal is known as spectrum analysis. We know that the signals which are analysed in any communication system are either purely random or will have noise component also. If the signal is random ,then only an estimate of the signal can be obtained. This is possible only if the statistical attributes of the random signals are known. February 10, 2012 Presented by Diwaker Pant

3. The signal energy is given by Parseval’s relation-: The density of the energy of x(t) w.r.t. frequency is represented by |X(f)| 2 where |X(f)| 2 = S xx (f) Where S xx (f) = Energy spectral density February 10, 2012 Presented by Diwaker Pant

4. Let R xx( Ʈ ) be the autocorrelation function of the signal x(t) where R xx( Ʈ ) is given by Rxx( Ʈ ) = The Fourier transform of autocorrelation function is given by S xx (f) Where S xx (f) is power spectral density of signal x(t). February 10, 2012 Presented by Diwaker Pant

5. Autocorrelation function of a random process is statistical average that will use to characterizing random signal in the time domain . Fourier transform of that autocorrelation function is called power density spectrum. Power Spectral Estimation method is to obtain an approximate estimation of the power spectral density of a given real random process . February 10, 2012 Presented by Diwaker Pant

6. To estimate the spectral characteristics of signal characterized as random processes. To estimation of spectra in frequency domain when signals are random in nature. February 10, 2012 Presented by Diwaker Pant

7. Estimated autocorrelation: Estimated power spectrum or periodogram: February 10, 2012 Presented by Diwaker Pant

8. Non-parametric PSE does NOT assume any data-generating process or model i.e no assumption about how data were generated. Methods that rely on the direct use of the given finite duration signal to compute the autocorrelation to the maximum allowable length (beyond which it is assumed zero), are called Non-parametric methods February 10, 2012 Presented by Diwaker Pant

9. Types of Nonparametric methods Bartlett method Welch method Blackman-Tukey method February 10, 2012 Presented by Diwaker Pant

10. Bartlett’s method for reducing the variance in the periodogram involves three steps . The N-point sequence is subdivided into K nonoverlapping segments where each segment has length L .This results in K data segments. For each segment, Compute the periodogram . Averaging the periodogram for the K segment to obtain the Bartlett power spectrum estimate. February 10, 2012 Presented by Diwaker Pant

11. Properties of Bartlett’s method Bias: Resolution : Variance : February 10, 2012 Presented by Diwaker Pant

12. The effect of reducing the length of data from N point to L=N/K , results in a window whose spectral width has been increased by factor K. Consequently ,the frequency resolution has been reduced by factor K. Reduction in the resolution have reduced the variance . February 10, 2012 Presented by Diwaker Pant

13. Measurement of noise spectra for the design of optimal linear filter Feature Extraction In biomedical , seismology For Meteorological data , Communication Engg. In industrial process control February 10, 2012 Presented by Diwaker Pant

14. ? Querry February 10, 2012 Presented by Diwaker Pant

15. REFFERENCES Salivahanan and Vallavaraj , Digital signal Processing Emanuel C.lfeachor and Barrie W.jervis Digital Signal Processing www.google.com www.wikipedia.com February 10, 2012 Presented by Diwaker Pant

16. February 10, 2012 Presented by Diwaker Pant