Given: You wish to design a band-reject filter using the bilinear transformation method. Your prototype normalized low-pass filter's analog transfer function is given below: 1 H(s) = s2 + V2s +1 The filter should have a stopband between 450 and 550 Hz, and the signal will be sampled at F; = 7.5 kHz. Find: Design a digital filter that meets the above requirements. Determine H(z) for the filter. Plot the filter's magnitude and phase response. Determine the implementation equation for y[n]. Finally, assume the below signal is sampled at the given sampling frequency and is input into the digital filter. x(t) = cos(2n100t) + cos(27500f) + cos(2n1.000t)

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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.