Using the Parks-McClellan algorithm, design an interpolator that increases the input sampling rate by a factor of I = 2.
1. Determine the coefficients of the FIR filter that has 0.5 dB ripple in the passband and 50 dB attenuation in the stopband. Choose reasonable values for the band-edge frequencies.
2. Provide plots of the impulse and the log-magnitude responses.
3. Determine the corresponding polyphase structure for implementing the filter.
4. Let x(n) = cos(0.4πn). Generate 100 samples of x(n), and process it using this filter to interpolate by I = 2 to obtain y(m). Provide the stem plots of the both sequences.