# The nyquist theorem is one of the deciding factor in data communication

In our case, should the input signal exceed 10 000 mV a 16 bit binary number with an equivalent decimal value of 65535 would still be returned to the computer. This error is called saturation of the ADC.

However, the input signal should span as much of the ADC input voltage range as possible, without saturating the ADC, since this increases the signal to noise ratio. However, the input signal to the ADC should also spanas much of the ADC input voltage range as possible, without saturating the ADC, since this increases the signal resolution. The sampling rate is the frequency expressed in Hertz Hz at which the ADC samples the input analogue signal. As mentioned before, the sampling interval is the time between successive samples: Generally speaking, the faster the rate at which a signal changes, the higher the frequency content of the signal, and the higher is the sampling rate needed to reproduce it faithfully.

This can be appreciated from the figure, which shows that the rapidly rising phase of the wave form is not represented as well in the sampled waveform as is the more slowly changing part. In fact, it can be proven mathematically that the sampling rate to be used must be greater than twice the highest frequency contained in the analogue signal. This critical sampling rate is called the Nyquist Sampling rate.

The figure to the right below illustrates the sampling of a sine wave using two different sampling rates. The highest frequency present in this signal is the frequency of the signal itself, since it is a simple sine wave, and so contains only one frequency. Note that the sampling rate in the upper figure is about ten times higher than the highest frequency present in the signal and so is about five times the Nyquist rate. The sampled signal is thus a reasonable approximation of the analogue signal.

The lower figure above shows the situation that results when the sampling rate is reduced to about 1.

## Nyquist Theorem

This sampling rate is thus lower than the Nyquist rate, and the sampled signal dashed line bears little resemblance to the analogue signal.

Note that the frequency of the sampled signal is much smaller than that of the analogue signal. This artifactual result due to improper choice of the sampling rate is called aliasing. Why not always sample at the highest rate possible? It is critical that the sampling rate be sufficiently high.

For example, in experiments in which the resting membrane potential of skeletal muscle is measured, a sampling rate of about 25-50 Hz is sufficiently high. In contrast, when measuring action potentials in nerve axons, which are much more rapidly changing events, a sampling rate of 10-20 kHz is required. However, for a signal of given frequency content, increasing the sampling rate beyond a certain point does not significantly increase the fidelity with which the signal is rendered.

- The Nyquist Theorem, also known as the sampling theorem, is a principle that engineers follow in the digitization of analog signal s;
- Suppose the highest frequency component, in hertz , for a given analog signal is fmax;
- Usually we are interested in signals of a particular frequency range or bandwidth;
- A few definitions to remember Desired signal;
- The sampling in an analog-to-digital converter is actuated by a pulse generator clock;
- The required sampling rate is determined by the accuracy of the digitizing process.

In addition, the cost of an ADC increases as higher sampling rates are desired. Finally, more computer processing time and storage space in memory or disk are needed to process the larger number of data points produced when the sampling rate is increased. Thus there is a tradeoff between fidelity of reproduction on the one hand, and computer storage space, computing time, and cost on the other. Filtering Any ADC has a maximum sampling rate.

In some circumstances, this maximum sampling rate is not high enough to satisfy the Nyquist conditions mentioned above.

In that case, one can pass the analogue signal through a low-pass filter before sending it on to the ADC. This filter acts to remove some of the high-frequency content of the signal that would otherwise alias down in frequency, producing spurious low-frequency content along the lines illustrated above. Note that this anti-alias filtering could remove high frequency information of physiological importance to the phenomenon under investigation.

If it is important to retain these higher frequencies, one has no choice but to use a better data acquisition system that has a higher sampling rate. A biological signal can be broken down into fundamental frequencies, with each frequency having its own intensity. Display of the intensities at all frequencies is a power spectrum. Usually we are interested in signals of a particular frequency range or bandwidth.

The bandwidth is determined by filters, which are devices that alter the frequency composition of the signal. There are three types of filter: Low frequency or in old terminology high pass. High frequency or in old terminology low pass. Filters one frequency, usually 60 Hz. Real filters or hardware filters alter the frequency composition of the signal. It means after filtering the signal, we cannot recover the frequencies that have been filtered. Digital filters change the frequency of the signal by performing calculations on the data.

It means you the nyquist theorem is one of the deciding factor in data communication record all the frequency components of your signal and by digitally filtering it, eliminate the unwanted frequencies. Any unwanted signal that modifies the desired signal is noise. It can have multiple sources. It is interesting to note that you can dither add white noise: Narrowband noise confines itself to a relatively small portion of the overall signal bandwidth as defined by Nyquist. Broadband noise occupies a significant portion of the Nyquist bandwidth.

For example, 60Hz-hum is narrowband because it typically limits itself to a 60 Hz component. Thermal noise is definitely broadband because its PSD is constant, meaning that it distributes its energy over nearly the entire spectrum. The higher the SNR, the better can you distinguish your signal from the noise.

A few definitions to remember Desired signal: If a gain is one, the signal remains unchanged; if the gain is higher than 1, the signal is amplified. If the gain is lower than one, the signal is reduced. It produces a distortion of the signal, i. The required sampling rate is determined by the accuracy of the digitizing process.