Sampled sound data

A recorded amplitude is −3 relative to a zero reference. Which reading keeps the recorded value?

The minus sign belongs to the amplitude value

Record values at separate times

A sampled sound representation records amplitude values at separate times. The sample rate is the number of samples recorded per second in each channel

A recorded amplitude can be positive, zero or negative relative to a reference. Its value is different from the sample's time or position in the list

The small tables here illustrate the representation. They do not contain every value of a continuous signal between the sample times

Read the requested time

A classroom sound model records one amplitude value at each listed time. Negative values lie below its zero reference; keep the sign when reading a value

What amplitude was recorded at 0.5 seconds?

The row at 0.5 seconds records amplitude 3

This is the recorded value at that instant; the table does not establish every value between the sample times

Read a negative sample

Assign bits to recorded levels

A binary codebook can assign a bit pattern to each allowed recorded level. The classroom model below uses four levels and two bits per sample

Use the supplied mapping exactly. These are assigned level codes, not a general rule for writing negative integers in binary

Store the sample codes in time order. Two samples of two bits each use four bits, even when the first code begins with zero

Join codes in sample order

Use this supplied classroom codebook. Its negative amplitudes are labels for recorded levels; the codes are explicitly assigned here, not a general signed-integer encoding

Store the first sample's two bits followed by the second sample's two bits

Write the four stored bits in order, with no spaces

The first amplitude -3 has code 00

The second amplitude 1 has code 10

Join them in order: 00 then 10, giving 0010

Keep both two-bit codes

Rate and bit depth describe different quantities

Sample rate counts samples per second. Bits per sample, often called bit depth, describes how many bits store each sample value

Two bits have four possible patterns. Four bits have sixteen possible patterns, allowing more distinct recorded levels if each is assigned a different pattern

More samples per second do not by themselves create more level codes. More bits per sample do not by themselves add more sample times

For one uncompressed channel, with no extra endpoint sample in the stated model

Count samples before their bits

A small uncompressed classroom audio model records 4 samples per second for exactly 2 seconds, using one channel

Every sample uses exactly 2 bits. The complete recording contains exactly \(\text{rate} \times \text{duration}\) samples, with no extra endpoint sample

Count sample data only: no header, metadata, padding or compression is included. The small rate illustrates storage counting, not usable recording quality

How many bits of sample data are stored?

Number of samples = \(4 \times 2 = 8\)

One channel's sample data = \(8 \times 2 = 16\) bits

There is one channel and no extra endpoint sample in this model; the stated exclusions remain outside this count

Keep rate and duration separate

This raw model records exactly two seconds in one channel, without headers, padding, compression or an extra endpoint sample. Start with four samples per second and two bits per sample. Predict the effect of doubling the rate only, test it, then reset and double the bits per sample only

What is different between doubling only the sample rate and doubling only the bits per sample in this model?

Two supplied signal descriptions both have amplitude 0 at time 0 and time 1. Between those times, A stays at 0 but B rises and falls. A recorder takes samples only at times 0 and 1. What follows?

Compare the listed sample times with the interval where the descriptions differ

Keep channels and file overhead explicit

A one-channel model stores one sequence of samples. Two channels store two separate sequences, such as left and right

When duration, rate and bits per sample are the same for both channels, their combined raw sample payload is twice the one-channel payload

Real audio files can contain headers, metadata, padding or compression. The stated raw sample formula does not by itself give every file's complete size

The low example rates make counting manageable; they are not recommendations for recording usable sound

A raw model stores four samples in each channel, at two bits per sample. There are two channels and no other data. How many bits are stored altogether?

Count one channel first, then include the second channel

Separate time, value and storage

Read the amplitude at the requested time and keep its sign

Use the supplied level codebook and preserve sample order when joining bits

Sample rate controls samples per second; bit depth controls bits per sample

Calculate only the raw payload described by the duration, channel and overhead assumptions; matching sparse samples do not prove identical values between them