Signal Waveform

Posted : admin On 8/22/2021
Signal

Signal Studio software for WLAN 802.11 signal creation; Instrument embedded license for live connection, downloading and offline playback of WLAN 802.11a/b/g/j/p/n, 802.11af, 802.11ah, 802.11ac and 802.11ax waveforms with the supported Keysight signal generators. Waveform is an unlimited app designed for modern music production. Developed to be creative and inspirational and with a minimal learning curve, our goal is to empower music enthusiasts. Unlike other apps, Waveform supports all major plugin and loop varieties and runs on all major desktop operating systems – now including Raspberry Pi. A sine wave signal can be first reproduced if the signal frequency is equivalent to (middle) or lower than f Nyquist (bottom). You can also notice that the sine wave is much better represented the larger f CLK is compared to the signal frequency f, as more points can be used to create the signal.

All modern real-time digitizers and oscilloscopes incorporate a wide band front-end amplifier and an Analog-to-Digital Converter (ADC). The inherent noise of the front-end amplifier tends to increase to the square root of the bandwidth.

A solution to the problem of characterizing signals in the presence or below the noise level is to use signal averaging accumulation. It is a well known technique used to increase the vertical resolution. The noisy signal is acquired many times. A memory buffer is used to add up N waveforms and then divide by N.

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There are a few restrictions: First, the signal must be repetitive. Second, the signal waveform must be stable in time with respect to the ADC sampling clock when in synchronous averaging mode or to the trigger event in asynchronous averaging mode. Thirdly, it should be noted that the averaging process removes only the random/uncorrelated noise on the signal.

It is important to note that in synchronous averaging mode the signal repetition may be more stable. The synchronous sampling guarantees that each period of the periodic signal is sampled with the same sampling phase. This allows averaging a periodic signal with a known period. The ADP7104 must be properly synchronized with an external clock source via 1 GHz external clock or 500 MHz, 250 MHz, 200 MHz, 100 MHz reference clock input/output.

In asynchronous averaging mode the noise in the trigger signal may cause the trigger time to shift from acquisition to acquisition and therefore can distort the averaged waveform. Asynchronous sampling can also be affected by the drift in the sampling time base.

Knowing the difference between both modes described above, allows to choose the most suited option for required signal averaging.

AmplitudeWaveform

Guzik ADP7104 16/32 Gsa/s 10-bit digitizer features both synchronous and asynchronous averaging capabilities. The averaging is carried out in the FPGA-s in real-time with 100% trigger utilization and up to 4B (4,000,000,000) total waveform accumulations. The real-time averaging functionality is available as a command line utility and as software SDK library API for system integration purposes.

Example:

ADC’s LSB RMS
(mV/LSB 0.0155)

uV, RMS

SNR, dB

2 microsecond 1 GHz LFM chirp

Signal

9.3

144.2

Before Averaging

Noise

26.9

416.9

-9.3

After 1M (1,000,000) Averaging

Noise

0.0382

0.592

47.7

Total SNR improvement

57

Operation throughput from command, arming to final averaged .csv file stored to SSD:

2.1 microsecond Pulse Repetition Interval (PRI) and 100% trigger utilization. Resulting .csv file 1.37 MB (1,437,932 bytes):

1 PRI elapsed time: 0.293267 seconds
1,000 PRI elapsed time: 1.27325 seconds
100,000 PRI elapsed time: 1.32839 seconds
1,000,000 PRI elapsed time: 3.28767 seconds
10,000,000 PRI elapsed time: 21.308 seconds
100,000,000 PRI elapsed time: 210.367 seconds
1,000,000,000 PRI elapsed time: 2100.55 seconds

ADP7104 per channel Synchronous Averaging Mode (Option ADC_AVG)

Sampling rate

Minimum accumulator length

Maximum accumulator length

Bandwidth

32 GSa/s

30 ns

40 uS

10 GHz

16 GSa/s

30 ns

40 uS

6.5 GHz

8 GSa/s

60 ns

80 uS

3 GHz

4 GSa/s

120 ns

160 uS

1.6 GHz

2 GSa/s

240 ns

320 uS

800 MHz

1 GSa/s

480 ns

640 uS

400 MHz

ADP7084 per channel Synchronous Averaging Mode (Option ADC_AVG)

Sampling rate

Minimum accumulator length

Maximum accumulator length

Bandwidth

20 GSa/s

48 ns

64 uS

8 GHz

10 GSa/s

48 ns

64 uS

4 GHz

5 GSa/s

96 ns

128 uS

2 GHz

2.5 GSa/s

192 ns

256 uS

1 GHz

1.25 GSa/s

384 ns

512 uS

500 MHz

0.625 GSa/s

768 ns

1024 uS

250 MHz

ADP7104 per channel Asynchronous Averaging Mode (Option ADC_AVGA)

Sampling rate

Minimum accumulator length

Maximum accumulator length

Bandwidth

32 GSa/s

80 ns

10 uS

10 GHz

16 GSa/s

80 ns

10 uS

6.5 GHz

8 GSa/s

160 ns

20 uS

3 GHz

4 GSa/s

320 ns

40 uS

1.6 GHz

2 GSa/s

240 ns

80 uS

800 MHz

1 GSa/s

480 ns

160 uS

400 MHz

ADP7084 per channel Asynchronous Averaging Mode (Option ADC_AVGA)

Sampling rate

Minimum accumulator length

Maximum accumulator length

Bandwidth

20 GSa/s

128 ns

16 uS

8 GHz

10 GSa/s

128 ns

16 uS

4 GHz

5 GSa/s

256 ns

32 uS

2 GHz

2.5 GSa/s

512 ns

64 uS

1 GHz

1.25 GSa/s

1024 ns

128 uS

500 MHz

0.625 GSa/s

2048 ns

256 uS

250 MHz

The Asynchronous Averaging using segmented memory approach uses the ADP7000 digitizer to acquire two signals: the synchronization signal and the signal-to-be-averaged.

The digitizer acquisition is triggered by the synchronization signal in multi-segment acquisition mode, where the signal-to-be-averaged is divided by individual segments each starting with its own synchronization event. The multi-segment acquisition greatly reduces the acquisition memory consumption, when the rate of synchronization events is low.

The acquired data is downloaded to the host computer for software post processing. Software performs precise detection of synchronization event locations with sub-sample accuracy. Then it performs sub-sample averaging of multiple segments of the signal-to-be-averaged. The sub-sample accuracy of both trigger detection and averaging improves the averaging accuracy when compared with the traditional approach. Efficient multicore algorithms are used for software post processing, so the Asynchronous Averaging performance is limited only by the data download speed from the digitizer to the host computer.

The software post processing implementation imposes some limits on the Asynchronous Averaging parameters. Particularly, only one signal channel is averaged at a time, the maximum acquisition size is limited by the digitizer memory, and the performance is limited by the data download speed.

The Asynchronous Averaging algorithm is implemented in GSA SDK library and is available as the command line utility and as software API.

Key specifications for the software implementation of Asynchronous Averaging with (Option ADC_SM):

SpecificationValue
Sampling rateUp to 32 Gsa/s for ADP7104
Up to 20 Gsa/s for ADP7084
Number of ADC inputs usedTwo: one for trigger and one for signal to average
Maximum acquisition size52.5 GSamples
Maximum segment size for 1M (1,000,000) averages1.6 us
Maximum averages for 10 us segment160,000
Time to process max. acquisition135-140 sec
Inter-segment dead time< 200 ns

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Sine, square, triangle, and sawtooth waveforms

Aline Waveforms And Their Meanings

A sine, square, and sawtooth wave at 440 Hz
A composite waveform that is shaped like a teardrop.
A waveform generated by a synthesizer

In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitudescales and of any displacement in time.[1][2]

In electronics, the term is usually applied to periodically varying voltages, currents, or electromagnetic fields. In acoustics, it is usually applied to steady periodic sounds—variations of pressure in air or other media. In these cases, the waveform is an attribute that is independent of the frequency, amplitude, or phase shift of the signal. The term can also be used for non-periodic signals, like chirps and pulses.

The waveform of an electrical signal can be visualized in an oscilloscope or any other device that can capture and plot its value at various times, with a suitable scales in the time and value axes. The electrocardiograph is a medical device to record the waveform of the electric signals that are associated with the beating of the heart; that waveform has important diagnostic value. Waveform generators, that can output a periodic voltage or current with one of several waveforms, are a common tool in electronics laboratories and workshops.

Signal Waveform

The waveform of a steady periodic sound affects its timbre. Synthesizers and modern keyboards can generate sounds with many complicated waveforms.[1]

Examples[edit]

Signal

Simple examples of periodic waveforms include the following, where t{displaystyle t} is time, λ{displaystyle lambda } is wavelength, a{displaystyle a} is amplitude and ϕ{displaystyle phi } is phase:

  • Sine wave(t,λ,a,ϕ)=asin2πtϕλ{displaystyle (t,lambda ,a,phi )=asin {frac {2pi t-phi }{lambda }}}. The amplitude of the waveform follows a trigonometric sine function with respect to time.
  • Square wave(t,λ,a,ϕ)={a,(tϕ)modλ<dutya,otherwise{displaystyle (t,lambda ,a,phi )={begin{cases}a,&(t-phi ){bmod {lambda }}<{text{duty}}-a,&{text{otherwise}}end{cases}}}. This waveform is commonly used to represent digital information. A square wave of constant period contains odd harmonics that decrease at −6 dB/octave.
  • Triangle wave(t,λ,a,ϕ)=2aπarcsinsin2πtϕλ{displaystyle (t,lambda ,a,phi )={frac {2a}{pi }}arcsin sin {frac {2pi t-phi }{lambda }}}. It contains odd harmonics that decrease at −12 dB/octave.
  • Sawtooth wave(t,λ,a,ϕ)=2aπarctantan2πtϕ2λ{displaystyle (t,lambda ,a,phi )={frac {2a}{pi }}arctan tan {frac {2pi t-phi }{2lambda }}}. This looks like the teeth of a saw. Found often in time bases for display scanning. It is used as the starting point for subtractive synthesis, as a sawtooth wave of constant period contains odd and even harmonics that decrease at −6 dB/octave.

The Fourier series describes the decomposition of periodic waveforms, such that any periodic waveform can be formed by the sum of a (possibly infinite) set of fundamental and harmonic components. Finite-energy non-periodic waveforms can be analyzed into sinusoids by the Fourier transform.

Gps Signal Waveform

Other periodic waveforms are often called composite waveforms and can often be described as a combination of a number of sinusoidal waves or other basis functions added together.

See also[edit]

References[edit]

  1. ^ ab'Waveform Definition'. techterms.com. Retrieved 2015-12-09.
  2. ^David Crecraft, David Gorham, Electronics, 2nd ed., ISBN0748770364, CRC Press, 2002, p. 62

Further reading[edit]

  • Yuchuan Wei, Qishan Zhang. Common Waveform Analysis: A New And Practical Generalization of Fourier Analysis. Springer US, Aug 31, 2000
  • Hao He, Jian Li, and Petre Stoica. Waveform design for active sensing systems: a computational approach. Cambridge University Press, 2012.
  • Solomon W. Golomb, and Guang Gong. Signal design for good correlation: for wireless communication, cryptography, and radar. Cambridge University Press, 2005.
  • Jayant, Nuggehally S and Noll, Peter. Digital coding of waveforms: principles and applications to speech and video. Englewood Cliffs, NJ, 1984.
  • M. Soltanalian. Signal Design for Active Sensing and Communications. Uppsala Dissertations from the Faculty of Science and Technology (printed by Elanders Sverige AB), 2014.
  • Nadav Levanon, and Eli Mozeson. Radar signals. Wiley. com, 2004.
  • Jian Li, and Petre Stoica, eds. Robust adaptive beamforming. New Jersey: John Wiley, 2006.
  • Fulvio Gini, Antonio De Maio, and Lee Patton, eds. Waveform design and diversity for advanced radar systems. Institution of engineering and technology, 2012.
  • John J. Benedetto, Ioannis Konstantinidis, and Muralidhar Rangaswamy. 'Phase-coded waveforms and their design.' IEEE Signal Processing Magazine, 26.1 (2009): 22–31.

External links[edit]

Wikimedia Commons has media related to Waveforms.
  • Collection of single cycle waveforms sampled from various sources
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