AM PM

1. 24-hour clock system

00:00:00 - 23:59:59

2. 12-hour clock system

12:00:00 am - 11:59:59 am

12:00:00 pm - 11:59:59 pm

no 00:00 am or 00:00 pm, it should be 12 midnight or 12 noon



It is incorrect to write 0:00p.m. The use of 0:00 implies a 24-hour clock system, while the use of A.M. and P.M. implies a 12-hour clock system. Therefore, it is absolutely wrong to use both together.

The 12-hour clock divides the day into two parts, 12 hours each. The middle of the day (midday) is the twelfth hour, noon, or the meridiem. A.M. refers to the hours prior to midday (Latin: ante meridiem) while P.M. refers to the hours after midday (Latin: post meridiem). Since the meridien is thought to occur right at the exact second of the 12th and 24th hours, it is most common to hear the times referred to as 12 noon or 12 midnight, rather than using a.m. or p.m. However, to be clear, 12:01p.m. refers to the time just after (post) the 12th hour, that is, the first minute after midday (noon); while 12:01a.m. refers to the first minute of the new day, therefore prior to (ante) midday, that is, just after midnight (after the 24th hour of the previous day).


The 24-hour clock does not need a reference to the middle of the day, the meridiem, which is why the suffix a.m. or p.m. used with this system is completely unnecessary, incorrect, and confusing. So you are wrong to say that “Okay, 0:01AM means something”. It actually doesn’t mean anything at all for the reasons I have given. 0:01 as written implies the 24-hour clock (although it would probably be written 00:01 instead). It refers to the start of the new day. The equivalent in the 12-hour clock would be 12:01 midnight (or 12:01a.m.). 


So if your friends ask you to meet up at 12:00a.m., it should be very clear to you by now that you would be left standing all alone and feeling silly if you showed up at midday, noon, 12:01 p.m., the 12th hour… They are asking you to show up at the first hour of the day, which is just after (or right at) midnight.
### AMPM、FM频谱分析及信号处理 #### 振幅调制(AM)频谱分析 振幅调制(AM)的频谱包括三个主要部分:载波频率 \( f_c \)、上边带(USB, \( f_c + f_m \))和下边带(LSB, \( f_c - f_m \))。信息信号的高频成分位于上边带,而低频成分则位于下边带。AM的优点在于实现简单且硬件成本低,因此广泛应用于早期广播系统如AM收音机[^1]。然而,AM也存在效率低的问题,因为载波本身不携带信息,并且上下边带冗余。此外,AM容易受到噪声干扰,抗噪性较差。 #### 频率调制(FM)频谱分析 在频率调制(FM)中,基带信号被用于调制载波信号的频率,使得载波频率随基带信号的变化而变化。FM调制产生一个带宽较宽的调制信号,其中包含无限多个边带。随着已调制信号的幅值增大,其频谱变得更加分散,边带包含更多的频率,并以载波频率 \( f_0 \) 为中心对称分布。例如,当中心频率为 \( f_0 = 11.97 \, \text{Hz} \),频率偏移为 \( \Delta f = 0.3861 \, \text{Hz} \) 时,频谱能量逐渐向两边扩展,且载波频率不再是幅值最高的频率[^2]。这种特性使得FM具有更高的抗噪性和更高质量的信号传输能力[^3]。 #### 相位调制(PM)频谱分析 相位调制(PM)与频率调制类似,但它是通过改变载波信号的相位来传输基带信号。PM的频谱结构与FM相似,同样包含无限多个边带,并以载波频率为中心对称分布。PM的频谱特性取决于调制指数,调制指数越大,频谱越分散,边带数量越多。尽管PM和FM在频谱结构上有相似之处,但PM对相位变化更为敏感,因此在某些应用中需要更精确的相位控制。 #### 信号处理中的AMPM、FM频谱分析 在信号处理中,AMPM和FM的频谱分析是理解调制信号特性的关键。通过对频谱的分析,可以评估信号的质量、带宽需求以及抗噪性能。例如,在AM信号中,可以通过滤波器去除不必要的边带以提高效率;在FM信号中,可以通过增加带宽来提高抗噪性能;而在PM信号中,可以通过调整调制指数来优化频谱分布。 ```python import numpy as np import matplotlib.pyplot as plt # 示例代码:生成AM、FM、PM信号并绘制频谱 fs = 1000 # 采样频率 t = np.linspace(0, 1, fs) # 时间向量 fc = 50 # 载波频率 fm = 5 # 基带信号频率 A = 1 # 载波振幅 k_am = 0.5 # AM调制指数 k_fm = 10 # FM调制指数 k_pm = 1 # PM调制指数 # 基带信号 m_t = np.sin(2 * np.pi * fm * t) # AM信号 am_signal = (1 + k_am * m_t) * np.cos(2 * np.pi * fc * t) # FM信号 fm_signal = np.cos(2 * np.pi * fc * t + k_fm * np.cumsum(m_t)) # PM信号 pm_signal = np.cos(2 * np.pi * fc * t + k_pm * m_t) # 绘制频谱 plt.figure(figsize=(12, 8)) plt.subplot(3, 1, 1) plt.magnitude_spectrum(am_signal, Fs=fs, color='b') plt.title('AM Signal Spectrum') plt.subplot(3, 1, 2) plt.magnitude_spectrum(fm_signal, Fs=fs, color='g') plt.title('FM Signal Spectrum') plt.subplot(3, 1, 3) plt.magnitude_spectrum(pm_signal, Fs=fs, color='r') plt.title('PM Signal Spectrum') plt.tight_layout() plt.show() ```
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