the analog to digital conversion process

The Analog to Digital Conversion Process

Joel Amulraj

Chennai, India Week 2 Assignment


• Sounds are analog - they are made of waves that travel through matter. People hear sounds

when these waves physically vibrate their eardrums.

• Since Computers are digital devices, they cannot understand these continuous pressure variable

analog signals, so they communicate digitally, using electrical impulses that represent 0s and 1s

( i.e., through Binary).

Binary Notations:

• One binary digit (0 or 1) is referred to as a bit, which is short for binary digit. One bit can only be

used to represent 2 different values: 0 and 1.


• To represent more than two values, we need to use multiple bits.

• Two bits combined can be used to represent 4 different values: 0 0,

0 1, 1 0, and 1 1.

• Three bits can be used to represent 8 different values: 0 0 0, 0 0 1,

0 1 0, 1 0 0, 0 1 1, 1 0 1, 1 1 0 & 1 1 1.

• In general, 'n' bits can be used to represent 2^n different values.

20 1

21 2

22 4

23 8

24 16

25 32

26 64

27 128

28 256

29 512

210 1,024

211 2,048

212 4,096

213 8,192

214 16,384

215 32,768

216 65,536

Which part of the computer component converts the analog to digital information??

“The Sound Card “

The most basic sound card is a printed circuit board that translates analog and digital information:


An analog-to-digital converter (ADC)

The ADC translates the analog waves of your voice into digital data that the computer can understand. To do this, it samples, or digitizes, the sound by taking precise measurements of the wave at frequent intervals.

A digital-to-analog converter (DAC)

If you were to play your recording back through the speakers, the DAC would perform the same basic steps in reverse. With accurate measurements and a fast sampling rate, the restored analog signal can be nearly identical to the original sound wave.

Capture and playback of digital audio

Air pressure

variations

Captured via

microphone

Air pressure

variations

ADC

Signal is

converted into

binary

(discrete form)0101001101

0110101111

Analogue to Digital Converter

DACConverts

back into

voltage

Digital to AnalogueConverter


Audio analogue to digital converters work by repeatedly

measuring the amplitude(volume) of an incoming electrical

pressure soundwave (an electrical voltage), and outputting

these measurements as a long list of binary bytes. In this way,

a mathematical "picture" of the shape of the wave is created.


The 2 essential parameters

There are 2 important parameters which control the quality of the audio conversion process. These are ...

Sample rate

& Word length

Number of samples taken per second.

Known as Bit depth.

It is the number of bits used to carry the data in each sample of audio.

Sample Rate ( in detail )

• Sample rate is the number of samples of audio carried per second, measured in Hz or kHz.

• Sampling rate defines the number of samples per second taken from a continuous signal to make a discrete or digital signal.

• Sampling involves taking snapshots of an audio signal at very fast intervals usually tens of thousands of times per second.

• For audio production, the least samples rate that is required is 44.1 Khz. The other sample rates are 48Khz, 88.2 Khz, 96 Khz, 192 Khz.


Why a minimum of 44,100 hz sample rate is required ? Nyquist theorem

It states that :

"The sample rate should be a little over twice the amount of the highest audio frequency (harmonic) to be

recorded if poor sound quality is to be avoided".

• Because humans can hear audio frequencies as high as 20KHz (20,000cps/Hz), a minimum sample rate of 44.1KHz

(or 44,100 sample measurements a second) was decided upon.,

Human audio spectrum = 20Hz to 20,000Hz (20KHz)

Highest audio frequency = 20,000Hz ... therefore ...

20,000 x 2 = 40,000 + "a little bit more" = 44,100 samples per second

Sampling frequency - Lower sample rates produce poorer quality

Because of less samples, The resulting waveform is not a smooth waveform like the original waveform.

Sampling frequency - Higher sample rates produce better quality recordings

Because of more samples, The resulting waveform is a smooth waveform like the original waveform.

The Bit Depth ( Word length )

Bit depth is the number of bits of information in

each sample, and it directly corresponds to

the resolution of each sample.

For example in digital world, information are

represented in binary ( 0 & 1) – base 2.

For 2 bit system – 2^2 ( 4 possibilities ) are there to

represent the information.

For 8 bits it is 256 possibilities.

Such like that a 16 bit system uses 65,536

possibilities to represent the sampled frequency.


So how many possibilities for 24 bit system?? Yes, it’s 16,777,216 possibilities

Examples of bit depth - Compact Disc Digital Audio, which uses 16 bits per sample,

and DVD-Audio and Blu-ray Disc which can support up to 24 bits per sample.

• The longer the word length the larger the file size, the less the distortion, the better quality the sound

• The shorter the word length, the smaller the file size, the more the distortion, the poorer quality the sound


Bit depth is not only used to represent the sampled frequency, but also decides the maximum amount of

amplitude ( loudness dB) that can be sampled. i.e the Dynamic Range of the signal.

Formula for calculating the loudness = 20 log 2^n ; ( where n is the no. of bits )

Example 1 : Calculate the loudness present in the sample rate of 44.1 khz which uses a 16 bit depth ??

20 log 2^ 16 = 96 dB

Example 2 : Calculate the loudness present in the sample rate of 48 khz which uses a 24 bit depth ??

“ Each bit contributes to 6 dB “


• Playing back the recorded audio in a different sample rate, changes it pitch and speed.

• Such like, if the recorded audio is played from a lower sample to a higher sample rate, then the pitch will be sound low and the speed the song ( tempo) will also be high

• If the recorded audio is played from a higher sample to a lower sample rate, then the pitch will sound low and the speed the song ( tempo) will also be high.


To conclude ,

Analog to Digital conversion happens by sampling the analogue signal using binary bits ( 0 & 1)

For the conversion to happen 2 parameters are important

The Sampling Rate & The Bit Depth ( word length )

• The Sampling Rate corresponds to the frequency of the signal

• The Bit depth corresponds to the Amplitude ( DR ) of the signal

Conclusion

That’s it Folks, It was really interesting in doing this assignment and collecting all these details.

Learnt a lot about these conversion process and even about sampling quantization too.

Hope I have done good on this assignment. Look forward to get a good review from you. If there is

any mistake kindly correct me. Thanks for your valuable time and going through this assignment.

Joel Amulraj

the analog to digital conversion process

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