Group 1: Sampling Theory
– Functions of space, time, or any other dimension can be sampled.
– Sampling in two or more dimensions is possible.
– Sampling involves measuring the value of a continuous function at regular intervals.
– The Nyquist frequency plays a crucial role in sampling to avoid misinterpretation.
– Anti-aliasing filters are essential to prevent frequencies above the Nyquist frequency from affecting samples.
Group 2: Practical Considerations in Sampling
– Continuous signals are sampled using analog-to-digital converters (ADCs).
– Various types of distortion can occur, including aliasing and aperture errors.
– Jitter, noise, and quantization are common issues in sampling.
– Oversampling can help mitigate some errors but has limitations.
– Analog noise becomes dominant in practical ADCs at audio frequencies.
Group 3: Audio Sampling Applications
– Digital audio uses pulse-code modulation (PCM) for sound reproduction.
– Sampling rates for audio typically range from 44.1kHz to 96kHz.
– Industry trends show a move towards higher sampling rates.
– The Audio Engineering Society recommends different sampling rates for various applications.
Group 4: Video and 3D Sampling
– Standard-definition television uses 720×480 pixels or 720×576 pixels.
– High-definition television uses 720p, 1080i, and 1080p.
– Temporal sampling rate is defined as the frame rate.
– Volume rendering samples a 3D grid of voxels for 3D renderings.
– Used in medical imaging, X-ray CT/CAT, MRI, and PET.
Group 5: Specialized Sampling Techniques
– Undersampling (bandpass sampling) and oversampling.
– Complex sampling for simultaneous sampling of related waveforms.
– Downsampling, upsampling, and multidimensional sampling.
– Crystal oscillator frequencies and in-phase and quadrature components.
– Sample rate conversion, digitizing, sample and hold techniques.
In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the term's usage in statistics, which refers to a set of such values.
A sampler is a subsystem or operation that extracts samples from a continuous signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points.
The original signal can be reconstructed from a sequence of samples, up to the Nyquist limit, by passing the sequence of samples through a reconstruction filter.
