Normalized frequency (signal processing)
When we talk about sound or any other type of signal that can be analyzed with math, we need to understand something called "normalized frequency".
Think of a signal like a piece of music. If you want to measure how high or low the notes are, you might use a ruler to measure the distance between them. But what if the music was really long, or really complex? It would be hard to get an accurate measurement that way.
That's where normalized frequency comes in. It's like putting the music on a scale or a number line, so you can compare it more easily.
To understand what "normalized" means, think about making cookies. If you have a recipe that calls for 3 cups of sugar, and you only have 2 cups, you can "normalize" the recipe by using less of all the ingredients. That way, the proportions are still the same, even though you have less sugar.
In the same way, "normalizing" a signal means adjusting it so that it fits within a certain range. This range is usually from -1 to 1.
For example, let's say we have a sound wave that goes up and down. The highest point of the wave might be +5 and the lowest point might be -3. If we normalize the signal, we'll adjust it so that those values fit within the -1 to 1 range. In this case, we would divide all the values by 5 (the highest point), so the signal would become:
+1, +0.6, 0, -0.6, -1
Now, we can compare this signal to other signals more easily, because we know they're all on the same scale. We can also do math with them more easily, like adding or subtracting them.
So, to summarize: normalized frequency is like putting a signal on a scale or a number line, so we can compare it more easily. It "normalizes" the signal by adjusting it so that it fits within a certain range (-1 to 1). This makes it easier to analyze and process signals mathematically.
Think of a signal like a piece of music. If you want to measure how high or low the notes are, you might use a ruler to measure the distance between them. But what if the music was really long, or really complex? It would be hard to get an accurate measurement that way.
That's where normalized frequency comes in. It's like putting the music on a scale or a number line, so you can compare it more easily.
To understand what "normalized" means, think about making cookies. If you have a recipe that calls for 3 cups of sugar, and you only have 2 cups, you can "normalize" the recipe by using less of all the ingredients. That way, the proportions are still the same, even though you have less sugar.
In the same way, "normalizing" a signal means adjusting it so that it fits within a certain range. This range is usually from -1 to 1.
For example, let's say we have a sound wave that goes up and down. The highest point of the wave might be +5 and the lowest point might be -3. If we normalize the signal, we'll adjust it so that those values fit within the -1 to 1 range. In this case, we would divide all the values by 5 (the highest point), so the signal would become:
+1, +0.6, 0, -0.6, -1
Now, we can compare this signal to other signals more easily, because we know they're all on the same scale. We can also do math with them more easily, like adding or subtracting them.
So, to summarize: normalized frequency is like putting a signal on a scale or a number line, so we can compare it more easily. It "normalizes" the signal by adjusting it so that it fits within a certain range (-1 to 1). This makes it easier to analyze and process signals mathematically.
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