Sure, let's create a test case generator for the given problem statement. The generator will create datasets with varying lengths and broken samples following the specified rules.

Here's a test case generator for the problem:

```python
import random

def tcgen():
    datasets = []

    # Number of datasets
    num_datasets = random.randint(1, 100)

    for _ in range(num_datasets):
        # Random length of the audio signal (N)
        N = random.randint(2, 1000)

        # Create the audio signal array with a mix of integers and 'x' (broken samples)
        audio_signal = []
        for i in range(N):
            if random.random() < 0.3:  # 30% chance that a sample is broken
                audio_signal.append('x')
            else:
                audio_signal.append(random.randint(-10**9, 10**9))

        # Append the generated dataset to datasets list
        datasets.append((N, audio_signal))

    return datasets

# Function to print the datasets in the required format
def print_datasets(datasets):
    for dataset in datasets:
        N, audio_signal = dataset
        print(N)
        print(" ".join(map(str, audio_signal)))
    print(0)

# Generate and print the datasets
datasets = tcgen()
print_datasets(datasets)
```

This Python script creates a function `tcgen` that generates multiple datasets according to the given constraints. The `print_datasets` function prints these datasets in the required format.

Here is a step-by-step explanation of the script:

1. **Generating the Number of Datasets**: We randomly determine the number of datasets (1 to 100).
2. **Generating Each Dataset**:
    - We randomly determine the length \( N \) of the audio signal for each dataset (2 to 1000).
    - We construct the audio signal array with a mix of integers and 'x' (broken samples). There is a 30% chance that any given sample is broken.
3. **Printing the Datasets**: We print each dataset followed by a zero to indicate the end of input.

You can run this script to generate multiple test cases for the given problem.