Decimated
Okay, so I need to figure out what "decimated" means. Let me start by recalling if I've heard this word before. I think it's used in different contexts, maybe math and history? Let me break it down.
First, the basic definition. The root word might be "decimate," which I believe means to destroy a large part of something. But how exactly does that apply in different fields?
In math, I remember hearing about decimated sequences or series. Maybe it's when you remove every nth term? Like, if you have a sequence and you take out every 10th element, that's decimating by 10? Wait, but why is that called decimation? Maybe because it's reducing the number significantly, similar to the historical term.
Historically, decimation was a punishment in Rome where a tenth of the army would be killed. So the term was originally about reducing by a tenth. But in math, does it always mean removing a tenth? Or can it be any proportion? Let me check examples.
If a sequence is decimated by a factor of 3, does that mean every third element is removed? So like, if you have 1,2,3,4,5,6,7,8,9,10, removing every third would leave 1,2,4,5,7,8,10. That would be decimating by 3. But then, is the factor always 10? Or can it be any number?
Wait, in some contexts, decimation specifically refers to removing every tenth element. But in more general usage, especially in signal processing or mathematics, decimation can refer to reducing the sampling rate by removing every kth sample, where k is the decimation factor. So if k=10, it's the historical meaning, but k can be any integer greater than 1.
But I need to be careful here. Let me think of an example. Suppose you have a time series with data points at every second. If you decimate it by a factor of 2, you take every other second, so the sampling rate becomes 1 Hz instead of 2 Hz. Similarly, decimating by 10 would reduce it to 0.1 Hz. So in signal processing, decimation is about reducing the number of samples by a factor, typically by removing every kth sample. But this process can introduce aliasing if not done properly, right? So you have to filter first before decimating.
But going back to the original question, the user just asked about "decimated." So maybe they want the general definition. Let me verify.
In general, decimate means to destroy or kill a large proportion, especially a tenth. But in mathematics and signal processing, it's the process of reducing the number of elements by removing every kth element. So the term has a specific technical meaning in those fields, which aligns with the general idea of reducing significantly.
Wait, but is there a difference between decimation and downsampling? In signal processing, downsampling is similar but usually involves抗混叠滤波 and then decimating. So decimation is the act of removing samples, while downsampling is the entire process including filtering. But sometimes the terms are used interchangeably.
Also, in combinatorics or sequences, decimation refers to taking a subsequence by selecting elements at regular intervals. For example, decimating a sequence by 2 would give every second element. But again, the key is that it's a regular interval removal.
So putting it all together, "decimated" in general means to destroy a large part, but in technical contexts like math or signal processing, it means to reduce a sequence or signal by removing every kth element, which can be a tenth or any other factor. The exact factor depends on the context.
I should also check if there are other meanings. In biology, maybe? Not that I recall. Maybe in other languages? The word comes from Latin "decimare," meaning to take a tenth as a tax or contribution, often as a punishment. So the core idea is reduction by a tenth, but extended metaphorically to any significant reduction.
Another example: if a population is decimated, it's been drastically reduced, not necessarily exactly a tenth. So the general usage is more about a large-scale reduction, while the technical terms in math/processing are about systematic removal by a factor.
So, to answer "decimated," the definition would depend on context. If it's in a historical or general sense, it's a large destruction or reduction. If in math/signal processing, it's removing every kth element from a sequence/signal to reduce its size by a factor of k.
https://www.18122.com/url/usdt/usdt1910.jpg
I need to make sure I'm not conflating terms. Let me verify with a quick check. According to some sources, in mathematics, decimation refers to the removal of every kth element from a sequence, resulting in a subsequence. The term is used in various areas like numerical analysis, digital signal processing, and combinatorics. The factor k is called the decimation factor. So if k=10, it's decimating by 10, which aligns with the historical tenth. But the factor can vary.
Therefore, the answer should explain both the general meaning (drastic reduction) and the technical meaning (removing every kth element in sequences/signals). Also, note that in technical contexts, decimation often requires proper filtering to avoid aliasing, but that might be more detailed than needed.
So the user might be looking for either the general definition or the technical one. Since they just wrote "Decimated," I should cover both possibilities but perhaps lead with the general meaning first, then the technical.
The term decimated has distinct meanings depending on context:
General/Historical Meaning:
To destroy or kill a large proportion of something, often implying a drastic reduction. Historically, it referred to a Roman military punishment where a tenth of an army was executed. Over time, it broadened to mean any severe depletion (e.g., "The pandemic decimated the workforce").
Mathematical/Technical Context:
In mathematics, signal processing, or combinatorics, decimation involves removing every k-th element from a sequence or signal to reduce its size by a factor of k. For example:
Decimating a sequence by 2 keeps every second element (1, 3, 5...).
Decimating by 10 removes every tenth element, aligning with the historical "tenth" concept.
This process is critical in digital signal processing (DSP) for downsampling, though it often requires pre-filtering to prevent aliasing artifacts.
Key Note: While "decimate" generally signifies drastic reduction, technical fields use it specifically for systematic element removal. The factor k (e.g., 2, 10) determines the reduction ratio.
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