Respuesta :
Answer: a) 51,200 bits. Â 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.
The number of bits is "115.2 Mbits".
A number of bit calculations:
Sampling rate [tex]= 40,000 \ \frac{\text{samples}}{\text{second}}[/tex]
store time= 3 minute
Depth of each sample = 16 bits
Converting the time minutes into second:
[tex]\to 3 \times 60 = 180 \ seconds\\\\[/tex]
Calculating the total number of samples in 3 minutes:
[tex]\to 40,000\times 180\\\\ \to 7,200,000[/tex]
Calculating the Number of bits:
[tex]\to 7,20,000 \times 16\\\\ \to 115,200,000\ bits[/tex]
Converts bits in Mbits:
[tex]\to 115,200,000\ bits\\\\ \to 115.2 \times 10^6 \ bits\\\\ \to 115.2\ Mbits[/tex]
Therefore, the number of bits is "115.2 Mbits".
Find out more information about the bit calculation here:
brainly.com/question/15849452
