-We will now have a closer look at the simplest carrier frequency modulation, the BPSK modulation. BPSK means Binary Phase-Shift Keying. At the modulator input, there is the binary train composed of 0s and 1s. The first two functions to implement, bits-symbols mapping and signal shaping, are the same as those implemented for baseband transmissions. We add a third function, the frequency shift, at the output of which we get the modulated signal. Let us start with bits-symbols mapping. We consider a binary phase-shift keying modulation. This means that each symbol can take two values. So one symbol equals one bit. We can conclude that the symbol rate Rs equals the bit rate Rb. The 0 bit is thus encoded as the -1 symbol and the 1 bit as the +1 symbol. Let me introduce an important notion, the modulation constellation. The values of the +1 and -1 symbols are represented on an axis. Let us continue with the signal shaping. It consists in associating a waveform, that is to say a signal, to each modulation symbol. Tb is the duration of a bit which equals the bit period. First example, the NRZ signal. Here are the signals associated to the -1 and +1 symbols. Those are gate functions with a Tb duration and a -V or +V amplitude. Here is the result we get with the binary train on the slide. The first 0 bit corresponds to a gate function with a Tb duration and a -V amplitude. The second bit, which equals 1, to a gate with a Tb duration and a +V amplitude, and so on until the end of the binary train. We see that the bit rate, Rb, in bit/s, equals the inverse of the duration of a bit, Tb. Let us now consider the distribution of power as a function of frequency, called "power spectral density" or "signal spectrum". This spectrum is centered on 0 and the signal power is mainly concentrated in a frequency band twice as large as Rb. How can we change the spectrum of this signal? By changing the shaping function. We will see how this is done with a second example, the biphase signal. Here is, for the biphase signal, the correspondence between the +1 and -1 symbols, and the output waveforms. These waveforms are different from the ones used for the NRZ signal. Here is the result we get for the binary train on the screen. The result for a NRZ-type shaping and the result for a biphase-type shaping. The two signals we get are different even though initial binary trains are the same. Regarding the spectrum, here is what we get. For the modulation with the biphase-type shaping, we get this spectrum. We see that energy is concentrated in a frequency band four times as large as Rb. Remember that for the NRZ-type modulation, power was concentrated in a frequency band twice as large as Rb. We can conclude that by using a biphase-type shaping, the occupied bandwidth is twice as large as the one for the NRZ-type shaping. Let us move on to the frequency shift operation. At the output of the signal shaping, we get a baseband that is to say centered on frequency 0. For satellite communications, we want to be centered on a frequency f0 called a carrier frequency. This will be done by the frequency shift operation. How is it done in practice? We multiply the baseband signal by a sinusoidal signal with a frequency equal to the carrier frequency. This sinusoidal signal is generated by an oscillator. Let us get back to the NRZ signal example. After signal shaping, this signal is centered on the null frequency. Let us perform the frequency shift operation. We get a signal centered on the frequency f0. In fact, the signal has been shifted around the frequency f0. We notice that the occupied bandwidth has not changed. Let us now conclude this episode. We have seen that the bandwidth occupied by the BPSK signal depends on the shaping function used. We have seen that frequency shift is implemented by multiplying the baseband signal by a sinusoid with a frequency equal to the carrier frequency.