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SamplersHow do they work?

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Sampling

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ADC

Sounds from the real world can berecorded and digitized using an Analog-to-Digital Converter (ADC).

As in the diagram below, the circuit takesa sample of the instantaneous amplitude(not frequency) of the analoguewaveform.

Frequencies will be recreated later byplaying back the sequential sampleamplitudes at a specified rate

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Sample Rate

Samples are taken at a regular time intervals called thesampling rate.

According to the Nyquist theorem (named after HarryNyquist), the highest reproducible frequency of a digital

system is 1/2 the sampling rate, often called the Nyquistfrequency.

A sampling rate of 44,100 samples per second, the rate atwhich CD's are encoded, can reproduce frequencies up to22,050 Hz, well above the 20,000 Hz limit of human hearing.

Frequencies that are recorded above the Nyquist frequencymay foldover at a much lower frequency than the original,which is called aliasing.

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Aliasing

If the signal to be sampled containsfrequencies that exceed one-half thesampling rate, these frequencies will besampled but will appear to be lower infrequency when outputted.

This phenomenon, called foldback oraliasing, occurs where rogue frequenciesappear in the signal.

These rogue frequencies are related toamount by which the signal's frequencyexceeds half sampling frequency.

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Aliasing

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Anti Aliasing Filter

To avoid aliasing, a steep (brickwall)filter is used. This filter is placedbefore the ADC input to prevent

signals above the Nyquist frequencyfrom entering the system.

Standard sampling rates are 44.1K

are 48K (and even 96K in somehigh-end recording systems).

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Anti Aliasing Filter

In essence the ANTI ALIASINGFILTER is a Low Pass Filter

if the sampling rate is 44.1kHz thenthe filter is used to remove anyfrequency above 22.1kHz, well abovethe frequency of normal hearing.

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ADC

The ADC 'measures' the instantaneousamplitude of the input signal at regularintervals - for CD quality it measures theamplitude 44100 times per second.

These measurements are thenrepresented as a series of 1 and 0s. Thesize of number which can represent thesemeasurements is determined by the bitrate.

The higher the bit rate the higher thequality and greater the dynamic range

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Bit Rate

The number of available values is determined bythe number of bits (0's and 1's) used for eachsample in a process called quantization.

When a sample is quantized, the analogueamplitude has to be rounded off to the nearestavailable digital value.

This rounding-off process is calledapproximation.

The smaller the number of bits used per sample,the greater distances the analogue values needto be rounded off to.

The difference between the analogue value andthe digital value is called the approximation orquantizing error

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Bit Rate

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Bit Rate

The greater the approximation error, thegreater the amount ofdigital or quantizingnoise produced.

6 dB of dynamic range for every additional bit

used per sample.

The CD/DAT standard 16-bit samples, with theirimpressive 65,536 values for quantizing, providethe theoretical playback system optimum of 96

dB dynamic range.

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Bit Rate

CD quality is 16 bit this means that each discrete samplemeasurement can be represented in 65,500 value.

The relationship between these values and the bit rate isgiven by

D=2n where D is the available number of values and n isthe bit rate.

We can see the that the quality of sampling/dynamic rangeis not a linear relationship so 16 bit is not twice as good as8bit but many times better

8 bit gives us 256 values for example - image colours onyour screen

16 bit 65,500 20 bit =2 20

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Bit Rate and Dynamic Range

The relationship between bit rate anddynamic range is given by

S=6ndB

so 8 bit is 48bB

16 bit is 96dB

20 bit = 120dB

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Memory

Once the signal has been sampled andconverted into a series of 1s and 0s it isthen stored in the samplers/computersmemory

RAM Random Access memory -this isthe computers/samplers memory areawhere the temporary storing and editingof samples occurs

Typical editing functions are topping andtailing, looping, reversing, time stretchingetc occur

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Editing

Editing Topping and tailing - remove noiseunwanted sections etc

Looping Used to elongate sounds - a section atthe end of a sample would be looped indefinitelyto produce sustain - save memory The transitionfrom the end of the sample to the loop point iscritical as these is where any differences inamplitudes etc will he heard. If not correct thenclick etc are heard, this is where we use xfades toeven out the velocities at the beginning and end

of loops. Like a loop of tape Time stretching Changing the pitch keeping the

time the same changing the time, keeping thepitch the same reversing - as it says

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Multi sampling

Take many samples from an instrument to reduce thephenomenon called munchkinisation.

If a single note on an instrument is sampled and put across thekeyboard then as we move up/down the keyboard from theoriginal pitch of the sample, it sounds less and less like the

original instrument. To over come this instruments are multi samples.

The samples can be velocity triggered to provide subtle nuancesof the instrument. As the trumpet plays louder it gets brighter andso on.

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Storage and Types

Originally samples were stored on51/2 floppy disks each disc couldonly hold a megabit

31/2 inch floppy disks could hole justover 1meg

Then zip drives, hard discs etc

Now stored on computer hard drives.

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DAC

DAC - this is where the signal is convertedback into an analogue signal i.e. acontinuously varying signal/voltage asopposed to a discrete digital signal.

Very simply the DAC emits a voltageproportional to the number inputted.

This creates a stair step reconstruction of

the original signal. A reconstruction filter (LPF) is used to

smooth the transitions of the stair stepsignal.

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Block Diagram of a Sampler

Random Access

Memory

Digital info

Stored in memory

where it can be

manipulated

Brick Wall filter

Anti Aliasing FilterDoes not allow any

frequency

above 20kHz to

pass through

ADC

Analogue to

digital convertor

DAC

Digital to

analogue

converter

LPF

Reconstruction

Filter

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Types

Stand alone - Akai

Keyboard

Computer- based - Logic's EXS24