Models and Theories in Human-Computer Interaction/The Nyquist-Shannon Sampling Theorem

The Nyquist-Shannon Sampling Theorem

The Nyquist Theorem is also called sampling theorem. It is used in signal processing and electrical circuit, the sample allows ADC(Analog to Digital Conversion) to generate a good analog waveform frequency. Sampling rate frequency refers to the number of samples per second. Nyquist formula: C = 2B log2 V (Bits/Sec), B refers to bandwidth in hertz(Hz), V refers to signal levels.The bandwidth of a signal is determined by the highest signal rate in the sine wave. The higher the frequency, the greater the bandwidth. According to Nyquist, if the transmitted rate is less than 2 times the bandwidth, then the frequency is insufficient to carry the signal.

The Shannon-Weaver model of communication has known as the "mother of all models". It concludes the concepts of signals, channel, noise, information source, message, probability of error, encoding, decoding, channel capacity, information rate and so on. The channel capacity refer to the reliable information signal for communication channel. It helps transmitting a signal through a noisy channels with a great understanding of error correcting methods, level of noise interference and data corruption. SNR(in dB) = 10 log10 (S/N), C = B log2(1+SNR); them refer to Channel capacity C (bit/sec), Signal power spectrum S(f), Noise power spectrum N(f), Signal to noise ratio (in decibels) SNR,and Bandwidth of the channel B. These formulas can be used for calculate the approximation of small, large, or constant of signal to noise ratios. In conclusion, the channel capacity is proportional to the bandwidth and SNR, which mean channel capacity and bandwidth can be increase linearly with the fixed SNR requirement. This way we can transmit a continuous signal with less power and noise.

Reference: https://www.st-andrews.ac.uk/~www_pa/Scots_Guide/iandm/part8/page1.html https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem