Please help with question d of this problem. PLEASE WRITE CLEARLY AND DO NOT TYPE THE SOLUTION. thanks Consider the moving average filter with length N = 21. For each of the followinginput signals f[k], compute the output signal y[k] from the moving average system. Expressyour answer as a real-valued cosine with a particular amplitude, frequency, and phase.(a) f[k] = 3 for all k (Hint: we can write this as f[k] = 3 cos(0k))(b) f[k] = cos(k)(c) f[k] = cos(k)(d) f[k] = cos(2 k)

What is Moving Average Filter? A Finite Impulse Response (FIR) smoothing filter called as a moving average filter is used to eliminate the noise and short-term overshoots from signals while preserving the underlying signal representation or sharp step response. It is a straightforward yet effective statistical method for de-noising time-domain signals. The majority of Digital Signal Processing (DSP) applications that deal with time-series data prefer using these filters. By eliminating noise and maintaining a precise step response, it is easy to use, quick, and produces excellent results. It is therefore among the best options for time-domain encoded communications. In the time domain, the Moving Average filter is an effective smoothing filter, but it performs terrible in the frequency domain. Moving average filters perform well in situations where just time-domain processing is used, but they can be a terrible choice when information is encoded both in the time and frequency domains or just in the frequency domain.Given length N = 21 The given filter in the question is a Moving Average Filter H(ω) = ∑K = -∞∞h(k)e-jωkh(k) = 121 n = 0,1,2,......200 otherwiseH(ω) = 121∑K = 020e-jωk= 121e-jω212e-jω2sinω(21)2sinω2= 121e-j10ωsin21ω2sinω2 a. f(k) = 3 = 3cos(0k)here, ω = 0H(0) = 121e-j10(0)sin(0)sin(0)= 121212cos21ω212cosω2H(0) =1y(k) = 3 b. f(k) = cos2π21k here, ω = 2π21H(ω) = 121e-j102π21sin21×2π212sin2π21×2H(ω) = 0 y(k) = 0 c. f(k) = cosπ11khere, ω = π11H(ω) = 121e-j10π11sin21π11×2sinπ11×2= 121e-j10π11×20.99H(ω) = 121e-j10π11×21= e-j10π11y(k) = cosπk11-10π11