Answer: a) 51,200 bits. b) : 10,240 bits.
Explanation:
If we sample a 3 - minute song at 40,000 samples per second, and we are told that each sample is represented by a combination of 16 bits, we can calculate the number of bits needed to store the song as follows:
N = 40,000 samples /sec . 16 bits /sample. 180 sec,. = 51,200 bits.
Now, if we compress the samples taken, after quantization, in a 5:1 relationship, this means that we will store only 1 of each 5 samples, essentially removing redundant information, so the number of bits needed after compresssion will be 51,200 / 5 = 10,240 bits.
It is interesting to note that if we apply the Sampling Theorem, that says that in order to be recoverable, a signal must be sampled at least two times during the shortest cycle, or at a frequency double than the highest frequency component in the signal, we can see that the signal is sampled at 20 Khz, which is usually the upper audible frequency limit.
