How many bits does it take to store a 3-minute song using an audio encoding method that samples at the rate of 40,000 samples/second, has a bit depth of 16, and does not use compression

Part ( a) 51,200 bits.

Part (b) : 10,240 bits.

THIS IS THE COMPLETE QUESTION

How many bits does it take to store a 3-minute song using an audio encoding method without compression that samples at the rate of 40,000 samples per second and has a bit depth of 16? What if it uses a compression scheme with a compression ratio of 5:1?

Step by step Explanation;

We will be making use of the Sampling Theorem in solving this problem, Sampling Theorem states that a signal must be sampled at for least twice in the process of completing it's shortest cycle, which means that the signal frequency having a double frequency a bit greater than the highest frequency component in the signal,

From the question, a 3 - minute song at 40,000 were sampled per second, and each of this sample is debited having combination of 16 bits.

To calculate the number of bits it take to store the song we will makes use of the below formula:

N = 40,000 samples /sec . 16 bits /sample. 180 sec,. = 51,200 bits.

Therefore , the 3-minute song can store in 51,200 bits.

If the sample were to be compressed in a compression ratio of 5:1, then we will be storing only 1 of each 5 samples, essentially removing redundant information,

Therefore, the number of bits required after compresssion with compression ratio5:1 is calculated below as:

N = 51,200 / 5 = 10,240 bits.

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