Signals exist in the form electrical currents and are primarily purposed for the transmission of information and data from a point to another. Signals exits in various physicals forms among them electromagnetics, mechanical and also exist in other forms where they convert to the electrical forms for the purposes of taking measurements (Blahut, 2012). The various types and shapes of signals as well as the parameter for representation are studied n this experiment. This experiment will explain and elaborate how conversion of signals occurs from sensors into data that bears meaning and can be used for the purposes of analysis instrumentation, monitoring or even control.
The most appropriate sensors and transducers are used in changing a physical scenario to an electrical signal. Electrical signals occur in numerous formats such as current, voltage, resistance, inductance, frequent and capacitance. These electrical signal formats used different parameters in the representation of a signal as shown below
Amplitude
Amplitude is an illustration of the strength of a signal and is used in determining the maximum value of a signal.
Frequency
This is the measurement of the number of times of occurrence of a repeated signal with a time span of one second. Frequency is measured in /second or Hz (Kennedy, 2013).
Phase Shift
Phase shift defines the difference in the angles between two or more periodic signals.
This experiment uses specific signal kinds including:
Differences were observed between the various types of the waves as shown in figure 3, 4, 5 and 6 with no changes in the frequency and the amplitude in all the four different waves.
Variations in the amplitude between the two signal waves had an effect as illustrated in signal B (5) and signal A (2)
The variation in the phase signal has an effect on the phase shift as can be observed in the two signal waves when the phase signal B is changed from 0 to 70.
It is observed from this experiment that a change in the wave type brings about the same change between the two different signals
Aliasing refers to the impact resulting from an imperfect reconstruction of a signal from the original signal (Blahut, 2012). This experiment aims at illustrating the effects and the causes of signal aliasing in different methods.
The Sampling Theorem states that the rate of the sample must be more than twice the highest frequency inside a signal for a baseband signal to be reproduced accurately in the sampled form, mathematically illustrated as fs>2BW. An adequate sampled signal, as well as an under-sampled signal, is shown in the figure below (Kennedy, 2013).
Is possible to extract the correct measurements from these two settings? Explain.
The experiment achieved the right baseband since the sampling rate was 1000Hz which was more than twice the Signal Frequency.
3.2 Change the Signal Frequency upwards slowly and take note of the deviations in the shape of the waveform. Note the frequency at which the correct measurement is lost.
The signal is observed to disappear at a Frequency of 500 Hz since the sample rate is 1000 Hz. At this point, it will not be possible to achieve the accurate signal for the baseband.
Setting the rate of sampling higher in relation to the measured frequency can be another alternative.
From the experiment, it was observed that the correct reading of the frequency could only be achieved if the sample rate was more than twice the highest frequency that is present in the signal fs>2BW (Kennedy, 2013).
This experiment aims at exploring and gaining an in-depth comprehension of the basics of Fast Fourier Transform and spectrum analysis. Fast Fourier Transform is a mathematical tool that resolves a specific signal into the addition of the sines and the cosines.
The Fourier Transform (FT): This is an analog tool primarily deployed in the analysis of the contents of frequency for continuous signals
The Fast Fourier Transform (FFT) is an algorithm applied in the rapid computation of the DFT (Blahut, 2012).
The Discrete Fourier Transform (FFT) is a digital technique for the analysis of the contents of the frequency of discrete signals.
Below are some of the important examples
The graphs were affected as the Amplitude changed to 7.5 Hz
There are 5 peaks which are different from the sine waves as a result of the shape of the wave
Figure 30 Square Wave as signal Simulation, Duty Cycle: 40%
A decrease in the number of peaks until they all disappear is observed. This pattern is attributed to the increase in the duty cycle percentage.
There are numerous various FFT algorithms depending on a vast range of published theories. The FFT algorithms range from complex number arithmetic which is simple in nature to group theory as well as number theory that is used in the resolution of a signal into the sum of sines and cosines (Blahut, 2012).
This experiment aims at exploring and providing insights into the use of Averaging in the improvement of the accuracy of measurement for signals that are noisy and are rapidly changing. Averaging modes are as follows:
Averaging is important in the reducing of the errors in measurements as well as improving the frequency of the domain analysis that permits taking readings of the signals in an easy way.
Measurement errors are reduced with signals at different averaging modes and the frequency domain analysis enhances the reading of the signals in a simple way as can be observed from the experiment (Kennedy, 2013).
Windowing is a standard technique used in signal processing which mainly serves to reduce the frequency smearing levels that are present in a dataset of a non-periodic waveform. This experiment used numerous types of windows aimed at gaining a better comprehension of windowing.
Windowing forces signals to be continuous thereby generating better results by lowering the levels of smearing present in a signal.
Signal spectrum and signal with Blackman-Harris windowed
The windowed signal is windowed as observed with the continuous signal having the same amplitude. The amplitude was observed to be decreasing from the original signal. Still, the peak was also observed to be reducing.
From the experiment, it was observed that windowing forces signals to be continuous and thus leading to the generation of better results as well as reducing the levels of smearing presented in the signal.
Conclusion
The above experiments elaborate and illustrate the single processing through 5 sub-experiments. Various types and shapes of signals as well as the most critical parameter for identification of a signal are not only introduced but also explained in details in these experiments. The experiments acted as a source of immense assistance to the senior student to understanding the methods of signal processing and the primaries meant for the analysis of signals that have the contents of their signals changing rapidly over time.
References
Blahut, R. E. (2012). Algebraic Methods for Signal Processing and Communications Coding. London: Springer Science & Business Media.
Kennedy, R. A. (2013). Hilbert Space Methods in Signal Processing. Cambridge: Cambridge University Press.
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