Design a discrete-time matched filter for cosine signal

Question

MATLAB Exercises

(a) Construct a signal plus noise random sequence using 10 samples of

X[n] = cos (2πf_ont_s) + N[n],

where N[n] is generated using randn in MATLAB and f₀ = 0.1/t_s. Design a discrete-time matched filter for the cosine signal. Filter the signal plus noise sequence with the matched filter. At what sample value does the filter output peak.

(b) Construct a signal plus noise random sequence using 10 samples of the following

X[n] = cos (2πf₁nt_s) + 10 cos (2πf₂nt_s) + N[n],

where N[n] is generated using randn in MATLAB, f₁ = 0.1 /t_s , and f₂ = 0.4/t_s . Design a discrete-time matched filter for the f₂ cosine signal. Filter the signal plus noise sequence with the matched filter. At what sample value does the filter output peak.