The relationship between the input x[n] and output y[n] of a causal digital filter is given as follows: (a) (b) (c) y[n] = x[n] + x[n − 2] + y[n − 2] Determine the poles and zeros of the system and sketch a plot of them on the z-plane. Determine an expression for the impulse response of the filter using long division. Evaluate the first 5 values of the impulse response. Design a digital filter for the above system using: (i) Direct form-I structure.

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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.