# 电气工程代写|数字系统设计作业代写Digital System Design代考|COE328

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Frequency-Shift Keying

Minimum shift keying can be generated using FSK by setting the frequency separation between the two frequencies equal to $1 / 2$ the frequency shift rate or data rate. Therefore, MSK is a continuous phase FSK with a modulation index of $0.5$. This is where MSK got its name, since it is the minimum spacing between the two frequencies that can be accomplished and still recover the signal with a given shift rate. It is rather remarkable that the same waveform can be produced via two different generation methods, each of which provides a different way of understanding, designing, and analyzing MSK systems. A simple way of generating MSK is shown in Figure 2-24.

A two-frequency synthesizer is frequency shifted by the binary bit stream according to the digital data. If the rate is set to the minimum bit rate, then MSK is the resultant output.
The frequency spacing of the FSK needs to be equal to $1 / 2$ the bit rate to generate MSK. The frequency shift provides one bit of information, as does the BPSK waveform, but the null-to-null bandwidth is only $1.5$ times the bit rate compared with 2 times the bit rate in the BPSK waveform. A simulation shows different types of FSK with different spacings with respect to the bit rate. If the frequency spacing is closer than $1 / 2$ the bit rate, then the information cannot be recovered. If the spacing is too far apart, the information can be retrieved using FSK demodulation techniques, but MSK is not generated. As the frequency spacing approaches $1 / 2$ the bit rate, then the resultant spectrum is MSK (Figure 2-25).

One of the problems with PSK systems is that the sidelobes can become fairly large and cause a problem with adjacent channel operation. The sidelobes continue out theoretically to infinity. The main concern is usually the first or second sidelobes, which are larger in magnitude. To confine the bandwidth for a particular waveform, a filter is required. The main problem with filtering a PSK signal is that this causes the waveform to be dispersed or spread out in time. This can cause distortion in the main signal and also more intersymbol interference (ISI), which is interference between the digital pulses.

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Ideal Shaping Filter

For no ISI, the sampling time of the pulse needs to occur when the magnitude of all other pulses in the digital signal are zero amplitude. A square wave impulse response in the time domain would be ideal, since there is no overlap of digital pulses and thus sampling anywhere on the pulse would not have ISI. However, the bandwidth in the frequency domain would be very wide, since a square wave in the time domain produces a $\sin (x) / x$ in the frequency domain.
Therefore, the best shaping filter to use for digital communications is a $\sin (x) / x$ impulse response in the time domain, which produces a square wave in the frequency domain. This provides ideal rejection in the frequency domain and also a sampling point in the center of the $\sin (x) / x$, where all the other digital pulses have an amplitude of zero. This produces the minimum ISI between symbols (Figure 2-26). However, a $\sin (x) / x$ impulse response is not possible since the sidelobes extend out to infinity. Thus practical filter implementations are used to approximate this ideal filter. Some of the practical filters used in communications are Gaussian, raised cosine, raised cosine squared, and root raised cosine, which are all approximations of the $\sin (x) / x$ impulse response. The $\sin (x) / x$ impulse response approximates a square wave in the frequency domain, which reduces the noise bandwidth, reduces out-ofband transmissions, and is designed to minimize ISI (Figure 2-27).

Root raised cosine filters are used extensively in communications and data links. They are employed in both the transmitter and the receiver, which basically splits the raised cosine filter, with half of the filter in the transmitter and half of the filter in the receiver. Therefore, the net result is a combination of the square root of the raised cosine filters, which leads to a raised cosine filter for the total data link system. The root raised cosine filter has slightly faster transitions in the time domain for the transmitter pulse, and since a matched filter is used on the receiver side splitting the raised cosine filter response provides a slight improvement in the performance.

Another type of filtering scheme uses a Gaussian-shaped pulse. A Gaussian-shaped curve is a standard bell-shaped curve showing a Gaussian distribution, which is used extensively in probability theory (see Chapter 6). The Gaussian-shaped impulse response also provides a good approximation to the ideal $\sin (x) / x$ impulse response (Figure 2-27). This provides effective use of the band and allows multiple users to coexist in the same band with minimum interference. One type of modulation that includes this Gaussian impulse response is Gaussian MSK (GMSK), a continuous phase modulation scheme that reduces the sidelobe energy of the transmitted spectrum. The main lobe is similar to MSK and is approximately $1.5$ times wider than QPSK.

# 数字系统设计代考

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Frequency-Shift Keying

FSK 的频率间隔需要等于1/2生成 MSK 的比特率。与 BPSK 波形一样，频移提供了一位信息，但零点到零点带宽仅为1.5与 BPSK 波形中的 2 倍比特率相比。模拟显示了不同类型的 FSK，其比特率具有不同的间距。如果频率间隔小于1/2比特率，则信息无法恢复。如果间隔太远，可以使用 FSK 解调技术检索信息，但不会生成 MSK。随着频率间隔的接近1/2比特率，则得到的频谱为 MSK（图 2-25）。

PSK 系统的问题之一是旁瓣会变得相当大并导致相邻信道操作出现问题。理论上，旁瓣一直延伸到无穷大。主要关注点通常是幅度较大的第一或第二旁瓣。为了限制特定波形的带宽，需要一个滤波器。对 PSK 信号进行滤波的主要问题是，这会导致波形在时间上分散或散开。这会导致主信号失真以及更多的符号间干扰 (ISI)，即数字脉冲之间的干扰。

## 电气工程代写|数字系统设计作业代写Digital System Design代考|Ideal Shaping Filter

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