Every Continuous time Signal is Analog Signal

Signal processing hardware

Arnaldo Mendez , Mohamad Sawan , in Implantable Biomedical Microsystems, 2015

Other analog processors of neural signals

Analog signal preprocessing has been incorporated by an increasing number of works to perform some tasks that were usually executed at the back-end stages using digital signal processing such as on-chip spike detection, spike features extraction, and wireless transmission of the isolated spike, the spike features, or both [ 26–32]. These works also demonstrate that analog signal preprocessing using relatively simple but effective analog architectures allows reducing the bandwidth and the power required to process and transmit the data by adopting the design principles presented in Section 4.2.

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Signal Processing, Analog

W.K. Jenkins , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

I Introduction

Analog signals are processed by specially designed devices, circuits, or systems to extract parametric information or to alter the characteristics of the input signal in some prescribed way. Spectral shaping is probably the most common form of analog signal processing and is typically done with either passive (containing resistors, capacitors, and inductors) or active [containing resistors, capacitors, and operational amplifiers (op amps)] analog filters. The active filter is probably the most common analog signal processor in use today. During the past few years, switched-capacitor filters have become popular as high-precision replacements for certain types of active filters that are to be realized in monolithic form as part of a more extensive integrated system. Switched-capacitor circuits, which contain capacitors, transistor switches, and operational amplifiers, have been successfully used for analog pre- and postfilters required at the interface between analog and digital systems. This subject is treated in more detail in Section VI. Both active filters and switched-capacitor filters are closely related historically to the analog computer, from which the term analog first originated.

Analog signals can be processed by many different types of devices, some of which are surface acoustic wave (SAW) filters, charge-coupled devices (CCDs), high-frequency distributed-parameter circuits, or optical circuits, to name only a few. Since it will not be possible to discuss all the different classes of analog processing techniques and devices, and because many of these are treated elsewhere, attention will be devoted to reviewing important mathematical tools used in analog signal analysis, discussing the connection between modern analog signal processing and its origins in the analog computer, and examining several particularly important historical topics in analog signal processing. These special topics include switched-capacitor filters, electronically tunable analog filters, nonlinear modeling by means of the analog computer, and image reconstruction for synthetic aperture radar by optical processing techniques.

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Overview of DSP Algorithms

Robert Oshana , in DSP for Embedded and Real-Time Systems, 2012

DSP systems

Analog signals are converted to digital signals through a process called sampling. Sampling is the process of taking an analog signal and converting it to discrete numbers. The sampling frequency (or sampling rate) is how many times per second the signal will be sampled. This is important because it restricts the highest frequency that can be present in a signal. Any signal greater than half the sampling rate will be folded into a lower frequency that is less than half the sampling rate. This is known as aliasing and will be discussed in more detail in the next section.

The inverse of the sampling frequency is known as the sampling period. The sampling period is the amount of time that elapses between the samples of the analog signal. This conversion is done by hardware that takes the best approximation of the voltage level and converts it to the nearest digital level that can be represented by the computer. The loss of information during the conversion is referred to as quantization.

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Analog-to-Digital and Digital-to-Analog Converters

Brahim Haraoubia , in Non-Linear Electronics 2, 2019

2.2.2.2 Shannon's theorem

Theorem formulation

An analog signal is faithfully represented by its samples if the sampling frequency is at least equal to double the highest frequency contained in the signal spectrum.

Example 1

Consider the sinusoidal signal s(t) shown in Figure 2.14a:

$\mathbf{s}\left(\mathbf{t}\right)={\mathbf{V}}_{\mathbf{m}}.\mathbf{sin}\left(\mathbf{\omega t}\right)$

Figure 2.14. Sampling and reconstitution of the original signal when the sampling frequency is equal to the frequency of the original signal. For a color version of this figure, see www.iste.co.uk/haraoubia/nonlinear2.zip

T = (1/f); f = (ω/2π); T period of the sinusoidal signal s(t)

T_e = (1/f_e); T_e and f_e are the period and the sampling frequency respectively.

It can be seen that after sampling (Figure 2.14b) and reconstitution, the signal obtained (Figure 2.14c) is inconsistent with the original signal s(t).

This is because during sampling, Shannon's theorem is not respected (the sampling frequency is chosen as being equal to the frequency of repetition of the processed signal).

Example 2

The same previous analog signal "s(t)" will be considered. Nonetheless, the sampling frequency f_e is set this time as equal to 11 times the frequency of signal "s(t)".

In Figure 2.15c , it can be noted that the signal reconstructed from samples presented in Figure 2.15b is virtually consistent with the initial analog signal "s(t)" (Figure 2.15a) because Shannon's theorem is respected.

Figure 2.15. Sampling and reconstruction of the original signal when the sampling frequency is very large compared to the maximal frequency of the signal. For a color version of this figure, see www.iste.co.uk/haraoubia/nonlinear2.zip

It should be noted that the spectrum of a sinusoidal signal contains only one component, which is the recurrence frequency of the signal. Any given signal may present a broader and more complex spectrum, which is addressed in Figure 2.15.

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PCB design for signal integrity

Kraig Mitzner , ... Dirk Müller , in Complete PCB Design Using OrCAD® Capture and PCB Editor (Second Edition), 2019

Simulating analog signals

For analog signals f is the frequency on the trace and NL is the length of the trace in relative wavelengths (e.g., NL would be 0.25 for a quarter wavelength trace at frequency f). To determine NL you need to know the wavelength, λ. You can calculate the wavelength using Eq. (6.21):

(6.21) $\lambda =\frac{v_{\mathrm{PD}}}{f}=\frac{1}{f\times t_{\mathrm{PD}}}$

where v _PD is the propagation velocity (distance/time) of a wave through a dielectric; f is the frequency of the wave; t _PD is the PT (time/distance) as described above.

So for a 66-MHz signal traveling through the same surface microstrip from the above example (ε _r =4.2), λ=110.8   in. The critical length for traces carrying analog signals varies depending on which book you read but is often cited as being λ/6, λ/15, or λ/20 (or somewhere in between). As with the digital signals, the shorter the trace, the better.

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Introducing Telecommunications

Carl Nassar , in Telecommunications Demystified, 2001

1.3.1 Some Introductory Definitions

An analog signal is a signal that can take on any amplitude and is well-defined at every time. Figure 1.5(a) shows an example of this. A discrete-time signal is a signal that can take on any amplitude but is defined only at a set of discrete times. Figure 1.5(b) shows an example. Finally, a digital signal is a signal whose amplitude can take on only a finite set of values, normally two, and is defined only at a discrete set of times. To help clarify, an example is shown in Figure 1.5(c).

Figure 1.5. (a) An analog signal; (b) a discrete time signal; and (c) a digital signal

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The basics

Bob Meddins , in Introduction to Digital Signal Processing, 2000

1.5 RECAP

•

Analogue signal processing systems have a variety of disadvantages, such as components needing to be changed in order to change the processor function, inaccuracies due to component ageing and temperature changes, processors built in the same way not performing identically.

•

Digital processing systems do not suffer from the problems above.

•

Digital signal processing systems sample the input signal and convert the samples to equivalent digital values. These values are processed and the resulting digital outputs converted back to analogue voltages. This series of discrete voltages is then smoothed to produce the processed analogue output.

•

The analogue input signal must be sampled at a frequency which is at least twice as high as its highest frequency component, otherwise 'aliasing' will take place.

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The Big Picture

John Semmlow , in Circuits, Signals and Systems for Bioengineers (Third Edition), 2018

1.2.3.1 Analog Signals

An analog signal can be mathematically represented by the equation:

(1.1) $x\left(t\right)=f\left(t\right)$

where f(t) is some function of time and can be quite complex. For an electronic signal, x(t) is the value of the voltage (occasionally current) at a given time. Some signals are so complicated that it is impossible to find a mathematical expression for f(t) and the signal must be presented graphically. Again we emphasize that all signals are by nature "time-varying," since a time-invariant value contains no information: it is just some meaningless number. ⁶

Often, an analog signal encodes the information as a linear change in signal amplitude. For example, a temperature transducer might encode room temperature into voltage as shown in Table 1.3 below:

Table 1.3. Relationship Between Temperature and Voltage of a Hypothetical Temperature Transducer

Temperature (°C)	Voltage (volts)
–10	0.0
0.0	5.0
+10	10.0
+20	15.0

This encoding could be defined by the equation:

(1.2) $\text{temperature}=2\times \text{voltage}\text{amplitude}-10$

Analog signals and linear encoding are common in consumer electronics, such as within hi-fi amplifiers, although many applications that traditionally used analog encoding, such as television and sound and video recording, now primarily use digital signals. An interesting exception is the resurgence of music recorded as an analog signal on vinyl (i.e., records), including analog playback, as it is thought by some to have better sound characteristics. In addition, analog encoding remains important to the biomedical engineer because many physiological systems use analog encoding, and most biotransducers generate analog signals. In living systems, not all analog signals are linearly encoded, although we often make that assumption as an approximation to allow us to use advanced signal analysis methods. In this book, the assumption is that all analog signals are linearly encoded unless otherwise stated.

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Signal Sampling and Quantization

Lizhe Tan , Jean Jiang , in Digital Signal Processing (Third Edition), 2019

2.4 Summary

1.

Analog signal is sampled at a fixed time interval so the ADC will convert the sampled voltage level to the digital value; this is called the sampling process.

2.

The fixed time interval between two samples is the sampling period, and the reciprocal the sampling period is the sampling rate. The half of sampling rate is the folding frequency (Nyquist limit).

3.

The sampling theorem condition that the sampling rate be larger than twice of the highest frequency of the analog signal to be sampled, must be met in order to have the analog signal be recovered.

4.

The sampled spectrum is explained using the following well-known formula

$X_s\left(f\right)=\cdots +\frac{1}{T}X\left(f+f_s\right)+\frac{1}{T}X\left(f\right)+\frac{1}{T}X\left(f-f_s\right)+\cdots \text{.}$

That is, the sampled signal spectrum is a scaled and shifted version of its analog signal spectrum and its replicas centered at the frequencies that are multiples of the sampling rate.

5.

The analog anti-aliasing lowpass filter is used before ADC to remove frequency components higher than the folding frequency to avoid aliasing.

6.

The reconstruction (analog lowpass) filter is adopted after DAC to remove the spectral images that exist in the sampled-and-hold signal and obtain the smoothed analog signal. The sample-and-hold DAC effect may distort the baseband spectrum, but it also reduces image spectrum.

7.

Quantization means the ADC unit converts the analog signal amplitude with infinite precision to digital data with finite precision (a finite number of codes).

8.

When the DAC unit converts a digital code to a voltage level, quantization error occurs. The quantization error is bounded by half of the quantization step size (ADC resolution), which is a ratio of the full range of the signal over the number of the quantization levels (number of the codes).

9.

The performance of the quantizer in terms of the signal-to-quantization noise ratio (SNR), in dB, is related to the number of bits in ADC. Increasing 1 bit used in each ADC code will improve 6-dB SNR due to quantization.

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Introduction to Digital Signal Processing

Robert Oshana , in DSP for Embedded and Real-Time Systems, 2012

Conclusion

Though analog signals can also be processed using analog hardware (i.e., electrical circuits containing active and passive elements), there are several advantages to digital signal processing:

•

Analog hardware is usually limited to linear operations; digital hardware can implement nonlinear operations.

•

Digital hardware is programmable, which allows for easy modification of the signal processing procedure in both real-time and non real-time modes of operation.

•

Digital hardware is less sensitive than analog hardware to variations such as temperature.

These advantages lead to lower cost, which is the main reason for the ongoing shift from analog to digital processing in wireless telephones, consumer electronics, industrial controllers, and numerous other applications.

The discipline of signal processing, whether analog or digital, consists of a large number of specific techniques. These can be roughly categorized into two families:

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Signal-analysis/feature-extraction techniques which are used to extract useful information from a signal. Examples include speech recognition, location, and identification of targets from radar signals, and detection and characterization of changes in meteorological or seismographic data.

•

Signal filtering/shaping techniques which are used to improve the quality of a signal. Sometimes this is done as an initial step before analysis or feature extraction. Examples of these techniques include the removal of noise and interference using filtering algorithms, separating a signal into simpler components, and other time- and frequency-domain averaging.

A complete signal processing system usually consists of many components and incorporates multiple signal processing techniques.

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