x(t) = cos(45πt) Generate samples from x(t). The sampling interval is 0.005 sec. Denote the samples as x1[n]. 不要使用Python

首先，我们需要确定采样频率，即每秒采样多少次。根据奈奎斯特采样定理，采样频率应该是信号最高频率的两倍，因此我们应该至少以90π为采样频率。假设我们的采样频率为100π，则每个采样间隔为0.01秒。

现在我们可以生成样本了。我们可以使用cosine函数，每0.01秒采样一次，总共采样1000次（因为信号持续100秒）。

样本生成的伪代码如下：

sampling_frequency = 100 * math.pi
time_interval = 0.01
num_samples = 10000

samples = []
for i in range(num_samples):
    t = i * time_interval
    sample = math.cos(45 * math.pi * t)
    samples.append(sample)

其中，`samples`是生成的样本列表，`num_samples`表示采样点的数量，`t`表示当前采样时间。

在实际应用中，我们可能会使用更高的采样频率，以便更准确地重建原始信号。

相关问题

x(t) = cos(45πt)，Generate samples from x(t). The sampling interval is 0.005 sec. Denote the samples as x1[n]. Plot x1[n].

To generate samples from x(t), we need to first define a sampling rate. Let's set the sampling rate to 200 Hz, which means we will take 200 samples per second.

We can calculate the sampling interval as follows:

sampling interval = 1 / sampling rate = 1 / 200 = 0.005 sec

Next, we can generate samples from x(t) using the sampling interval:

x1[n] = cos(45πnT), where T = 0.005 sec

To plot x1[n], we can use Python and matplotlib. Here's the code:

import numpy as np
import matplotlib.pyplot as plt

# Define sampling rate and interval
fs = 200
T = 1 / fs

# Define time axis
t = np.arange(0, 1, T)

# Generate samples
x = np.cos(45 * np.pi * t)

# Plot samples
plt.plot(x)
plt.xlabel('Sample index')
plt.ylabel('Amplitude')
plt.title('x1[n]')
plt.show()

This will generate a plot of x1[n] with the sample index on the x-axis and the amplitude on the y-axis.