Undersampling in software defined radio

The continuous signal is represented with a green colored line while the undersampling in software defined radio samples are indicated by the blue vertical lines. In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal.

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. Sampling can be done for functions varying in space, time, or any other dimension, and similar results are obtained in two or more dimensions. T seconds, which is called the sampling interval or the sampling period. Reconstructing a continuous function from samples is done by interpolation algorithms. Most sampled signals are not simply stored and reconstructed. But the fidelity of a theoretical reconstruction is a customary measure of the effectiveness of sampling.

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This results in deviations from the theoretically perfect reconstruction, collectively referred to as distortion. Some amount of aliasing is inevitable because only theoretical, infinitely long, functions can have no frequency content above the Nyquist frequency. Aliasing can be made arbitrarily small by using a sufficiently large order of the anti-aliasing filter. Aperture error results from the fact that the sample is obtained as a time average within a sampling region, rather than just being equal to the signal value at the sampling instant. Jitter or deviation from the precise sample timing intervals.

Noise, including thermal sensor noise, analog circuit noise, etc. Slew rate limit error, caused by the inability of the ADC input value to change sufficiently rapidly. Quantization as a consequence of the finite precision of words that represent the converted values. Although the use of oversampling can completely eliminate aperture error and aliasing by shifting them out of the pass band, this technique cannot be practically used above a few GHz, and may be prohibitively expensive at much lower frequencies. Furthermore, while oversampling can reduce quantization error and non-linearity, it cannot eliminate these entirely.

Jitter, noise, and quantization are often analyzed by modeling them as random errors added to the sample values. Integration and zero-order hold effects can be analyzed as a form of low-pass filtering. Digital audio uses pulse-code modulation and digital signals for sound reproduction. In effect, the system commonly referred to as digital is in fact a discrete-time, discrete-level analog of a previous electrical analog. 20,000 Hz range of human hearing, such as when recording music or many types of acoustic events, audio waveforms are typically sampled at 44. PCM, MPEG audio and for audio analysis of subwoofer bandpasses. Wideband frequency extension over standard telephone narrowband 8,000 Hz.