Does anyone know how to compute the following questions?  I have been over the notes several times and I am confused on what we should do.  I am pretty good on everything else but these questions have me stumped.

1. Suppose we are recording music using a microphone (mono) with cut-off frequency of 44 Khz. We use an ADC (Analog-to-Digital Converter) to digitize the output of the microphone, and then we write the digital signal onto a disk with size 120 MB (1MB=10⁶ bytes). What is the minimum sampling period we should use if we want to be able to record at least 30 minutes of music (assuming the signal is quantized with 16 bits) with the least aliasing?

2.      Suppose we are recording music using a microphone with cut-off frequency of 30 Khz. We use an ADC (Analog-to-Digital Converter) to digitize the output of the microphone, and then we write the digital signal onto a disk with size 100 MB (1MB=10⁶ bytes).

a.      What is the minimum sampling period we should use if we want to be able to record at least 15 minutes of music using 16 quantization bits?

b.      What is the bandwidth of the pre-filter we should use in order to avoid aliasing?

3.      With reference to question above, suppose that we have recorded 15 minutes of music on the disk. Now we want to copy the music content onto a disk which contains only 60 MB, by subsampling the original signal.

a.      Which subsampling ratio should we use to make sure that all 15 minutes of music will fit into the new disk using 16 quantization bits?

b.      What is the bandwidth of the pre-filter to avoid aliasing?

4.      Suppose that we have 15 minutes of music on the 100 MB (1MB=10⁶ bytes) disk, which is digitized with the sampling rate f and 16 quantization bits. Now we want to copy the music onto a 60MB disk. Instead of subsampling, we want to reduce the size of the digital signal by performing a coarser uniform quantization on the already digitized signal.

a.      How many quantization levels should we use to make sure that all 15 minutes of music will fit into the new disk?

b.      What is the difference in quantization SNR between the signal before and after the coarser quantization? (Recall how to compute SNR and its measurement unit. For every bit we add/deduct when quantizing an input sample, by how much does the quantization SNR increase/decrease approximately.)

Also, I will be in the study room outside of A-210 tomorrow around 1:00pm if anyone would like to get together to study before class.  If someone could come and help me with these questions that would be great.  Thank you.

Sir KKNAUR, I will meet you there at 1.