The question is below, please help! You would like to use a 16-bit ADC to sample

Question

The question is below, please help!

You would like to use a 16-bit ADC to sample and digitally store some music records you dug up at your parents' (maybe grandparents'?) house. If the ADC is capable of sampling up to 50 kSamples/s, What is the minimum time required for each sample conversion? How many bytes of storage would be required to record the 2014 Record of the Year winner ("Get Lucky" by Daft Punk at 4 min, 8 sec for the radio ed it) if operating at the maximum sample rate? If the highest frequency in "Get Lucky" is 8kHz (there is a lot of bass!), what is the minimum sampling rate that would need to be used to accurately reconstruct the song? How many bytes of storage are required at this lower sampling rate?

Explanation / Answer

minimum time required will be when ADC is working at highest sampling rate 50khz . Minimum time is

1/50000 sec = 20 microsecond

b length of song =4min 8 sec= 248 sec

samples per second =50k

therfore total number of samples =50k*248 =12400000

1 sample requires 16 bit. therfore total memory required is 16*12400000 bits =198400000 bits

=24800000 bytes

c

using nyquist criteria. minimum sampling rate will be twice the highest frequency i.e we need to sample at 16Khz

d

length of song = 248 sec

samples per second =16k

therfore total number of samples =16k*248 =3968000

1 sample requires 16 bit. therfore total memory required is 16*3968000 bits = 63488000 bits

=7936000 bytes

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