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Basics of Numerical Calculation and Series
Published in Caio Lima Firme, Quantum Mechanics, 2022
Let us now apply the Fourier series to a square wave. A square wave has a non-sinusoidal periodic waveform in which the amplitude alternates between fixed minimum and maximum values with the same interval between minimum and maximum. Let us imagine the minimum in f(x) as 0 and the maximum as 1 and the interval between minimum and maximum is π.
Fundamentals
Published in Carl Stephen Clifton, Data Communications, 2020
Waveforms are a graphical representation of the direction and amplitude and constant period or timing of voltage or current. A square wave is a waveform with square sides, top, and bottom which indicates abrupt changes of electrical phenomena such as electrical current. An example might be turning a switch on or off. Square waves are generated when computers communicate using binary bits and serial transmission. Each positive-going square or pulse indicates a one value and each negative-going pulse or the absence of a square pulse indicates a zero value. See Figure 2.15.
Short-Range Communication Technology in the Internet of Vehicles
Published in Yunpeng Wang, Daxin Tian, Zhengguo Sheng, Jian Wang, Connected Vehicle Systems: Communications, Data, and Control, 2017
Daxin Tian, Jianshan Zhou, Yingrong Lu, Yunpeng Wang, Zhengguo Sheng
Now, we set the simulation time from 0 to 3600 s. And then we employ a changing environment in the simulations where a square wave with period 900 seconds is adopted to simulate the time series for the varying activity α. The maximum and the minimum peaks of the square wave are set at 1 and 0, respectively, and the wave's duty cycle (i.e., the percent of the period in which the signal is larger than 0) is set at 60%. The simulated varying activity α is given in Figure 5.5.
WristDial: An Eyes-Free Integer-Value Input Method by Quantizing the Wrist Rotation
Published in International Journal of Human–Computer Interaction, 2021
Eunhye Youn, Sangyoon Lee, Sunbum Kim, Youngbo Aram Shim, Liwei Chan, Geehyuk Lee
For tactile feedback, a tactile stimulus is produced at the change in the input number. A user can recognize the current input by counting these stimuli. WristDial uses a pulse-like waveform as a tactile stimulus. Because the play rate of tactile stimuli generated by the wrist rotation is controlled by the user, a stimulation that is short yet perceptible can be used as valid feedback. We set the primitive signal to a 250 Hz pulse because the optimal sensitivity of the Pacinian corpuscles, which respond to vibration and rapid pressure change, is 250 Hz (Makous et al., 1995). The signal form is a square wave with a duty cycle of 50%.
Design of IF-RF-Based Heterodyne Transmitter Using Current Steering DAC with 5.4 GHz Spur-Free Bandwidth
Published in IETE Journal of Research, 2022
Abhishek Kumar, Santosh Kumar Gupta, Vijaya Bhadauria
Considering data = 1, the Fourier series representation of square wave (IF output) gives odd harmonics of sin/cos functions: and, These harmonics are feed to RF DAC to get RF output (RFout). The spectrum of RF output is obtained by taking Fourier transform of Equation (8): Since, to synchronize IF and LO frequency , both the signals must be taken from the same Phase Lock Loop. The even harmonics are cancelled out due to double differential architecture and converting the signal into square wave. Since, the output consists of only odd harmonics, so LO frequency is assumed to thrice of IF frequency . Considering up to 6th-order harmonics of intermediate frequency, the output harmonics are obtained by combining (9) and (10): The harmonics and have been canceled on adding harmonics of in-phase and quadrature-phase output. So, the output of IF RF transmitter is (for analysis harmonics, frequency is important not its magnitude, so magnitude is neglected in below equation): The output spectrum consists of signal frequency and frequency due to the DC value of square wave at zero frequency. The first harmonics is at , and the 3rd harmonics is at , which is equivalent to . Therefore, the harmonics-free bandwidth of the proposed architecture is obtained as , i.e. 9×600 MHz = 5400 MHz (operating at 2.4 GHz resulting IF frequency to 600 MHz). This has been verified from the simulation results in Figure 17. Due to large spur-free bandwidth, the circuit does not require a bulky sharp bandpass filter or harmonic rejection filter.