已知f(t)<2FCj@）,则f《-4t〉的傅里叶变换为

根据傅里叶变换的性质，当时域信号的时间尺度扩大4倍时，频域信号的频率尺度缩小4倍，即

F(w) = 1/4F(4w)

因此，f(-4t)的傅里叶变换为：

F{f(-4t)} = 1/4F{f(4w)} = 1/4F{f(w)}

其中，F{ }表示傅里叶变换。

所以，f(-4t)的傅里叶变换为1/4倍的f(w)。即：

F{f(-4t)} = 1/4F{f(w)} < 1/2FCj@

相关问题

keystore加载私钥字符串代码

以下是使用Java加载私钥字符串的示例代码：

import java.io.IOException;
import java.io.StringReader;
import java.security.KeyFactory;
import java.security.NoSuchAlgorithmException;
import java.security.PrivateKey;
import java.security.spec.InvalidKeySpecException;
import java.security.spec.PKCS8EncodedKeySpec;

import org.apache.commons.codec.binary.Base64;
import org.bouncycastle.openssl.PEMReader;

public class LoadPrivateKeyFromString {
    public static void main(String[] args) throws NoSuchAlgorithmException, InvalidKeySpecException, IOException {
        // 私钥字符串
        String privateKeyString = "-----BEGIN PRIVATE KEY-----\n"
                + "MIIEvAIBADANBgkqhkiG9w0BAQEFAASCBKYwggSiAgEAAoIBAQCzOn8XlPzG2J/W\n"
                + "C2mMfBd6CQcF0CvzZ8BnL3L2J8M6rVq8EHXv5Tc1zRlWbR9z5O3DZwVcGlYs+J2w\n"
                + "wGJYX1LjEjK1gNlRqZyUzJH7v+7zCzqLQxTnB0nZ3g1e5Hq9QhJ6tQJjB8e9Ih6m\n"
                + "oRtYK4VJ2jN7+3L5KdWLr1+PzGdJxXK5+Qn0yK0nJ+Vf7+Q1fZ8sK56uNwK7L6Gq\n"
                + "P9LZVg4w8OrG9JDhQqR7jpmN0nJ2mVQ4iZgRsd/FZ2xG4rXV4GyNeL2T3gmmKqL9\n"
                + "hjR2w+G2Z0tN+Zd9HNmJ6MD9y2e2FPO3JHaKZqL1xu3U6O9zJNJP6r8o+qgHkDOa\n"
                + "YSmOD7o3AgMBAAECggEAMOv5y5vTfjQXz1Kx5uJIwDYyqk7tZJU7yeKsX+5fCQwK\n"
                + "C0pPp7g6b1q5O1mVNTVgkZ9+FcJ9LZLdG7CvE1Zt/D5fHj5rD7v7G7d3+TZnN3Qe\n"
                + "7vTQhx1r9QX3C8z+7Vr1EVnZKkY5hk9T4E5+o6j6+g5n3Jq8+7v+8VTPdXhBb0L6\n"
                + "EI6jQe5uGqsy0ajZq4Fv/9lV8hZrZ6jQzpJiWQjUo3u2s0Zu6oW8N5a+8FZQ5JtN\n"
                + "jnv+3rJ9I5dJxwveZb+VJZLJ6AQRblRiO0U2I2LxWw9+8yN4y5nUx4LEZL0rBEq2\n"
                + "ZplL7s0k7gG5H6bqZ8jT6ZfpJd5p8rI4r+0cTg4c4QKBgQD9vBl2YtQOYxZ9Mm8A\n"
                + "6bQXwWz8z3Cx2yQieSg4fIjx2U9L9R5zQrM6GtTJ9zCv8u8N0JQc9+GJ7Za7rp+P\n"
                + "WzCpJl7qPMAFQ1ZoeW6e3f+ZIvQ3uQBtZ7J9jO+xu4c8H+YXu4XNqOlg8LqWgY8C\n"
                + "Jm1o7yPbK1/0t+7BwT8L/OSzVQKBgQDG4aJxGKyjyIe2Mv7Kf0wGwQrM7WUuVwQ\n"
                + "x6B1CJqJpXj0fWV/6qz8xj0VfL8Bw8A8Ck5dPQjxYXVE7Ovz7vX4qX5c4TQ3n/3Y\n"
                + "oN3o4ZG6Z1Bz4i8/aq4Z3+8UJ9vEmo4c5qEfFb2m3b2b+8p7FkRbXbLwyfP0r+9E\n"
                + "Hcl8GJ2jN8BsqL9Zt+qJNyHnNQKBgQDvRrQ6oL7E6KoJLwZQMzI1w22s5TQeJ3G\n"
                + "uN7mVXy9yJ4NCoajZoG6uG1YJj+2FjLj9xTf5g7G2aJX6GtZ0UrZy7Lq4lUlzJQq\n"
                + "v5nY6CpJz6OiKuV6hXnoV4c3pC0yHq+7yKgFv3y1wM4/5oL/jiAsiHIAP5gN8Cq\n"
                + "pWl2wW6OuQKBgQDpVWbGcBbT3ul8cUu4sfqCgG1EzZjyVbA1PbZTfzvRnW/wbLj9\n"
                + "d6Rv0zSgGfLWVfQg7QpuK1CJpRdYlDZn+KXnUoH/m9qY+9Gd4XjQHbJdKo+9OAjS\n"
                + "1LwRbGZ7F8LXVJ8ZJhQDh7ZnnSvQxnq0L6Lyaq1b3S3h4fpQ+3X6E3b7NQKBgQCU\n"
                + "jy8LpRcFh6OJ8XeQ9f9vJt7zA7Y3PJa0JzjRc9aCfRwsB1fVpJgOj1ZsKZx4sE2H\n"
                + "wWwCjT2nWFT7N5X/gHc+Qj4Ggf2gKz0uZc3E4eNNLfh9zqSkkx+H9KtV5N25OvG6\n"
                + "QJmQjH4ZloX7N+2yjv6C9Xs3KQKBgBn54Y8AYmJb1K0yRz5ZlX1vP8RJZ2pGzL6/\n"
                + "l2fgk/3aiIrsZKm5tTfJ7M4Xz3sA5wL/5IaGFS3NwEzKjrYQk0P7XQVXVbK5jN6h\n"
                + "ZKvJmduZP0KAzUyqg6Yg9j3ZZAnuZAzYtX4sB8wU8/qRQfD0h/7IG5lzAoGBAKcM\n"
                + "mPVzD7jyYJ7lqEj4jmP0ZzFfMYcUQJ5z9H4LQ9KJ5SCVxGXoW8XvqGxV63RvIyUu\n"
                + "z3JfZxwZvK2GmsCUZfQkqQoYZ0DGLSsJ4P6C9R6Rfz3I2YmZdY0qC0xFl4m9YfFp\n"
                + "wQJY9LZp2tI27Bz8HGK3KJzX\n"
                + "-----END PRIVATE KEY-----";

        // 将PEM格式的私钥字符串转换为PKCS8EncodedKeySpec格式
        PEMReader pemReader = new PEMReader(new StringReader(privateKeyString));
        byte[] privateKeyBytes = pemReader.readPemObject().getContent();
        PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(privateKeyBytes);

        // 使用KeyFactory加载私钥
        KeyFactory keyFactory = KeyFactory.getInstance("RSA");
        PrivateKey privateKey = keyFactory.generatePrivate(keySpec);

        System.out.println("Loaded private key: " + privateKey);
    }
}

需要注意的是，上述示例代码使用了Bouncy Castle库，因此需要将其添加到项目依赖中。同时，示例代码还使用了Apache Commons Codec库，用于Base64编解码。如果您的项目中已经包含这些库，则可以直接在代码中使用它们。