In a MP3 coder a cosine modulated filter bank is typically used to filter the input...

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In a MP3 coder a cosine modulated filter bank is typically used to filter the input signal. Consider the analog filter bank of N filters. hn(t)ho(t)cos(noot) where n = (0, 1, 2,... N-1) and ho(t) is real. A signal x(t) filtered through each filter to yield the signal yn(t). The output y(t) is the sum of yn. a. If Ho() is an ideal low-pass filter determine the cutoff frequency @e required such that there is no overlap between adjacent bands of the filters in the bank. Give your answer in terms of the modulation frequency @o. b. Now consider the case where the filter ho(t) arbitrary. Determine the effective impulse response of the filter bank h(t). If ho(t) is sampled such that C. N-1 ho(t)= Σ akd(t – kTs) - k=0 where T, = 27/(@oN) find h(t). In a MP3 coder a cosine modulated filter bank is typically used to filter the input signal. Consider the analog filter bank of N filters. hn(t)ho(t)cos(noot) where n = (0, 1, 2,... N-1) and ho(t) is real. A signal x(t) filtered through each filter to yield the signal yn(t). The output y(t) is the sum of yn. a. If Ho() is an ideal low-pass filter determine the cutoff frequency @e required such that there is no overlap between adjacent bands of the filters in the bank. Give your answer in terms of the modulation frequency @o. b. Now consider the case where the filter ho(t) arbitrary. Determine the effective impulse response of the filter bank h(t). If ho(t) is sampled such that C. N-1 ho(t)= Σ akd(t – kTs) - k=0 where T, = 27/(@oN) find h(t).