实现一个链表，使其内部数据为不定长多维数据，并实现对它的初始化，求数据元素个数，插入、删除、取数据元素，判断为非空操作。并对多维数字信号进行均值滤波、上采样、下采样

非常好的问题！我可以为您提供以下代码来实现链表：

class Node:
    def __init__(self, data):
        self.data = data
        self.next = None

class LinkedList:
    def __init__(self):
        self.head = None
        self.count = 0

    def is_empty(self):
        return self.head is None

    def insert(self, data):
        new_node = Node(data)
        new_node.next = self.head
        self.head = new_node
        self.count += 1

    def delete(self, data):
        current = self.head
        previous = None
        while current is not None:
            if current.data == data:
                if previous is not None:
                    previous.next = current.next
                else:
                    self.head = current.next
                self.count -= 1
                return
            previous = current
            current = current.next

    def get_count(self):
        return self.count

    def get_data(self, index):
        if index >= self.count:
            raise IndexError("Index out of range")
        current = self.head
        for i in range(index):
            current = current.next
        return current.data

    def mean_filter(self, window_size):
        current = self.head
        while current is not None:
            if isinstance(current.data, list):
                for i in range(len(current.data)):
                    if i < window_size or i >= len(current.data) - window_size:
                        continue
                    current.data[i] = sum(current.data[i-window_size:i+window_size+1]) / (2*window_size+1)
            current = current.next

    def upsample(self, factor):
        current = self.head
        while current is not None:
            if isinstance(current.data, list):
                current.data = [current.data[i//factor] for i in range(len(current.data)*factor)]
            current = current.next

    def downsample(self, factor):
        current = self.head
        while current is not None:
            if isinstance(current.data, list):
                current.data = [sum(current.data[i:i+factor])/factor for i in range(0, len(current.data), factor)]
            current = current.next

这个链表可以存储不定长多维数据，可以进行初始化、插入、删除、取数据元素、判断非空等操作。对于多维数字信号的均值滤波、上采样、下采样，我在链表中添加了相应的方法，可以直接调用。

例如，如果您有一个链表 `my_list`，其中存储了多维数字信号，您可以这样调用方法：

my_list.mean_filter(3)  # 对信号进行均值滤波，窗口大小为3
my_list.upsample(2)     # 对信号进行上采样，采样因子为2
my_list.downsample(2)   # 对信号进行下采样，采样因子为2

希望这个代码可以帮助您实现您的需求！