Academia.eduAcademia.edu
All Topics
Engineering
Signal Processing
Digital Signal Encoding

Digital Signal Encoding

description10 papers
group15 followers
lightbulbAbout this topic
Digital Signal Encoding is the process of converting information into a digital format suitable for transmission or storage, utilizing various encoding schemes to represent data efficiently and accurately. This field encompasses techniques for transforming analog signals into digital signals and optimizing data representation for communication systems.
lightbulbAbout this topic
Digital Signal Encoding is the process of converting information into a digital format suitable for transmission or storage, utilizing various encoding schemes to represent data efficiently and accurately. This field encompasses techniques for transforming analog signals into digital signals and optimizing data representation for communication systems.
Identification and characterization of EYD1, encoding an erythritol dehydrogenase in Yarrowia lipolytica and its application to bioconvert erythritol into erythrulose
by Jean-marc Nicaud

2025, Bioresource Technology

In this study, gene YALI0F01650g has been isolated and characterized. Several experimental evidences suggest that the identified gene, renamed EYD1, encodes an erythritol dehydrogenase. An efficient bioreactor process for the... more
descriptionView Paperarrow_downwardDownload
Extracting and Retargeting Color Mappings from Bitmap Images of Visualizations
by Jorge L Poco

2025, IEEE Transactions on Visualization and Computer Graphics

Fig. . Automatic extraction and redesign of color mappings for a geographic heatmap. The bitmap image on the left uses a questionable rainbow color palette. Our methods automatically recover the color mapping, enabling applications such... more
descriptionView Paperarrow_downwardDownload
Combating Data Leakage Trojans in Commercial and ASIC Applications With Time-Division Multiplexing and Random Encoding
by Daryl Beetner

2024, IEEE Transactions on Very Large Scale Integration Systems

Globalization of microchip fabrication opens the possibility for an attacker to insert hardware Trojans into a chip during the manufacturing process. While most defensive methods focus on detection or prevention, a recent method, called... more
descriptionView Paperarrow_downwardDownload
Additional Insight on SAGE-based Carrier and Residual Frequency Offset Estimations in OFDM Systems
by Khoa Trần Lê

2024, Wireless Personal Communications

Insight on estimations of the space-alternating generalized expectationmaximization (SAGE)-based carrier ω and residual frequency offset with the inclusion of inter-carrier interference (ICI) power using Cramer-Rao's lower bound (CRLB)... more
descriptionView Paperarrow_downwardDownload
Retrieving Music Semantics from Optical Music Recognition by Machine Translation
by David Rizo

2022

This work is supported by the Spanish Ministry HISPAMUS project TIN2017-86576-R, partially funded by the EU, and by CIRMMT’s Inter-Centre Research Exchange Funding and McGill’s Graduate Mobility Award.
descriptionView Paperarrow_downwardDownload
Design and Development of Secure Efficient Wireless Communication System based on FHSS
by Samir Jasim

2021, Journal of Engineering and Applied Sciences

As far as there is a need to increase the efficiency of data transfer, the trials of developments communication systems are appeared. In this study, four modulation techniques and three PN sequence code lengths are studied, to indicate... more
‘ig. 7: BER versus E,/N, in FHSS system with MSK modulated signal Fig. 8: BER versus E,/N, in FHSS system with GMSK modulated signal
‘ig. 10: BER versus E,/N, in FHSS system for three PN code lengths
Fig. 9: BER versus E,/N, in FHSS system of four modulated signals
Fig. 5: BER versus E,/N, in FHSS system with CPM modulated signal
Fig. 3: Frequency synthesizer output Fig. 4: AWGN channel output RESULTS AND DISCUSSION In Fig. 3 the spectral component is pointing to 2 MHz, however, a 2 MHz here stands for 34 MHz, the actual component, since, the analyzer split the 64 hopping frequencies into two halves by set 32 frequencies in the positive side and the same It is more appropriate to view the hop spectrum and channel spectrum before listing the main results sections for this Fig. 3 and 4 show that, respectively.
descriptionView Paperarrow_downwardDownload
Encryption of signals using Chaos
by Chaitanya Varma

2021

Non-linear dynamics is a subject that has its beginnings in the mid-1600s when it was developed to understand Kepler's Laws of planetary motion and universal gravitation. It has since developed into a subject with numerous uses in... more
descriptionView Paperarrow_downwardDownload
Towards the digital encoding of Hispanic White Mensural Notation / Hacia la codificación digital de la notación mensural blanca hispánica
by Antonio Ezquerro

2020, Anuario Musical (Revista de Musicología del CSIC)

In this work, the elements necessary for digitally encoding music contained in manuscripts from the centuries 16th to 17th are introduced. The solutions proposed to overcome the difficulties that generate some of the aspects that make... more
descriptionView Paperarrow_downwardDownload
Incremental learning for recognition of handwritten mensural notation
by David Rizo

2019

This paper presents an ongoing research on handwritten symbol recognition in early music scores. The help of human supervision is needed for a correct edition and publication of these collections. A suitable strategy is needed for... more
descriptionView Paperarrow_downwardDownload
Notes on Harmonic Analysis
by George Benthien

2018

This paper discusses some of the numerical aspects of practical harmonic analysis. Topics include Historical Background, Fourier Series and Integral Approximations, Convergence Improvement, Differentiation of Fourier Series and Sigma... more
One of the simplest methods for estimating the area under a curve is to connect equally spaced ordinates by straight lines and to approximate the area under the curve by the area under the polygonal line (see figure 2.6). .6 The Trapezoidal Rule and Fourier Series
Thus the coefficients in the interpolation formula (5.22) can be obtained using the Discrete Cosine Transform. There are fast algorithms for computing the DFT that are called FFT (Fast Fourier Transform) algorithms. Similarly, there are fast algorithms for computing the DCT that make use of FFT algorithms.
Figure 4.1: Pressure impulse response computed by the method described in this section.
where @ is chosen so that the exponential term is approximately zero att = T. The function k is zero att = 0 and is approximately zero at t = T. Thus, we can obtain 1/n? convergence b' extending K to [—7, 7] as an odd function. The Fourier transform R of the extended function k is given by The application of this technique to a problem in acoustics is illustrated in figure 4.1 [12]. Here we have the pressure response due to an impulse acceleration of a radiating surface element. Notice that the response is zero for negative time, jumps to a finite value at time zero, and then decays tc zero at large times. Figure 4.2 shows the same time response computed by numerically performin; an inverse Fourier transform of the frequency response without employing the modifications sug. gested in this section. Notice that the response is not as smooth and doesn’t have the right behavio: for small times. Since there is a jump at time zero, the inverse Fourier transform converges to the average of the right and left hand limits (0.5 in this case).
This series does not converge at any point. If sigma factors are applied to the first m terms of this series, we get
Table 4.1: Properties of Fourier Transforms It is easily shown that the Fourier transform has the properties shown in the table below:
This may have been obtained, for example, by truncating a Taylor series. In defining the shifted Chebyshev polynomials 7;*(x) we obtained the relation x = cos” 6/2. Using this relation, we can compute the powers of x as follows In general it is very difficult to get the coefficients of a Chebyshev series using the integral ex- pressions in equations (3.16) and (3.28). In this, section we will describe another way to obtain approximate Chebyshev expansions. Suppose we are given a polynomial approximation to a func- tion f defined on [0, 1], i-e.,
If e is an eigenvector of R with eigenvalue A, then it follows that
where / is an identity matrix whose row and column dimension is the number of nodal points within a symmetry block. The matrix R has the property RY = J where J here is an identity matrix with row and column dimension equal to the total number of nodes. Suppose e is an eigenvector of R with eigenvalue A, i.e., Re = Ae. Then and hence AN = 1, ice., the eigenvalues of R are the N-th roots of unity. The eigenvalues A, of R can be written as follows
i.e., the DFT of an even sequence is also an even sequence. Applying the same type of argument to odd sequences (x_» = —Xn), it can be shown that the DFT of an odd sequence is also odd. Combining these results with the previous result for real sequences, we see that the DFT of a real and even sequence is real and even, and the DFT of a real and odd sequence is imaginary and odd. Shift Theorem Suppose we have a sequence of values Xo,... , Xy—,. Consider the sequence y,, defined by
Figure 4.2: Pressure impulse response calculated by a direct inversion of the frequency response.
If we substitute the definition of g from (2.60) into (2.61), we get This relation is known as the trapezoidal rule with end correction. It usually gives much greater accuracy than the trapezoidal rule if the values of the derivative f’ at the end points are known or can be accurately approximated.
Figure 2.5: Approximation of square wave using sigma factors
Table 2.1: Function values of e* The exact answer for the integral is given by
Again the inverse discrete cosine transform has the same form as the discrete cosine transform except for a factor of 2/N. Thus the same algorithm can be used for both the transform and its inverse.
Let us sample x at N equally spaced points in [0, 7). If At = T/N, then
Figure 2.2: Approximation of delta function using sigma factors.
Figure 2.7: Example function for trapezoidal integration.
Define a new sequence yo,..., yn—1 by
By the convolution theorem and the definition of the inverse DFT, we have
Thus, the even terms of {Xn} can be computed using equation (6.24) and the odd terms can be computed recursively using equation (6.21) starting from X; = Ro/2. The procedure can be summarized as follows:
It is easily seen that the matrix R is given by We can define a discrete rotation matrix operator R by
descriptionView Paperarrow_downwardDownload
Digital Encoding And Decoding
by George Benthien

2018

Many electronic communication devices today process and transfer information digitally. Examples are cable televisions, cell phones, cable/DSL modems, and wireless routers. Digital information is specified by a sequence of zeroes and ones... more
Figure 7: Amplitude modulated signal corresponding to the bit sequence (101110).
Figure 8: Frequency modulated signal corresponding to the bit sequence (101110). two transmission frequencies. The one having the largest output over a symbol period corresponds to the frequency used in that symbol period. 3.3. Continuous Phase FSK Modulation (CPFSK) A continuous phase FSK signal has the form
Figure 4: An example of a Manchester encoded signal.
where d7(t) and dg(t) are the same digital signals used previously. The functions d; and dg are continuous at odd multiples of 7’, and sin( $f) is zero at even multiples of 7’. Therefore, the second term on the right-hand-side of equation (10) is continuous. Since cos( 3 +) vanishes at odc 2T multiples of T, the signal x(t) will be continuous if we can modify d7(t) so that it is continuous at even multiples of T. This is easily done. We only need to shift d;(t) to the left by T as i: illustrated in Figure 12. With this modification x(t) is called an MSK signal. We will now show that the MSK signal x(t) is in fact a continuous phase FSK signal.
.6 Quadrature Amplitude Modulation (QAM) Amplitude and phase modulation are often combined. In Quadrature Amplitude Modulation (QAM, the signal has the form
One of the most popular forms of phase modulation is Quadrature Phase Shift Keying (QPSK). In QPSK the phase ¢(t) takes on one of the four values 21/4, 32/4, 52/4, or 77/4 in each symbol period. The signals corresponding to these four phase angles are A[cos(2z fet) —sin(22 fet) | /V2, A[—cos(2x fet) — sin(2xfet)|//2, A[—cos(2x fet) + sin(2xfet)]/V/2, and A[cos(2z fet) + sin(2x fet) |/V2. If we let A = V2, then the pair (J, Q) takes on the values (1,—1), (—1,—1), (—1, 1), and (1, 1). Each signal x(t) corresponds to a unique pair (J, Q). Figure 9 shows the points corresponding to the pairs (J, Q) for QPSK along with the associated symbols. Figure 9: Constellation diagram for QPSK modulation.
Table 1: Four bit to five bit conversion table. The five bit codes were selected so that there is no more than one leading zero and no more than two trailing zeros. Thus, when the codes are strung together, there can be no more than three consecutive zeros. The string of bits after the replacement are transmitted using NRZI. As we saw before, NRZI effectively handles strings of ones. An example of a 4B/5B encoded signal is shown in Figure 5.
Figure 16: Diagram showing the steps in Orthogonal Frequency Division Multiplexing. with the PSK and QAM modulation schemes can be looked upon as defining mappings between symbols and complex values. Using one of the constellation diagrams we assign the complex number corresponding to the first symbol to Xo, the complex number corresponding to the second symbol to X;, and so on until the complex number corresponding to the N-th symbol is assigned to Xy-_1. We then obtain a sequence of time values {x,,} by means of the inverse DFT defined in equation (32). This sequence is in general complex. The real and imaginary parts of this sequence can be converted to continuous functions of time on the interval 7 using a digital-to- analog converter (DAC). The real and imaginary functions of time on each symbol period are often used to modulate carrier signals cos(27 f-t) and sin(2z f-t) respectively. A diagram of the process is shown in Figure 16.
The simplest digital signal representing a bit sequence uses just two voltage levels and represents a 1 by the higher voltage and a zero by the lower voltage. This type of encoding is called NRZ (Non-Return to Zero). An example of an NRZ encoded signal is shown in Figure 1. Although simple, this method for encoding digital information has some serious drawbacks and is seldom used. First, it is difficult to keep the clocks of the source and receiver synchronized if there happen to be long sequences of ones or zeros. The receiver uses transitions in level to determine clock cycle boundaries. Second, it is impossible to distinguish between a long sequence of zeros and the absence of a signal. Third, a long series of zeros or ones causes the average signal value, which is used to distinguish between high and low values, to drift. Thus, for many reasons, it is desirable to have frequent transitions between the high and low values.
Figure 15: Constellation diagram for 16-QAM modulation. QAM signals can be demodulated using a coherent scheme like that used for phase shift keying. Multiplying the signal s(t) by cos(2z f-t) and using trigonometric formulas for double angles, we get
Figure 2: Example of NRZI encoding.
In Manchester encoding 0 and | bits are represented in a clock cycle by the signals shown in Figure 3.
Figure 6: An example of MLT-3 encoding.
Figure 13: Smooth FSK signal corresponding to the bit sequence (101110). By adding and subtracting equations (18a) and (18b) we obtain
frequency limit of an MLT-3 signal will be about one-fourth that of a Manchester encoded signal. In Fast Ethernet (100 Mbps) MLT-3 is applied to the signal generated by 4B/5B and NRZI. Higher order block codes such as 8B/10B and higher order multi-level methods such as MLT-5 are used in higher speed Ethernet networks.
to represent 3 bits per symbol. This modulation scheme is called 8-PSK.
Figure 17: Example of Direct Sequence Spread Spectrum. The signal d(t) must be known by both the transmitter and receiver. Often the pattern of plus and minus ones in d(t) is generated by an algorithm based on some shared seed. The signal s(t) has a noise-like appearance and thus provides some protection against eavesdropping. Figure 17 shows an example of the various signals that make up a DSSS signal.
Figure 11: Constellation diagram for 8-PSK modulation. some systems use a modification of phase shift keying called Differential Phase Shift Keying DPSK). Instead of using phase angles relative to a fixed standard, DPSK uses phase angles relative o the phase in the preceding symbol period. DPSK is simpler to implement than ordinary PSK, out has larger demodulation errors.
descriptionView Paperarrow_downwardDownload
Physical Layer – Part 2 Data Encoding Techniques Networks: Data Encoding 1
by madhu sri

2016

descriptionView Paperarrow_downwardDownload
sampling
by V Victory

2015

descriptionView Paperarrow_downwardDownload
This page describes MSK(Minimum Shift Keying) and GMSK(Gaussian Minimum Shift Keying
by Ronik Doshi

2014

Keying) modulation techniques. It covers GMSK modulator and GMSK demodulator based on QPSK modulation method.