Introducing 

Prezi AI.

Your new presentation assistant.

Refine, enhance, and tailor your content, source relevant images, and edit visuals quicker than ever before.

Loading…
Transcript

  • Sampling Rate

The representation of a digital signal is discrete, that is to say, it is a collection of discontinuous values.

Every captured value is referred to as a sample.

The capture of samples takes place at a constant periodic interval, this is called "Sampling Period".

The duration of the interval determines the range of frequencies that can be represented correctly in a system.

The shorter the interval, the higher the definition of the signal and the greater the range of frequencies that can be represented.

  • Sampling is the process through which a signal is periodically measured and stored in memory.

  • Once the signal is captured in its digital form it is important to be able to reconstruct it as an analogue signal, so it can be processed and then reproduced again.

  • In order to respect this there are certain aspects that must comply.

Sampling

Digital Representation of Sound

Sampling

The acoustic signal is captured by a microphone, which works as a transducer, moving the signal from its acoustical form to an analogue voltage variation, then an "Analog to Digital Converter" produces a digital representation of it.

Nyquist Frequency

Named after the engineer Harry Nyquist, this frequency is the highest frequency you can sample before aliasing begins to occur.

The process implies two steps: Sampling and quantization.

Given that the sampling period is a time interval, we can measure how many intervals fit in one second, that is known as the Sampling Rate or Sampling Frequency.

The unit used to measure the sampling rate is Hz

The most used sampling rate is the one used by C.D. technology and it has a value of:

44,100Hz

Sampling Rate

Sampling Theorem

In order to be able to reconstruct a sampled signal with a period T, it is necessary that the sampling rate is high enough to allow for a minimum of two samples to exist per signal period T.

In other words, the sampling frequency must be at least twice the value of the highest frequency carried in a signal.

If this condition is not met, the original signal is substituted by an alias with a frequency different from that of the original signal.

The frequency of the alias signal can be calculated as follows:

Aliasing frequency = sampling frequency - original frequency

It is due to this behavior that the phenomenon is also known as "folding"

Bit Depth

The amount of bits used to represent a sound sample is known as "Bit Depth"

The bigger the number of bits used, the smaller the quantization noise.

The dynamic range of a recording system depend on the bit depth.

The higher the bit depth the higher the dynamic range.

C.D.s use a bit depth of 16 bits, this is a very commonly used bit depth.

Typical bit depths used in audio systems:

8bits, 16 bits, 24 bits y 32 bits.

Aliasing is a phenomenon by which two signals with different frequency fit into the same pattern of samples.

Aliasing

Given that the digital representation of sound is discrete, what takes place between recorded samples is not available any more to be reconstructed. It is therefore important to use a fast enough sampling period.

For audio applications it is important to remember that the human hearing range goes from 20 Hz to 20,000Hz.

Considering this, and using the Sampling Theorem, we know that we should use a sampling rate of at least 40,000Hz.

A standard sampling rate of 44,100Hz has been adopted since the use of the C.D. was generalized and is implemented by many commonly used formats.

If the sampling period is not fast enough, when the signal is reconstructed a digital artifact called aliasing takes place.

Ideal Sampling Frequency for Audio Processing

Digital

Processing

of

Sound

Quantization

Discrete Amplitude Resolution

Representing a sound sample in binary numbers is a process by which information is inevitably lost.

The loss of information introduces an error in the signal representation.

This error is known as:

"Quantization Noise"

Smoothing Filter

Antialiasing filter

This Lowe Pass Filter is applied after the signal has been recreated and is used to smooth its shape from a staircase shape to a continuous line.

This filter is used before the signal is sampled such that frequencies higher than the Nyquist frequency are removed, thereby avoiding aliasing

Example:

Given a sampling rate = 11,000 Hz

What is the Nyquist frequency?

Aliasing:

for a signal with a frequency = 7,000 Hz

the recreated signal will have a frequency:

11,000 Hz - 7,000 Hz = 4,000 Hz

Learn more about creating dynamic, engaging presentations with Prezi