Nyquist rate

Gratton et. al. in [34] describes a least squares regression method to model heartbeat artifacts and to filter it out adaptively. Since the heartbeat rate is approximately 1 Hz, it is necessary that data is sampled at a sufficiently high rate (e.g. above the Nyquist rate) so as to represent and filter the artifacts out correctly and have minimal impact on the signal of interest itself [98]. 

Figure 8.8 Frequency response of at linear interpolation sample rate converter with L = 4 showing better stopband rejection around 0.5n (or at the original Nyquist rate) but increased rolloff in the passband below 0.25tc of almost -7 dB.

Aliasing Refers to an often detrimental phenomenon associated with the sampling of continous-time waveforms at a rate below the Nyquist rate. Frequencies greater than one-half the sampling rate become indistinguishable from frequencies in the fundamental bandwidth, that is, between DC and one-half the sampling rate. 

Nyquist rate To obey the Nyquist sampling theorem, a bandhmited waveform should be sampled at a rate which is at least twice the Nyquist frequency. This minimum sampling rate is known as the Nyquist rate. Failure to follow this restriction results in ahasing. 

Recent high-speed ADC applications. (From Song, B.-S., Nyquist-rate ADC and DAC, in The VLSI Handbook, Chen, W.-K., Ed., CRC Press, Boca Raton, FL, 2000, p. 54-5.)... 

ADC sampling rate, and is producing the fundamental wave at a quarter (20 MHz) of the ADC sampling rate. In this very configuration can one extend the intermediate frequency in the simple way that was described above, by utilizing the DDS-image frequency and the super-Nyquist sampling scheme. 

The effect of DP-2) is to produce a virtual pulse whose length is the width of the central lobe. Of course, this is never completely perfect since it does have side-lobes, but waveforms have been described for which the performance in this respect is excellent. DP-3) means that the Doppler frequency shift is being sampled at a discrete set of time points. If the sampling rate is faster than the Nyquist of the Doppler frequency shift, then the Doppler can be unambiguously extracted. 

Figure 3.13 (a) Values of charge-transfer resistance of different systems based on carbon, using the redox probe Fe(CN)6 . (b) Nyquist plot of different carbon nanotube composites in the presence of the redox couple, (c) Table with the electron-transfer rate constants calculated from cyclic voltammet data by using Nicholson method. Adapted with permission from Ref [103]. Copyright, 2008, Elsevier. 

---