A signal x(n) is to be resampled by a factor of 5/2. It has a total bandwidth of 0.8π, but we want to preserve frequencies only up to 0.7π and require that the band up to 0.75π be free of aliasing in the resampled signal.
1. Using the Parks-McClellan algorithm, determine the coefficients of the FIR filter that has 0.5 dB ripple in the passband and 50 dB attenuation in the stopband.
2. Provide plots of the impulse and the log-magnitude responses.
3. Using the fir2 function, generate a 101-length sequence x(n) whose frequency-domain sampled values are 0.7 at ω = 0, 1 at ω = 0.3π, 1 at ω = 0.7π, 0.5 at ω = 0.75π, 0 at ω = 0.8π, and 0 at ω = π. Process x(n) using this filter to resample it by a 5/2 to obtain y(m). Provide the spectral plots of both sequences.