6. The power spectral density of a white noise process is 10 and it is passed through an ideally shaped bandpass filter centered at 50Hz and with a bandwidth of 4Hz. a) Draw the frequency response of the bandpass filter. b) Draw the exact Power Spectral Density of the narrowband noise. c) Draw the exact Power Spectral Density of the in-phase component of the narrowband noise. d) How is the in-phase component of a bandpass signal extracted? e) What is the autocorrelation function of the white noise process, before it is passed through any filter?

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Filter

A filter is a device or process which removes some of the unwanted features or components like frequencies from a signal in signal processing. The feature of filters is the complete or partial suppression of some part of the signal, and filtering is a class of signal processing. This most often means removing some frequency bands or some frequencies. In the frequency domain, the filters do not exclusively act, especially in the image processing field many other targets for filtering exist. Without having to act in the frequency domain, the correlations can be removed for certain frequency components and not for others. The filters are widely used in electronics and telecommunication, in television, radio, radar, audio recording, music synthesis, control systems, computer graphics, and image processing.