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fixing 1d convolution markdown file #879

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Oct 12, 2021
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fixing 1d convolution markdown file #879

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12 changes: 6 additions & 6 deletions contents/convolutions/1d/1d.md
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Expand Up @@ -57,7 +57,7 @@ With this in mind, we can almost directly transcribe the discrete equation into
{% sample lang="cs" %}
[import:63-84, lang:"csharp"](code/csharp/1DConvolution.cs)
{% sample lang="py" %}
[import:18-27, lang:"python"](code/python/1d_convolution.py)
[import:20-31, lang:"python"](code/python/1d_convolution.py)
{% endmethod %}

The easiest way to reason about this code is to read it as you might read a textbook.
Expand Down Expand Up @@ -192,7 +192,7 @@ Here it is again for clarity:
{% sample lang="cs" %}
[import:63-84, lang:"csharp"](code/csharp/1DConvolution.cs)
{% sample lang="py" %}
[import:18-27, lang:"python"](code/python/1d_convolution.py)
[import:20-31, lang:"python"](code/python/1d_convolution.py)
{% endmethod %}

Here, the main difference between the bounded and unbounded versions is that the output array size is smaller in the bounded case.
Expand All @@ -204,7 +204,7 @@ For an unbounded convolution, the function would be called with a the output arr
{% sample lang="cs" %}
[import:96-97, lang:"csharp"](code/csharp/1DConvolution.cs)
{% sample lang="py" %}
[import:37-38, lang:"python"](code/python/1d_convolution.py)
[import:41-42, lang:"python"](code/python/1d_convolution.py)
{% endmethod %}

On the other hand, the bounded call would set the output array size to simply be the length of the signal
Expand All @@ -215,7 +215,7 @@ On the other hand, the bounded call would set the output array size to simply be
{% sample lang="cs" %}
[import:98-99, lang:"csharp"](code/csharp/1DConvolution.cs)
{% sample lang="py" %}
[import:40-41, lang:"python"](code/python/1d_convolution.py)
[import:44-45, lang:"python"](code/python/1d_convolution.py)
{% endmethod %}

Finally, as we mentioned before, it is possible to center bounded convolutions by changing the location where we calculate the each point along the filter.
Expand All @@ -227,7 +227,7 @@ This can be done by modifying the following line:
{% sample lang="cs" %}
[import:71-71, lang:"csharp"](code/csharp/1DConvolution.cs)
{% sample lang="py" %}
[import:22-22, lang:"python"](code/python/1d_convolution.py)
[import:25-25, lang:"python"](code/python/1d_convolution.py)
{% endmethod %}

Here, `j` counts from `i-length(filter)` to `i`.
Expand Down Expand Up @@ -263,7 +263,7 @@ In code, this typically amounts to using some form of modulus operation, as show
{% sample lang="cs" %}
[import:38-61, lang:"csharp"](code/csharp/1DConvolution.cs)
{% sample lang="py" %}
[import:5-15, lang:"python"](code/python/1d_convolution.py)
[import:5-17, lang:"python"](code/python/1d_convolution.py)
{% endmethod %}

This is essentially the same as before, except for the modulus operations, which allow us to work on a periodic domain.
Expand Down