It is desired to design a 4× oversampling digital FIR interpolation filter for a CD player. Assume the following specifications: audio sampling rate of 44.1 kHz, passband range [0, 20] kHz, stopband range [24.1, 88.2] kHz, and stopband attenuation of 80 dB. Using the Kaiser window design method, determine the filter length and the total computational rate in MAC/sec for the following cases:
a. Single-stage design implemented in its polyphase form.
b. Two-stage (2×2) design implemented in its polyphase form. What are the design specifications of the two stages?
Draw a sketch of the magnitude responses of the designed filters versus frequency in the range 0 ≤ f ≤ 176.4 kHz, and of the two individual filter responses in the two-stage design case. What are the computational savings of design (b) versus design (a)? Can a 20 MIPS DSP chip handle the computational rates?