Shannon in 1948. His results on sampling theory made possible the new areas of digital communications and digital signal processing.
Lazarus Multiple Lfm To One Pas Download As PDFFrom: Power Electronics Handbook (Fourth Edition), 2018 Related terms: Energy Engineering Semiconductor Amplifier Resistors Impedance Oscillators Transistors Amplitudes View all Topics Download as PDF Set alert About this page Micro-Doppler Effect in Wideband Radar Qun Zhang.Yong-an Chen, in Micro-Doppler Characteristics of Radar Targets, 2017 3.2.1 Linear Frequency Modulation Signal The LFM signal transmitted by radar is expressed as (3.9) p ( t ) rect ( t T p ) exp ( j 2 ( f c t 1 2 t 2 ) ) where (3.10) rect ( t T p ) 1, T p 2 t T p 2 0, elsewhere where f c is the carrier frequency, T p is pulse width, and is modulation rate.The envelope of LFM signal is a rectangle pulse, whose width is T p.
But the instantaneous frequency changes with time going by and it can be expressed as: (3.11) f i f c t From Eq. LFM signal is proportional to time. If the time width of an LFM signal is T p, its bandwidth will be T p. Thus, its time-frequency product T p 2 1, and the time domain waveform is demonstrated in Fig. Figure 3.1. The time domain waveform of LFM signal. Lazarus Multiple Lfm To One Pas Full Chapter URLView chapter Purchase book Read full chapter URL: Sampling Theory Luis Chaparro, in Signals and Systems Using MATLAB (Second Edition), 2015 8.2.7 Sampling Modulated Signals The given Nyquist sampling rate condition applies to low-pass or baseband signals. Lazarus Multiple Lfm To One Pas Software Defined RadioSampling of bandpass signals is used in simulations of communication systems and in the implementation of modulation systems in software defined radio. For modulated signals it can be shown that the sampling rate depends on the bandwidth of the message or modulating signal, rather than on the maximum frequency of the modulated signal. ![]() Thus a voice message transmitted via a satellite communication system with a carrier of 6 GHz, for instance, would only need to be sampled at about a 10 kHz rate, rather than at 12 GHz as determined by the Nyquist sampling rate condition considering the maximum frequency of the modulated signal. The sampling of x ( t ) with a sampling period T s generates in the frequency domain a superposition of the spectrum of x ( t ) shifted in frequency by s and multiplied by 1 T s. Intuitively, to avoid aliasing the shifting in frequency should be such that there is no overlapping of the shifted spectra, which would require that ( c max ) - s ( c - max ) s 2 max or T s max If the message m(t) of a modulated signal x ( t ) m ( t ) cos ( c ) has a bandwidth B Hz, x(t) can be reconstructed from samples taken at a sampling rate f s 2 B independent of the frequency c of the carrier cos ( c ) Thus, the sampling period depends on the bandwidth max of the message m ( t ) rather than on the maximum frequency present in the modulated signal x ( t ). A formal proof of this result requires the quadrature representation of bandpass signals typically considered in communication theory. Example 8.4 Consider the development of an AM transmitter that uses a computer to generate the modulated signal and is capable of transmitting music and speech signals. Solution Let the message be m ( t ) x ( t ) y ( t ), where x ( t ) is a speech signal and y ( t ) is a music signal. Since music signals display larger frequencies than speech signals, the maximum frequency of m ( t ) is that of the music signals or f max 22 kHz. To satisfy the Nyquist sampling rate condition: the maximum frequency of the modulated signal is f c f max (6622) kHz 88 kHz, and so we choose T s 10 3 176 secsample as the sampling period. However, according to the above results we can also choose T s 1(2 B ) where B is the bandwidth of m ( t ) in Hz or B f max 22 kHz, which gives T s 1 10 3 44 secsamplefour times larger than the previous sampling period T s, so we choose T s 1 as the sampling period. The continuous-time signal m ( t ) to be transmitted is inputted into an AD converter in the computer capable of sampling at 1 T s 1 44,000 samplessec. The output of the converter is then multiplied by a computer generated sinusoid cos ( 2 f c nT s 1 ) cos ( 2 66 10 3 ( 10 - 3 44 ) n ) cos ( 3 n ) ( - 1 ) n to obtain the AM signal. The AM digital signal is then inputted into a DA converter and its output sent to an antenna for broadcasting. Origins of the Sampling TheoryPart II As mentioned in Chapter 0, the theoretical foundations of digital communication theory were given in the paper A Mathematical Theory of Communication by Claude E.
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