1. If you want to quantize a signal using 10 bits per sample (that is, using a 1
ID: 1798073 • Letter: 1
Question
1. If you want to quantize a signal using 10 bits per sample (that is, using a 10 digit binary number), how many discrete values can you represent?
2. To represent a number with an accuracy of 1 part in 1,000,000, (that is, 1 million, decimal), how many bits would you need?
3. Your personal musical player stores a lot of songs. Let’s suppose that your song is stored using 16 bits (that’s two bytes) to represent each “sample,” and that samples are recorded every 10 s. Your song is recorded in stereo, so there are two channels (left and right). How many bytes of memory are required to store a 3 minute long song? How many songs could be stored on a 4 Gigabyte player? Luckily compression is very effective for music, so we can reduce the required memory by more than an order of magnitude compared to the raw sample data.
4. Fill in the following table, providing the missing binary or decimal values.
Explanation / Answer
1. you can represent 2^10 discrete values i.e. 1024 discrete values. 2. For this accuracy you need atleast 1 million levels or discrete values. Hence 2^n = 1,000,000 Now 2^19 = 524,288 and 2^20 = 1,048,576 Therefore for atleast an accuracy of 1 part in 1,000,000 you need 20 bits. 3. No. of samples per second = 1/10u = 100,000 samples No. of bytes used per second = 100,000*2 = 200,000 bytes No. of bytes reqd for a 3 min song for one channel = 3*60*200,000 = 36,000,000 bytes For stereo or 2 channels = 2*36000000 = 72,000,000 bytes on a 4 gigabyte player no. of 3 min songs that can be stored = 4*1024*1024*1024/72000000 = 59.65 songs = 59 songs without compression 4. Decimal = Binary 43 = 101011 49 = 110001 1023 = 1111111111 will give the decimal ones in a bit
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.