x(t) = 5 cos( 2n 3000t) + 5 cos(2n 6000t), for t 20, %3D Sampled at a rate of 12000 Hz, 1. Sketch the spectrum of the sampled signal up to 20 KHz. 2. Sketch the recovered analog signal spectrum if an ideal low pass filter with a cutoff frequency of 6 KHz is used to filter the sampled signal in order to recover the original signal. 3. Determine the sampling frequencies, which will achieve Nyquist rate, aliasing, sampling theory. 4. Is the signal single or multitoned frequency? 5. Determine the average power for the signal

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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.