You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


1. Field of the Invention
The present invention relates to a bandpass filter with wide bandpass characteristics and steep attenuation characteristics which is used suitably for UWB (Ultra Wide Band) in the wireless communications field, and communications equipment using the bandpass filter. UWB is expected to be utilized as a data transmitting medium for PC peripheral equipment such as external storage devices, printers and scanners, or as a data communications medium for digital TVs, projectors, digital steel cameras, digital video cameras, etc.
2. Description of the Related Art
In recent years, attention is being given to UWB as a means of communications. This UWB is different from wireless local area network (herein after referred to as “W-LAN”) in communication length and data transmission rate.
According to IEEE802.11.b, one of the standards for W-LAN, the communication length is 30-100 m, transmission power is 500 mW and transmission rate is about 11 Mbps. On the other hand, in UWB, while communication length is as short as 10 m for a passband of 3.1-4.9 GHz, the transmission power is as low as 100 mW and the transmission rate is 100 Mbps for a communication length of around 10 m, and 480 Mbps for a communication length of less than 2 m, and therefore, data transmission at higher rate is possible as compared with W-LAN.
As discussed above, one of the features of UWB is achieving a high transmission rate by use of a wide frequency band. Its fractional bandwidth (bandwidth/center frequency) is greater than 40%, or 110% or more depending on the case.
Another feature of UWB is that its average transmission power density is defined to be as low as −41.25 dBm/MHz or less. The value of −41.25 dBm/MHz corresponds to a radiant power generating an electric field strength of 54 dBμV=500 μV/m at a distance of 3m from the wave source.
To take an example of a spectral mask under an outdoor circumstance, with the range of 3.16 GHz to 4.75 GHz being set as the base(0 dB) for bandwidth of wireless equipment, it is defined so that it is less than −20 dB at 3.1 GHz and less than −30 dB at 1.61 GHz. Meanwhile, since it is necessary to prevent interference with W-LAN (IEEE802.11.a/b/g) in substantial conditions of use, there are respective attenuation characteristics required for 2.48 GHz and 5.15 GHz.
As described above, a bandpass filter inserted in transmission and receiving signal flow paths in wireless communications equipment for UWB is required to have a wide frequency band (fractional bandwidth of 40% or more) and low loss and high attenuation.
SAW filters and BAW filters using crystalline quartz or piezoelectric ceramics that have high Q factor as the base material have been conventionally used as bandpass filters with low loss and high attenuation in narrow frequency bands. The fractional bandwidths of these are 3-4% or less at a center frequency of 2 GHz, and passbands thereof are 0.06-0.08 GHz, which are two orders of magnitude narrower than those of UWB. Since bandwidths in these materials are determined depending on the electromechanical coupling coefficients of crystalline quartz and piezoelectric substrates, extending the bandwidths to be used as bandpass filters for wider frequency bands has been difficult when the material is taken into consideration.
For this reason, using a dielectric filter including a plurality of dielectric resonators with high Q combined together has been known as one approach for obtaining a bandpass filter with steep attenuation characteristics in a frequency band of 2-5 GHz. However, in order to produce a dielectric filter so that it has a center frequency of 3.98 GHz, a bandwidth of 1.6 GHz, and attenuation of less than −30 dB at 2.48 GHz and 5.15 GHz where W-LAN operates, the size thereof is bound to be as large as about 10×3×1.5 mm, which is disadvantageous. Dielectric filters thus fail to have a wide passband and small size at the same time.
A primary object of the present invention is to provide a small size bandpass filter with a wide passband in UWB and steep attenuation characteristics in a narrow frequency band, and wireless communications equipment using the same.